MIL-STD-414
11 blvs7
-
~M
ORfkMOO$-10
MILITARY
SAMbLING
STANDARD
PROCEDURES AND
FOR INSPECTION
TABLES
BY VARIABLES
FOR PERCENT DEFECTIVE
1.
I
.—
I
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.—- .—
_
mL-sTD-414
11 JEW 1957
OFFICS
OF TEE
~ANT
SECRETARY
Wuhlngkm
$5, D. c.
11 JUIU lb7
Supply and Logi.ti..
Sarnpflng
Varl.bl..
OF DE~
Procedures
and Table.
for Pe=cent Ddectlva
for fa.p.
ctlo.
by
MIL-STD-414
1. Thi. .tandard h.. ~en approved
and i. mandatory for . . . by the Departm.
●ffectivm 11 June 1957.
the M. force,
2. h ●ccordance
Diwl. im k.. d-.ifp.t.d
Air For.. , r.. p.ti..ly,
.tandard.
.:
>.
Recommended
by the De Pru’ne.t
of Defense
rAto of the Army, the Navy. and
rnth e.tabli.bed
proc.dur.,
the Sfandardi..
ticm
Bureau of Ordnance. -d
tha Chemical -Carp.
. . Amp
N.v-Air
For..
custodian.
.1 thi.
correction..
sddltlenn,
or deletion.
.hould be
atior. Divi. iom, Of fic. of the As. imta.t Sec...
and Logistic.),
Wa.hin@an
Z5. D. C.
●ddr . . ..d to the Stanbrdi.
aary of Def.a.e
(Su@y
I
,.
Il.
..—
--
.,-...,--
UJlvl-hn-ls
Esu
INTRODUCTION
SECTION
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table,:
Table
Table
Table
Par:
A-1
A-2
A-3
J
U3LConveraion
Table
. . . .
Sample Size Code tiNers
. . .
Char.cteri*tie
Curve.
Operating
Plmm of S.ctiOa# B, C, and D
San@.
Sise tie
Letters
B
SINGLE
Ex8mpl. *:
Example
Example
SPECIFICATION
B- I
B-2
Table.:
Treble E.- I
Table
Part
1s
OF tibfPL3t4G
B-Z
Examplea:
Example
B-3
Exarn@e
B-4
Table
Example of Cdcafattoiw:,
sPeciflcatiOn
fAmil-Form
Example of Calculations:
Sp*cificatiea
Ltmit-l%rm
SPECIFICATION
Table
B-4
Table
B-5
f3J
though
Q)
1
:
. .
5
.
35
. . . . . . . . . . . . .
Simgle
1 . . . . . . . . . . .
Sin~le
2 . . . . . . . . . . .
UhUT
. . . . . . . . . . ,
.
Mmmter Table for Normal
Impecti.n
(Double Limit
LiInif)
Table, :
Table
Table
B-6
B-?
Table
L-8
37
38
39
40
41
43
44
●nd Tightened
and f%rm
2-
. . . . . . . . . . . .. . . . . .
. . .
Mssier
Table for R=duced faspectiom
. . .
(Double LImitmnd Form Z-Single
Limit)
Table for 3SatimatiaEthe Lot P. rcent
De fective . . . . . . . . . . . . . . . . . . . . . . . .
EST1MATION
OF PROCESS
AVZSAGE
AND
FOR
RZDUCEL
AND TIGHTENED
C3UTEINSPECTION
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I
I
B- 3
siIl#le
Part
. . . . . . . . . . .
. . . . . . . . . . .
10. Sampfiq
(Graphfor
tiample
of Cdcrdatiomm:
Double Specifi.
c8tioa LAnit-Cke
AQL vai.4 far Upper
. . .
and Lawe r Specification Limit Combined
Example of Calculatinna:
Double Specification Umit-DIfferem
AC3L values for
Upper sud fmwer Specification
Umitm
. . . .
...
I
. . . . .
M..ter
Tabie for Normal ●nd Tighteoed
3nmpecti0n (Form l-Sinnle
fAmit)
. . . .
.
Maater Table for Redueed impection
(sOrrnl-singl.
LiJnii)
. . . . . . . . . . . . . .
DOUBLE
H
LIMIT
T, blem:
I
PL.#JS
VAR3ABIL1TY
UN3U40WK-STANDARD
DEV~TION
METHOD
B
SECTION
D&9tiRIPT30N
GENERAL
A
“ii
45
46
47
5?.
54
Value. of T for Tigbtenad k#p8!cti011 . . . . . .
of Estimated
k;
P.rcent
~ts
Defective far Roduc=d Inspection
. . . . . . .
.
Value. of F for h4asimum Standard
Deviafioa.[MBD)
. . . . . . . . . . . . . . . . . . .
58
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
56
I
APP=dk
B
‘iii
. .
.
.
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—,
—
xlL-mTb414
11 Juts 1097
coNTmzTa-caitinmd
SECTION
VASliABILfTY
C
Part
1
sU40LSSPECZF1CATION
kxmlfb:
E8urlph
c-l
3hampie
Tsblea :
Tsbie
Tabi*
1“
Part
u
C-Z
C-1
c-z
DOUBLE
Exaf+em:
Ex.mple
C-3
Example
C-4
Table,,
Table
C-3
Table
C-4
T.ble
C-5
Part Zu
Table.:
Table
Table
c-6
C-7
Tablo
C-8
APWIUUB
D
P8rt 1
C
LZMIT
. . . . . . . . . . . . . . . .
Simsle
Eauanph of Ckicniatidm:
S~cificatiOa
Umit-FOrm
i
. . . . . . . . . .
Exuriplm of Cakuiati0a9:
StnSle
Specification
Limit. Form 2 . . . . . . . . . .
Mast-r
Tabie for Normal ●nd Tightene4
Inspection (Form I_ Siql.
Limit)
. . . . . . .
Msst.r
Tabls for Reduced lnapecUorI
(FOrml-SiOgl.
LImlt)
. . . . . . . . . . . . . .
SPEC1IVCATION
L3M3T
. . . . . . , . . . . . . . .
Example of Caleulxtioms:
Doubl. Sp.eUi catiem LiniIt-Oae
AQL value [or Upper
and tiwer Spocifieu40m Limit Ckmblaed
. , . .
Exunple
o{ Caiculaiiom:
Double Specif{ c-ion
Limit-D4ifar8st
AQL vahm. for
UpPer u8d Lower SPRIcZflcacJon LImitm
. . .
A.hmI.r Tabl. for fdmnul .md Ti#hte.ed
~P=c~a
(-ble
Limit 4
Ferm z _
Sias!e Z&nit)
. . . . . . . . . . . . . . . . . . . .
Maater Tabl@ #or Reduced lmpectiom
(Dauble L&nit Fown&Simgle
IAnIt)
. . . .
Ttile for Ectinmiinsthe
Lot Percent
Dekctive
. . . . . . . . . . . . . . . . . . . . . . .
Vaium. of T Ior .Tigbtmmd h,pecticm
.“. . . . .
z-bits
Of Eotiated
kt S%rcemt
. . , . .. . .
Defective for R.duced Z.cmp.ectioa
Value. of ~ 10, M&um
Awe ra~e
Rsn#e(w)
. . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
VARZASZL3TY
61
.
63
64
6S
66
b7
69
70
71
7Z
73
D-l
&urnpZm D-3.
Ttbim.,
Tabic
D-l
Tmbb
D-Z
80
B2
84
85
WWN
SZNOZ.E SPSCW1GATZON3A3AZT
Exmpleo
:
Exumple
1!
~.——
METHOD
ESTIWTZON
OF PROCESS
AVIXfAGE
AND
cRZT3ZRJA PVR REDUCED
AND TZOHTSNED
INSPECTION . . . . . . . .
., . . . . . . . . . . . . . . . . . . . .
.,.
SEC7WN
ZINKNOWN-~S
. . . . . . . . . . . . . . . .
ZZxampta of Caieubtlms: Siasis
*c4fkati0n
Z.imit-rofm
1
Si+e
Example of c+IeuidzioM:
Smcification
ZAtaia_FOsm
Z
ST
. . . . . . . . . .
89
. . . . . . . . . .
90
d
Ti#btened
Msst*r
Table fof Normal
Zzmpoeuom {Form
1-Sk+
Umlc)
. . . . . .
titer
Table [or Reducmd tJ1.p~=tiO_
(FOrml-Slr@*LimitJ
. . . .. . . . . . . . . . .
,9I
9s
.. . . . .,.—
....=_
“-
comzNls-cOfmffwd
P*T5 u
DOUBLE
5PECfF1CAT10N
LlhffT
. . . . . . . . . . . . .
95
3hampfe*:
3kAmpfe
D-3
Exunple
D-4
Tables:
Table
P*rt
Ul
T.bla
D-4
T.ble
D-5
Master T*le
for Normal and Tightened
fn. pectim (Double Limit and Form ZSimgleumlt) . . . . . . . . . . .
. . . . . . . . . .
Master
T&ble for Reduced 3nop.ctiom
[Ooubk Limit..d
Form Z-Single
Limit) . . . .
T-ble for Estimating the fat Percentage
Defective
. . . . . . . . . . . . . . . . . . . . . . . .
SST1MATION
OF PROCB
AVESAG!C
AND
CSJT&R3A FOR REDUCED
AND TIGHTENED
INSPECTION
. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .
Tsble#:
Table
Table
APP*6
D-3
Esampk
af Cdctdationw
Double SpecUication L6mit-Oa*
AOL vahm UpPar and
fmwer Specification. fAmit Combirmd
. . . . .
Double +pecUi Emmple of .Calculatioms:
c-tion L6mit-D3ffereut
AOL value- for
Limits . . . .
UpVr
d
kwer
Specification
D-6
D-7
D........
97
98
99
101
103
104
106
Value. of T for Tightened frt. pection
. . . . . .
Limit- of Ectinutod
IAX Percent
Defective for Reduced hmpecfiom
. . . . . . . .
108
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
110
I
I
mlL-8’m-414
llhfislm?
INTRODUCTION
Thi. Stamdardwa.
prepmred to meet ● growing IIeeo for tbe U. of standard
ptmm for Jampection by vari*ble.
in ti~rnmatn
procurement,
DIIpply
and .torage,
and maintenance
ia.pciion
opa ratiozm.
Tbe variabf..
sampJ&s
which can be rnea.tirmd on ● coattnplane .pply to ● ●in@e quality characteristic
in term. cd percent de fectiue. The
tm.. scale, and for which quality i. ●xpressed
theory unclerlying the developrne.t
of the wari.bte.
.aniplim~ plaua, including the
oparatiq
charact=rimtic
curve.. a.awne.
that rnea.urem.mt.
of tba quattty char.
●cteristic ● re independent, identicslfy di.tribufed normal random varisblea.
●u’npliq
I
..mpfing pfmn., warlah!es
umpfiag
plamm
1. comparium
with atfributa.
have tbe ●dvanta~e of ummfly remdtin~ & cmmide rsble .avinem in #ample ●ifor .xmnparabl.
a..uruice
. . to the correctness.
of decision.
in judging . .in#le
quality characteristic,
or for the .arne sample size. greater a.mirance
is obtained using variable,
plan..
Attribute.
sampling
pfan. have the advantage of
greater simplicity,
of being applicable
to either .ingle or rnuttiple quality characteristi c., and of requiring no knowledge about the distribution
of the contlaueu.
rn. a.ur. rmenc. of any d the quality cfur. txeridc..
● rm mot to be um.d
It 10 imporfsmt to mot. tfut variable.
.amptfmp pha.
i.di. crirninat.ly,
,impfy bec.u.e. it i. po..ible
to obf.in vaxi.bk.
tnea.urarnemt
● .smnp,data. fn conmlderq
appfieatlon.
where the rmrmatity or irtde~nde.ce
tion. may be que.ticmcd,
the user i. ●dvi.ed to cm-..ult hi. technical agency to
detci-rh in. the fe.. ibility of appfi calion.
Thi8 Srandard 1. divided into four .ectimm.
Section A describe.
@n. rat
procttlur. a of the .amplimg plan..
Secfic.m. B utd C de.crib.
.Pcifi.
procedure.
i. unknovr.,
In Section B
and ●pplic ation. of the .arnpIing plan. when w.=iability
of lot .%and. rd d.vi.tion
i. used .s lh. fn. i. 10. an ● .timat. of the
the .stirn.te
unknc.w. variability,
and in Section C the average
rams. of the sunpf.
1* used.
Section D desc=ibes
the plan. when variability
is known.
Each of Sectiono B. C, and D i. divided into fbree part.: (l) SAMPJIIW PIUM
for the Single S~cifieuiom
Limit Ca.e, 111)Sampfimg Plans for th. mubl.
Spcific. tion Limit Case, and (3JJ) Procedure.
JorEsthnation
cd Proce..
Average
and
● rid Reduced
Ja. pection.
Criteria
fer Tighmned
For tba ●ingle s~cification
limit ca. e, Lhe ●cceptability trite rio. i. giv=n im two foran.: Form 1 amd Form Z.
Either of the fonnc may be u.ed, ●ii-ici they ● rc idettticti a. to .ainple sise -d
or rejeetabilify.
III deciding whether w u.= Form 1
deci ion for lot ●cceptability
or FQrrn Z, the followin~ poiDt . should be bo=n. in mind. Form I provide.
the lot
●ccept ability cri~. rion without ●.titn.tirtg 10I percent defective.
The Form 2 101
Theme e#li acceptability
criterion
require.
emtirnates of Jot percent defective.
mate. at.o .r.
~quimd
for e stiznatbn of tha proea ● a ●verage.
Operating Characteristic
Curve. fn Table A-3 how fhe r=latioa.ftip
betweem
for the quality cbaractari.tic
quality and percent of lot. expected to be ●cce~able
inm~et.d.
A. stated, the .e Ope rating Characfe ri ‘tic Cur-.
are &sed 011tbe
raadanalrom
a ciorsnti distribution.
..#urnpiari
that meam. mment. ● re .ekctedat
plan. in SectiW.
S, C. ~d D w. m mstcbed
The corre spending ●unpfin~
closely ., po.. ible ~der
● .y.tem
Of fixed .unpfe
.Ise with re. pcct to their
Opcraling
Characteristic
Cu?wes. O~raUng
Chsracteristjc
Cum.
in T.bf. A-3
h..= been computed for the .mpling
p]an. b... d orj th. ..timate
of lof .tudard
deviation ef unknown ..ri.bility,
Thy are eqully
.pplie.ble
ior .arnpllns plan.
and theme bam.d
hoed on th. averaga
range of the .awIpI. of unfmown variability
on known variabUity.
●.
C.rtaim cln..cmri.:ic.
concerning the sunpliag
phm. in S..tiom.
B amd C
-d
tbosa la S9ction D dwufd b, moud. Pkn.
baa.d on fba ● mtima& ot umk=09m
Wariablllty require fe~r
.M@e
wit.
for cm~ra~e
. ..”ranca
-baa
tb ● d.
Mate of lcM .taadard tiwl.si~
i. “..d than _bg.
ib .~..ae
rua~. d ffn .-+
in u.ed: on fhe ottwr tid,
plan. Vsbg the .W~.gG
r~ge
of the #AM@. r.quira
VII
-—
mb61v—414
11 June 19s7
●imphr
compuuttmm.
Plarm umlnn bm=variablltty
-qutre
con*l&rablT
f-r
sample tmk far comwrabk
amUJrMC* tbaI ● ich=r of the plans whw =TIabtuty
of k#umII -rkbiUty
Is ● ●rtnsent am.
1s uakam:
@we wer, tba roquir=mw.t
The user 1s. dvised
to co.milt
MS tectalcal~uc~
bdom
WPIYLW cunptiaj
piano U.tng bDOwa w8rIAbuuy.
Tath B-8 provids ● values of tbe f~ctor F to compute tfia maxfmum standard
dewiation hfsD. The hfSD se-s
M ● ~uide for the magnitude of tht eatirnate of
lot standard de-scion
when u-in
Plazm for tbm double spcff
ication limit c--e,
deviation of un.bn.arimtdUty.
SimifArly
based on the ● intimate of lot .taa~rd
Table C-8 provides vmlue- of the Iactor f to com~te
the maximum average range
ruige of the
MAR.
The MAR ●or.ew m a g de for tbe magnitude of the average
do.bfe
.pecific.tia.
limit . . . . . ba.ed . . the
●rnple wk.
usin# planm for “ke
t
wariddlity.
Tba edmate
of lot ●tmdard
ave rage range of the cunple of unbam
U it is Iem thm the hfSD or MAR.re.
deviation or ● verage range of the ●mpk,
●t=ctively. hslps *O immure. but doe. mot guarmt.e,
lot accept. bfllty.
● re gimn III tha a-ix
to Part JU cd the
AU ●ymbols and their definition.
h Ulumtratim
of the com~tiom
and proc.durma
.~ed IIJ
applicable
#*ctim.
uf Part- I and 11 of tbe spplkable
the .unpling
plans i. give. i. the ●nmplec
.ection.
The computathmm irwolve simple ● rithmetic operation.
such am .dditina,
●ubtractio”.
multiplicuion,
&d dIvimion of mwnbera, or ● most, the taking of ●
.quare root of ● number. The user should become funiliarwith
the g.neral procedure. of Sectian A. and refer to she ●pplicable sectioa for detailed iawtructiom
●pccific procedure..
cornpu.
ions. md tables for [he Barnpliag plan..
regarding
I
I
~14
11 Jmfe 14s7
1,
SECTION
1’
GENERAL
DESCRIPTION
A
OF SAMPLING
PLANS
1’
Al.
SCOPE
Thi 8 Sammkrd =stablimhes
All
Pur
+’
mmplnng
P anm and procedures
for inopec ticm by variable ● for use in Government
P*.c. reme.t. s.ppfyuad
stora~.,
and rnAJltetts.cc
inspection
op8rati0rIm. when .ppli cabfe this Standard #hall. be referenced
in
the specification,
contrzct, or in8pcctien in.tructic.r. m, and the provision,
set forth
herein shall #ovem.
Al. ? III*PC ction. lnmpeclion i. tiw pro . . . .
of measur, ns. ●xamining. testing. gaging. 0.
othe rwise comparing
the “unit of product”
(See Al .4) with the appkabfe
requirememla.
Inspection
by
AI.3
lnspcctiby Variables.
variables
i. inspection wherein
r+ specified
quality characte-ri. tic (See AI.5)
on a unit
of proeuct
i. measured
on . continuous
feet per sec.cale. .u. h ● . pound-. iwheo,
ond, etc., And ● rneamtreme. t is recurd. d.
A1.4 Unit of Product.
The unit of product
i. the entity of product in.xcted
in order
to dew rrnine it; measurable
quality char● cteristic.
Thim may be a single article, a
pair. a ●et. ● component of an end product,
or the end product itself. The unil of product may or may K.t be the sune ● s the unit
of purchame,
supply,
production,
or
thipmer.t.
1’
A 1.5 Quality Characteristic.
The quality
charact. riatic for varxablee
in. pecti4n is
that characteristic
ef i unit of p,oduct that
is actually m.a. uzed, to determim
conformance with ● given requirement.
I
A1. b Specificaticm
Limit..
The ●peclflcation Iimtt(e)
is the requi rerncnt
that ●
quality characleri.
tic .hould
meet.
Thi*
● n ● . upper
req.~rement
may be exprenmd
●prc~f ication limit; or 6 lower pacification
specification
limit, called herein ● .in~le
limit; or bolh upper and lower .~cifieatiem
limit.,
called herein a double ●~cificmion
limit.
...
A 1.7 Sampli.~
Plans.
A sampling
pfan 1.
the rmxnber c.<
a PrOCedUr* *h*ch ●peciiies
units of product
from ● lot which ● re to h
itmpected, arid th. cril. rion Xor aecepfabil ity of the lot. Sampling pfazm desipated
in
thi. Standard are ●pplicable to the insPcof a
tfon of ● chgfs quality cbaracteri-fke
unit of product.
Tfm se pfwm may be used
whether
pracuremrml
inspection
i. per.
km’rmd at the plant of ● prime coatract?r.
wbcontractor
or vendor. or ● t destination,
-S90 may be uaod when AppTOPrU1O in
-d
●ppfy and storage. and main fanaace fL18pection ofm rattom.
A3.
CLASSIPTCAITO?f
OF DEFECTS
AZ. I Mtthodof Cia8sifring~fect@.
Asf8m .ificat, c.n al defect- . . the ● rmine ratio. of
defect.
of the unit of product claasifi. d
according to their irnporfaace.
A defect 19
● deviation
of the unit of product fr-am, requirement.
of the specifications;
drawiags,
Purcha.e
da~cripfia”.,
and aay cbu~c
Defects
the reto in the contract
or order.
normally
belong
to one of fhe fOllO*g
classes;
however. defects may be plkced k
other ciao. cs.
AZ. 1.1 Critical
Defeeto.
A criticaf defect
i. .“. that iudeme. t and axmrience
indicate
coule reeult ;.. hazardou. “or unssfe conditions for individual.
u.ing or m.imaining
the product; or, formajnr end it.rn9 unit~of
or famba. ●
product, such a. ships, aircraft,
d.f. ct that could prevent
fmrforrnaaco
of
their tactic-i
fumction.
A2. I.2 Major Defects.
A major defect i8 a
defect. other than critical, thaf coutd result
in failure, ormateritlly
reduce the usability
of the unit of product for its intended fmrpobe.
A2. I.3 Minor
Defects.
A minor defect is
on. that doc n not materially reduce the usability of the unit of product for itm intem&d
from ●stablislmd
Purposa. or i- ● deprfurc
atandard9 hating .0 signUi CUIt bOa CinI OrI
the effective u.e or operation of th@ unit.
A3.
PERCENT
DE FECTTVE
co. Tti
A’3.1 =.PT89.88.
Of NO. CMtfO_
of pro dues 9fnff
e$fcnt of nonconformance
be expre-scd
i. terms of percent &faetive.
A3.Z
Percent
fectiv-.~acterimtic
f%.feetiwe.
Tbe
percent
d.-
of ● Ii%.
lox of prodv;t”i.
th~ number of unit. of praduct de fectiwe for that cfuractc ri.tic divided
by the tataf number of unitm of product And
● man
multidimd by on. hundred. Expressed
Percen:
rkfectiv8 .auatiorx
Number of Aefectivea x 100
Numbs r of dtm
1
.—.
—
.. .
Mk+m+la
lx Jlfffe 1957
Ad. ACCEPTABLE
A4. 1 Acce@abZc
QUALITT
Ouaiil
LEVEL
bwl.
Tba =a CBOmlnaf
in farm. of percaat d8f*c value ●xpr*s.e.i
tive .Pcif ied for ● sbigle quUity characteriatic.
Grtain
numeried
vaftws o; AOL
r=~img f ram .04 to 1S.00 parce.nt am ●hO-a
i. Table A- 1. Whe. . ranof AOL VUWi. .pecified. it dull he treated ● s if it wore
equal to the WdUC of AQL for which ●mfa2i0c
and which i~ bcluded
plms ● re lu-whed
within the AOL range.
When the •~c~ted
AOL i- a particular
value other tb& tivme
for which oamplhg
pfanm ● re furniched, the
AOL, which i- to be used in ●pP2yihg the
yovi.ions
of this Standard, .Itafl be ., .ho~
m Table A- 1.
●
A6.2 Choice of SarnfAim Plain.
SunpUaB
~D
u!d PIWCEOU-9 a:e pro-dad
in d8C tion B if Variddlity
10 uabnown amd the
.taadamf de rf.uion mathd is !mwd, h Soc ticm C U variability i wunbaewn a?id the range
matbod i c uced. and in Secfioa D if .ariabUity
is bnown. Urdesa otkrwi.e
●pcffied, un.
●-d=rd
dewiafim method
b-n
variabiUty,
●unF41rtd plans. and the ●ceef=ablfifv crl terbr. d Farm 2 (for the 9ic@e specification
iimit case) Aaif be used.
A7. SAMPLE
Determination
of Sample Sise.
The
.Unpl.
.,h, tha mm’lfmr of unttm of prodsamph aIws
uct drawn frcan ● lot. Retati~
● m Aesimated
by cute letters.
The 8ampf4
sise cod= Iette r“depcitds on the.inq=ticm
le.ve: and the lot ●1=4. There ● m fiva hA7. I
A4.2 Specifying AOL1 c. Tin particular AOL
vafue le be used for ● ●ingle quality char● ctarimtic of a given product must be ●peeified. fn the CM. of a double ●Pcifi.athm
for
limit. ● ith. r an AOL value it #PcUied
the total percent de fecti..
muaida of bath
up~r -d
lower specification
Umita, o. t-e
AOL value. are specified. om. for the upper
limit and another for the lower Ifmit.
AS.
I
I
SUBJbflmAL
OF
•f=ctiOale=J~:
PRODUCT
-d
v.
ff~e-~
A7.2 Dr.wimB of Samples. A sample 10 om.
or mere unit. ol product drawn from . lot.
UnItc of ttn munfdo Aa2i be, ,al~ct,d
withO* re#ard to t?bdr q.safity.
A5.2 Lot Sise.
The lot ● im 1. tha number
of unit. d product in ● lot, and may differ
f rem the quantity de.i#r.atmd h fbs comtraet
●biprnellt.
or order a, ● lot for prod”ctlar.,
or Ether Purpo..,.
A6. I
IV.
NOTICE-5P.
c ial
Reservaticm
for
Critical
CharackrnB1ic8.
Tbe Go.errm’i.nt
re. e.vo. tbe rmhl to in smct emryunit
mbmkkd
hy the ;uppfier
fos critieti etir.c uad to reject the remainder
of the
te!rimko,
● defect is fouud. Tbo
lot Immedlafelyafter
GOvemirnent timo rcr:rvee
tht right to ●ampfe fo~ criticmf d. f.ctc evm ry let aubmittad
by tk ●uppUer arid to reject any I-* if A
sample dr.wm thrnrefr~
is fo-d
to contain
ow or more. criticti
da fects.
A5. 1.1 Formation
of Lots.
Each la; shall,
● s far ● mla practicable,
con.iwt of unit. cd
product of ● .ingla type, gssde, ~Ass, size,
or cornpo. itkn manufactured
under e.. enri.Ily the same conditimit.
LOT
L U. fU.
othe rwhe ●pecffiod Ia-fmctien Ieval IV shali
k used. The ●unple .i.e cod. letter applicable to the .pcifi.d
izi.pectim
l.wel arid
for lots of given sise .hdl be obtained from
Table A-2.
A5. I lat.
The tsrrn ,,1ov hall nmmn ,virtcpecti~lot,
-’ i.e., a collection of unit. of
product from which ● sample is dram! ad
inopec~td to dete rm”me complhrme with fhe
acceptability
criterion.
A6.
SELECTION
ACCEPTABILITY
Acce Sabfiity
●bility of a lot of
Criferien.
The
●cca@-
● for ● 8tLmatfmg 22n preeomm
Proe.dure
awrage
@
criteria
for ticbtaned and re dweed in. fmcftan bared
=
th
Umpacthn
romiito of pmeedinc
lots are provided in
Part uf of dactiorm B. C. and D.
br
imapc:kta
ddf
be detennh.d
byum of ~
of the .ampling plait. a..oeiaf.d~tb.
.pec Tbi. Standard
ffied value of the AOL{S).
provide 8 ●ampliag plaa. baaad ombaowa 4
bvariability.
fn the Iatfar
can
● m provitid,
two affa mativo met+,
bared on the e ●tfmaia of im ●fattdard dovi.
atioa and the die r on lb am rqe range of
the t-fate.
These .r.
r. f.rred
to . . the
standard
dowiatio.
method and tbe rinse
method. For tha case of a single cpeeifiea tiatl unlit, lb
acc.ptabiu~
criterion
Imaterial
●iknitid
AS. SPECIAL
PVOCEOURE
POR APPLICATION
.F
MIXED
VARIABLBSAlTT21BLfTES BA?APLJNG PLANS
8
--
I
i
i
● lu
prwid=d
●ttrlbcuaa
for
-Wunpumg
tbOM h ,T=tih A-S
I
I
tin
Miad
w8*bl9Dphmm bon18 ad
that
az-t W#idk.]
Amptm wwI&mc. oximta
Condltlon A.
W
tbm produ ct cubmittod for iaapctioa IS
● mhctod by Ch #Upfli, Z tO meat tfM ,IWXiZ
proee ● m
Ikatlan
ltmit(s)
by ● ●creemlng
f rmn ● Iarae r qus.mtity of product which 1.
not being produced wltbln tba ,Pclfication
A lot
me of
mcdm Ui* ●ccef%abi
the fouo’wln’ Comtitiem. i. .*tL.fic.&.
A. 7bo lot com~i4s
variab14 ● ●cca*bllIty
terlm of section B, C. or D.
Camdltkm
Ilmlt(al.
ttn apprsprmta
CodltiaQ
B.
warrant
tb=
mttributem •ara~i4is
tbt
Other condltiorm adst
u, .
of a .arlablac*-.
Caa6itLm
tbe
A9.2
Definition..
11.1.2
The
Ist cmIPU*s
of
+tb
pragrapb
of bAIL-sTD-!05.
A9.4. 1 U Condition A ia not ●atiefied, pro.
coed iri accordance with tk ● tt tibute ● oM’l plirig plan to meet Condition B.
A9.Z. 1 in.pactlom by Attrlbut8s.
fnspectioa
tba unit
by ●ttribute. I* inwpectkoa wbardc.
of product is Chsdfied
simply m defective
or mandcfectiwe with reapact to a given re qtiire.mom 07 s.t of nqutrnmentm.
A9.4.2 lf Condition B ia not cati;lied,
the
lot doe # not meet the 8ccepabilicy
crlte rian.
● lnmP8c A9.Z.Z Mind
Variabla ● -Attrib*
tion. tinnd varimhle ● -attributes
inmp8ction
~mgpcction
of ● ●arnfie by sttributa ● . in
● ddition to inspection
by variable. mmlready
●unple, before . demad. of ● previo.a
e ki,on .ao ~o.,*: ca~qsi!iv.o
r .*I- c-bili~
~
● M ctihmtie.
‘.
‘-
A9.5 Se=rltY
of Iaaopaetion.
The proce❑ f m.pecti.m
rel=rred
to
dures for .everity
in ~rarraph
A8 are
net ●ppficsbl.
for
mixed Vaziable..attribum.
inm~ction.
NOTICEWhen Gouerrmtemt drawin#..
SPedfiCatiOmn, or othc.r data ● re u.e4 tar
UIY prmme
other than In connection wltb a
definitely relamd Government
procurement
opa ratloa.
thm Lbit.d
States Gow rrunent
tbe=aby imzur, no re. pm. ibility
or my obligation wbtcoevcr;
and the fact that the
Co.ernnteztt may have form.latd.
f.rnimbed.
the ●aid Lrswiags,
or In uIy way ●pplied
●wcificationa,
or other data (* II@ t. ‘=
rm~arded by implication or otherwime ● in
mY m-e
r licerming the tilde r or any otha r
pcr*On or corporation,
or conveying
any
u**.
rights or p rmis. ion to m-nufbctufe,
or ●ell aay patented invention thu may in
mn7 =*T h ra~-td
tbreto.
of Samplirtc
Plans.
The
A9.3 Selection
miaad *arlable..
att YiS -plmg
plan
●elected
in UCOdUICe
with thn
stall
h
fcdlovim~
A9.3.1 Select
M ● ccorduaca
B.
●cceptabif ity crita rkm
with
crl -
the vsrlableo
#vnpliag
plm
with Section B, C, O, b.
I
I
a
—
ror spd56d
A03. va3u.eI
a236q WiIhin mmu r-got
Use thh AQl
Vazue
—
to
0.049
0.04
0.050
to
0.069
0,O65
0.070
to
0.109
0.10
0.164
0.15
to
0.Z19
0.Z5
0.Z80 to
0.439
0.40
0.440 to
0.699
0.65
0.700 Ie
1.09
1.0
1.10
to
1.64
1.5
).65
to
2.79
Z.5
2.80
to
4.39
4.0
4.40
to
6.99
6.5
7,00
to 10.9
10.0
11.00
to 16.4
15.0
O.lloto
0.165
m
m
““”
6610
1JOIB35DF31
111 to
180
Be&c
181 to
300
Et
301 to
500
C32GIK
501 to
800
DFHJL
801 t“
1.300
1.301 to
3.200
3.ZO1 to
8.000
m
8.001 to
2z,000
I
I
DFH_j
EGIKL
FHJLM
Gl
Lhi
N
HJMNO
ample .i;e code letter.
given in body of
Uble ● re appli. abze when the indicated in●ptctim levelw are to be “med.
4
. - --,-
I
mL-sm-414
11 Smn 1*
TABOpraCinC
Clmr.ete.si.tic
of t%cti~m
A-S
CtMW9.
B, C, 4
for
Sun@iD*
Plan.
D
I
-.
I
a
!!
OPERAllNG
A.3
I Cures *
—
m?l~s p-i
bed -
ml,. +ti
B
0“4!.-
.V1.wlty “.
SAMPLE SIZE COl)E LETTER
“.o.lld*
iq.k.llnl )
CHARACTERISTIC CURVES FOR SAMPLING PLANS BASEO ON STANOARO OEVIATIOM METHOO
TABLE
;f
W
4:
ii!
.4
-0
.——
TABLE
..
A.3
.
so
30
40
w
M
‘m
00
w
WARAC7ERISTIC CURVES FOR SAMPLING PUJ49 SASEO ON STANOARO OEVIATION METHOO
10
oPERAnNo
.——.
100
——.
.—
U%RATINO CW#fWTERISTIC
.
CURVES FOR SAMPUNO PLANS BASEO ON STANOARO OEVIATION METHOO
ii~
-----
‘0
bo
w
-0
#
.—.__—
TABLE
h .3
10
I b,
IQ
*
Ut Is#.ul
M,I., rq!lmom -
●*9k“-
w
E
40
30
t9#wq pm, bed m mm,.dti
w
m
+.do”t
I“tpn,
”,
!m
“.”l*
44,1, 1“1, I., -
..I.W,
SAMFI-E SIZE CODE LETTER
1
a
40
IYERATINO CHARACTERISTIC CURVES FOR SAMPLING PLANS BASEO ON STANDARD 0EVIA710N METMOD
._
loo
1
[ corm f“ S*,
nM-#An.u.O..,o
.
d Iuo9 k , m,t”b.+”,
hl-,tWllrdcfhh-lMhh
-rw.
-94
A.3
SIZE cow
BASEO
* “,”(++
,,uk,td )
ON STANOARO OWIATION
!
OUAU1’V
0? W3Mt?lC0LOTS I 1.,.md 4./.,!1..)
?wI.bm, “
LETTER
F
:,
,,
,19.1,b,,,d m .,”,. 9A,4 9.#t“-
SWR_E
OPERAnNG CHARAC~RISTIC CURVES FOR SAMPLING PL;NS
7ASU
t!
.-
METHOO
.-
.-
A.3
wu
QASED ON STANDAm
$lTER
F I Cenfh.edI ,
SIZE COW
OPETiATING CHARACTERISTIC CURVES FO+7 SAMPLING PIANS
TASU
*
OEVIATION ME I MOO
0
10
Ri
loo
A .3
_—
.W1.bflllrw. “...lld+
S1ZE COOE LETTER
G
I C.*.B IV ..v96, p!ru b.n.d w <a’. ..IM •.~ l.-
SiMFLE
~.i..l.nl )
OPERATING CHARAC7ER15TfCCU17VESFOR SAMPLING PLANS 8ASEC ON STfi?!DLRD DEVIIITION METHOD
TABLE
:~
ii
*
l___
I
x
Ii
A. ;
%.-
-
-
-
k.+.bl.
( h pod
B-m, 1“9101. -d
OUUllY Or SWMlllfO 10U
G ( Con!lnwd)
hv., m”,
tihdb, I
8ASE0 ON STANOARO OWIATION
SAMFLE SIZE CODE LETTER
OPERATING CHARACTERISTIC CURVES FOR SAMPUNQ PL+W
TMLE
-.
METMOD
w
“
I tiwl
&
,@h,
,h.,
H
W4 know,.“i,blll!, “,
SIZE CODE LETTER
b.sd m ,,”,, 44
SAMFtE
,,,,d,+
wI.,IA
)
WERATINQ CHARACTERISTIC CURVES FOR SAMPLING PLANS BASED ON STANDARD OEVIATION METHOO
TABLE A-3
-----
*
A.3
OPERATINO CHARACTERISTIC CURVES FOR SAMPLIN6 PLANS BASEO ON STANDARD OWIATION METHOO
TABLE
.
.
-a
m
e
I hi
A.3
tlmt k.d
m rm~. AA
I
-t h-
.wI*WI, u.
SAMP.-E S1ZE CODE LETTER
.m..lhlb H.1..lrd )
CURVES FOR SAMF1.lNO PLANS SASEO ON STANDARD DEVIATIDN METHOD
la st+q
OPERAllNO CIWACTERISTIC
TASLE
?s
TABLE
A -3
I ( Contllwl )
SAMPLE SIZE COOE LETTEfi
OPERATINO CHARACTERISTIC CURVES FOR SAMPLIN13PLANS BASED
.,
ON STANOARD OEVIATION METHOD
A-3
●w
J
O..*k-l
.“lMI,
SIZE COOE LETTER
f Cnns for ‘u#l., ph. h,,d m m,,
SAMW
“,
“Al+
b+’.w
I
OPERATINO CNAIIACTERISTICCURVES FOR SAMPUNO PLANS BASED ON STANOARO OEVIATII?N METMOD
TAME
?&
*
E!j
y
I
I
O~RATINO
A .,3
lb..,
k
M@”,
,1.., b.).t -
SAMRE
(Conm.td)
Is.,. AM##Lu.n,O-l.bill*
J
I
Um “,-II*
Iqwdmf )
8ASErI ON STANDARD DEVIATION METNOD
SIZE CODE LETTER
CHARACTERISTIC CURVES FOR SAMPLINIJ PL~NS
TASK
.- .——
I
!3
TABLE
2
A. 3
{ C-w, *
K
“a h.-
W,bdll, w, ,,,,”1;4$ qulw.1”1j
SIZE CODE LETTER
,1.@q ,1,., b,,d m ,..,; 4.*
Sf+@LE
OPERhTINQ CHARACTERISTICCURVES FOR SAMPLING PLANS BASEO ON STANOARD OEVIATION METHOD
,,.
g“ !!
+
3
y
.-
h .3
{ -t
b
*I
h-i
~,,
p-t
ht.,
m-
m lul\s -
“ bm+tl.
“4 i-
K ( Cennn.t~)
.9
,“,,o,wz
●***W+ +!”.1-1 I
dmltt,1“,!, 1- -d
.ul.w~
SAMFLE SIZE COOE LETTER
OPERATINO CMbRACTERISTICCURVES FOR SAMPLING PLANS BASED 0:1 STANDARD DEVIATION METHOO
TABLE
.,
f
1
c@ERAnNo
A-3
t *8
f-
Wt
}1-
b-d
m m,,
dn4 -8 in-
L
vul,blhtj w, cud!+
SAMFtE S1ZE CODE LETTER
WIV,lon!I
CHARACTERISTIC CURVES F(XI SAMPUNG PLANS BASED ON STANDARO DEVIATION METHOO
TA9LE
:x
=!5
cmmo
A.3
L
t Con!h..d )
SAMFtE SIZE COOE LETTER
CMbRACTERNWICCURVES FOR SAMPLING PLANS BASED ON STANDAR5 DEVIATION METHOD
TASLE
o
,
A -3
Tli+n*d
-W!* 9! 91UW * -
*
,:
,“,,,,,,..
[ h ,,remtW.nil,. )
,,nwdl,ll, ,,u(v,M }
“, 8.,,,!,,,, O@,, c“.,, f- w,,,
Lois
,,* hnwmvwl,blhl,w,
of WBulmo
?&I,%f,~,,, m,-,
ou4m
1“ ,,q,!h, ,hns b,,,d m ,,.9, ,A,b
mmaItofbl,npwl,*
$.h
h
“01...19 ul
- s 4
419!?IM-.
I h,,,
!4”
SAMPLE SIZE CO@E LE TTEII
OIWMTINO ChARACTERISTIC CUfWES FOR SAMPLING PLANS BASED ON ST.ANOAROOEVIATION METHOD
TABLE
~y
Cm$
a
:!E
~f
gln
I
A -3’
m+dall?--dtiwr-eh
etiti—rti-1,
mb9md d
b- * “
● lnwm
il
m,, ~.,
Wm
I W-.sa ?0?snplhl, ,19.s b-d
604
“d
i.-
..rl.bnll, “.
“m!h!lf @!mlWd)
* -
..9 k+.
0“.l,t, L“.1. 4- W.*I h+.,llo...
of WSM171C0
1.079 { 1.ptm! 4.1..!1.,I
m ““,0
M ( Contln..d )
SAMPLE SIZE CODE LETTER
OPERATING CHARACTERISTIC CURVES FOR SAMPLING PLANS BASEO ON STANDARD DEVIATION METHOO
TABLE
...
,.
..
.
A .3
thl*.
dm#w9*s!h**-t.4
bh
-=@-nM-h.b9..9wwnl8
.
-d
94e
h , 4
4M”MI.,
f I&w, b
,udq
w.,
nw,
-
-
LOU
,,, ”l,tq
~.,.di,,, )
M*,*,*).”
I
I I. ,,,,”1 ..h.th. I
.“l.b.t,l, “.
“. Auvl.bl. 0“.!1!,1“,1, t. “-”,
aumm or woumo
,!,”, b,,.d m ,,”,, “Ihd -4 t.-
N
SAMFtE SIZE CODE LETTER
OPERATING CHARACTERISTIC CURVES FIX? SAMPLING PLANS BASEO ON STANOARD OEVIAilON METHOO
TASLE
A. S
OPERAllNQ CHARACTERISTIC CURVES FOR SAMPUNG PLANS GASED ON STANOARO OEVIATION METHOO_..
TAGLE
m
A.3
i G“,
1“ a+,
,Im, $,,,4 m ,,.,.
44
o
ON STANDARD DEVIATION METHOD
W, t-mm.ar,.bdlt,w
SAMPLE SIZE COOE LETTER
DPERATING CHARACTERISTICCURVES FOR SAMPUNG PLANS BASED
TABLE
..
.
-.
.— -—-—-—.
r5
TASLE
A .3
I Cnrm fw “w-q
PIM1bm.d m r9ng.4M
-4 k.-
O I Contln.*d)
v“i.bill!, “.
SAMPtE SIZE CODE LETTER
.,,,.lhl~
qll.,1-l I
OPERAnNG CHARACTERISTIC CURVES FOR SAMPLINO PLANS BhSED ON STANDARD DEVIATION METHOO
-——
B
A. 3
W +., d lb ,Wcmld It, *ml*4 1,“
-w.
**ti
.,-,,
.
*4
d M
k , 4M”MI*
t C4WW8
t- ,qll.,
..fbti .,, &.cu vwl.btit+,,,,
,,,.”1,+
MA) f,~,,,
0!
unu
“.
,,.,..1”1 )
kr@.b!. Owl,!, L,.,t, t- w.,+ b!,,.,,,o”,
9UALIT7Of 9u9Ul~D LOTS I 1.,,,w,TI d,f,,l),, I
,Im, b.,.d m rq.
P
SAMFtE S! 2E COOE LETTER
OPERATING CHARACTERISTIC CURVES FOR SAhiPLINQ PLANS BASED ON STANOARO oEVIATION METHOO
TABLE
.i
:
!/
d:
gi
~15
lbdat?l-wddbf,-?-abb
---**”O--*,
Wdd-b@--dak$*Mm
“
( e--m 1- -I
A .3
m Ire,, d
-4 i“-
I Conllnwd1
.“kbllllj “,
“oatId+ tq.lnl.! )
lb,,, nw,., -
-.
“. k~,.,,.
0,.1!,, L“.1, I- -..1
In,,,,,,..l.
OUALIWOr SWUl17t0 101S I 1.,.r.m$ #.1..lh.1
)Iul W
P
SAMPLE SIZE COOE LETTER
CURVES FOR SAMPLING PLANS BASED ON STANOARO OEVIATION METHOO
TABLE
.——
_
_
a
d a
-.woM*ubal
k
-,,.
* d
mmkuilm~tibl,~,,bb
-04
A -3
41,+.MI..
.“i,blmy
,,,m,,
W., flpt
.I -
d,,
_“,.,!M!
W. k.pl.bl. IWI~ L...l, l,, f.x.,1 I,TV,,I,W
1
OUAUW OP $uBMITrCo
LOTS ( h ,.,,,”9 ,.1,,1,.,)
Q
I Cuml fw t.wh”, 01,”,},,.4 m f.”,, ..*W .. . b.“,
)
RA5E0 ON 5T,ANDAR0DEVIATION METHOC
SAMFtE SIZE cooE LETTER
opERATING CHARACTERISTIC CURVES ,FOR SAMPLING PLY
TASK
,.$,
TASLE
.,
A.3
I h,
f-
,+*,
,S..,
b.,d
01 ,,.,.
dti
)
mm,bin.., .whb,hly
Q ‘( Cm
fln.,d
“.
,,,4+
w@vdcd I
BASED ON STANDARO DEVIATION METHOD
SAMPLE S1ZE COOE LETTER
OPERAllNQ CHARACTERli~lC CURVES FOR SAMPLING PIANS
.,
B
SSCTIW
VARIABIIJTY
uNKNowN-sTANDAmf
Parf
SINGLE
S1.
SAMPIJNG
PLAN
FOR
SPECIFICATION
LXM!’T
SINGLE
B1.1 Use of SamPtinfl
PlaJw.
To determin.
whsther
the lot me=t.
the ● ccept ability criterion
with respect to ● particular quality cfuracteristic
a.ud AQL. -Iue.
the applicable
campling
plan shafJ be uced
with lb. proviaionm of S.c in ● ccordance
uc.n A, Generai
Description
of Samplmg
Plan. .-d
th.. e in %hi, part Of th. Standard.
B 1.2 Drawi..qof Samplem. AfI .amplew ● hall
be drawn in accordance
-’th paragraph A7. Z.
of Sample
Size Code
B1. 3 Determination
●zce cod ● letter ●ha
~.
Th e .smpla
be selected
from Table A-Z in ● ccordance
with parasraph
A7. 1.
SELSCTING
THE
SAMPLING
WHEN FORhf 1 IS USED
I
SPEUF3CAT10N
Thi. pArl Of the Standard deocribe.
the
procedure*
for us. whh plani for ● oingle
ape .ifiution
limit when variability y of fhe
lot with re.pect
to the quality charae%eri. deviation
tic i. unknown ● nd the .tandard
method ia u#ed. The acceptability criterion
i. given in two equivalent iorm9. Tbeoe are
identified as Form 1 -d
Form.2.
B2
DEvlAnoN
LUA3T
BS. Z.2 Accepu bility brmant.
The acc.pc.gtotbemundility
corutaaf k. correewmt
ple size mentioned ia pnagraph
B2.2.1, ia
indicmed in the column of the nuster table
cor re~pmxling to tbe applicable
A(2L value.
Table B-1 i. entered from the fop for normal inopecfion
● nd from
the bottom for
tightened inspection. Sampling plum for reduced inspection are providd_ in Table B-2.
B3.
LOT-BY-WT
ACCEPTABILITY
PROCEDURES
WHEN
PURIM 1 LS USEI?
B3. 1 Acceptability
Criterion.
Tbe degree
of conformance
of ● q uafit y cb8ractericti c
limit
with respecf
lo ● single specification
.W1
be judg.d by th~, qusntity (u-XJI* or
fl-L)/i..
B 3.2. Corn
tatien. TtIt following
quantity
.haff b(“-X)/’
., (x-L)/.,
d,pendiagon whether the specification
limit i,
~ qper
or lower limit, +ere
U
L
X
.
i.
ii.
i.
tk upper specification
limit.
tbe lower specification
limit,
the sample mean. and
de.rlatioa.
the ● .tirnate of lot ●sn&rd
PM
B3.3
Acc
ability Crite rfon.
BZ. 1 Maater sampling
Tables.
Th= muter
●anmlmn
tables for mlana based or. -riabilit~
-MI
for ~ ●ingle specification
limit vben
using
the ctaadard
deviation
Table B- I
method ● re Tables B-1 .nd B-Z,
in .m=d ler norm.] and tighter.ed iriapection
art< Table B - Z for reduced imspeetioit.
M.
B 2. Z Obtaining
the Sa?nPlinK PIan.
The
.mnpl.tig plan cons.st. .1 ● .unple
.i.e 8d
m ● ~nociafed ●Cc.eptability COtI.unt. 1 The
sampling
plan i. obtained
from
Mater
Table B-1 -, B-.?.
The foLIowfnr ‘soP*
=~u...
t.. . . mllowed:
B2.2.1 Sam Ie Sise.
The #ample .ise ●houm m
tabl - eo.-..
p-.fing
~ t e ma.,..
.-.1.
..cnple ●ice cute tetter.
Z*
*O
Cumpare the
abifttywmst-nt
k. ff (u-x)/m
or (x- f.)/a ia
equal to .ar gre8ter tlun k, the lot meets the
=cc~tiIf.fty
criterion: if (U-X)1.**
(X-f-)1~
ia l.mm Uu8 k or nerative, 3hrm the M &es
not meef the •=e~llity
criterion.
t31JM3tMRY FOR
~~MNG
PLAN
OPXRATION
WREN
FORM
•~marise
OF
s m
‘he PrO -
(1) Daterrnirw the sxmple .i.ecode
lti ter from Table A-2 by uming the let sise and
in.pccfion
leeel.
MIL-m-414
11 Jt333e1957
(2) Obfai. Pk. from Mamer
or B-z by .eleeting
the sample
the ac..ptabill$y
constant k.
cpecifteation
limit. The percentage of Macoaforming
product is cstimattd by wiieria’
T~le
B-5
with the quglity index and the
sample ● ize.
Tab)= B-1
size n and
of n
(3) Select at random the sampl=
lrorn
the let; inspect ● nd record the
mea. urernem of she quality characteristic
fer each utiit of the sample.
unit.
B6. Z GE-I
utatio” of Qtufit
~-lity~-X)~rnpE~
if the specification
limit i. ● a upper limit
U, or OL . (X- L)/t if it is a Io-er Jimit L.
Th* quaatitie..
X ● md s. ● re the ●arnpl.
mean ● nd e.timm e of lot standard deviation.
respectively.
(4) Cmnp.te the s.mpIe
mean ~ and
dcvistic.n . . and
estimate of lot sts”dard
● ISO compute the quantity
(u-X)1.
for an
u per specification
limit V or the q~ntity
lids
3..
A-L)/.
for ● k.wer .peciticatio~
15) M the quantity (u-X)/s
or (X-W.
i. equal co or greater than k, the 10I meets
criterion:
it’ (u-X)/.
or
the ●c.ept.bilicy
thes the
(X-L)/.
i. [e.. (ha--- k or negative,
lot doe’ rwtmeel Iheaccepttii
lily criterion.
B5.
SELECTING
THE SAMPL3NG
WNEN
FOfUd Z 5S USED
~e
-ii-t-d
P.,. em d.f=~tiin d
the upper specification
limit, or
by ?z.. th. estimated
percent defective below
the lower .pecifi catian limit. Tbe ● stimated
Pc*.=.:
defective
PU or PL i. obtained by
enterina Tabk B-5 with Ou or QL and the
●ppropriate ●anple size.
W.
lot
P2AN
●bove
S35.1 h4asccr Sampling Table..
Th. ma. ter
.ampJmg tables for plans based onvariabil ity unknown for a single specification
limit
when using the m~nd-rd deriatitm method
sre Table. B-3 ● nd B-4 of Part If. Tsble
B-3 is used for normal a“dai~htened inmpec eion and Table B-4 .fc.r reduced.inspection.
336.4 Acceptability Criterion.
Gmpare
the
estimated lot pereent deIectivepU or pL with
the maximum allowable percent defective M.
U PU Or Pl, 1. eqUf to or leas thn U, the
if Pu
lot rneets the acceptability
criterion;
or p~ is greaier
than M or if Qu or Q
is
,negative,
then the 10: does not meet \he
acceptability
criterion.
the Sampling
Plan.
B 5.Z Oblainin~
The
sarnpli”~ plan co. ss.ts of . .unpl.
,Ize and
maximum alk.w=ble percent
sn ● ssociated
da$eclive.
The samplin~ plm i. obtained
from MaDter Table B-3 or B-4.
B7. SIJ71SMARY FOR
OPERATION
SAMPL3NG
PL.AN WHEN
PORM
USED
The fellc.rnng step. .umrnariz.e
cedure. to be fallc.u.ed,
65.2.1 Sample Size. T)M ●mnple mice n is
● hewn m the ma. tcr table cortespendin~
10
each sam>le .iz. code letter.
OF
2 3S
the pro-
(1) Determine the ●mple .i=e code let ter from Table A-2 byu. ing the lot size md
the inspection level.
135..?.Z Maxim. mAllow8ble
Percent De fee● llowable
p.=. ent det$ve. The rrmxim.tn
● stimate. correspond.
=live
M for ample
img to the .unple
size m=nt ioned
in
pa:agrmph 95.2.1 is ittdicated in the column
of the nm.ter
table .xxre.pondiytg
to the
●Pplic=ble AOL value. Tabl. B-3 i. =nt=,.d
from tbe top for normal inspection -d
from
the bottom lo, lsghter.ed in. peetion. Sam -li>g plan. lcIr reduced inspection ● rm prov-l
d ea ,. ~a~,e ~-,.
(Z) Obtain plan from Master T=ble B-3
or B-d by .elecfi.~
the .unple
.ixa n attd
the maximum allowable percent defective M.
(3) Select ● t random the #ample of n
unit. frmn the Iof; inspect UId record the
m.asurernemt
of the quality charact. rimic
cm each .unh of the ●ample.
(4) Cmnpute3h= sample mean X arid the
ectimale of lot .ta”dard
devfatian . .
(5) Compute
the quality
index Q
Jfi:
limit
(U-X)/ * if ● n upp. r .pe.ific.tie,.
●P.*ified. or OL = (x. L)/. if ● lctwerspec iiication 1;...;. L <. snecif; ed.
B6.1 Acceptability
Criterion.
The dc~ree
of conformance
Of a quallty characteristic
limit
with respect m ● ai.ngle specification
hall
b, judged hy the percent of rmnem-,
Iorm,ng product outsidt the upper or low+r
%.
Ex_pie
B. z for .a cemplete
(6) Det~rmb-Ic the estimated lot pereent
de fecnive pu er pL from Table B-5.
●xample of thb. prOc*dure.
:38
Mu.-sm4l4
11 Juoe 19S7
is~reatertl.an
U Orif QuOr C3~ is aepti
e,
then the lot doe. ml meet the ●ccepmbi r IIY
criterion.
fi) ff the e.timated lot percerndefective
PU Or PL i. ~ud
to or 1... than the maxi.
mum .dlowable
percent defective M. the lot
if PU Or PL
meet. the ●cc.pt~bil$ty criteriom
EXAMPLS
Exmnple
Single
Variability
ExAmple
Limit-Form
- Standard
I
Deviation
Method
of operation
for ● cer:aindevic.
i. .pecifi.d
● . .?09” F.
The rn.timum
temperature
A lot of 40 item. i. submitted for inspection.
Zn. pection Z-evel IV, normal inspection, with AQL = 1-% i. to be u, cd.
From Tables A-2 ● nd B-1 i! i. aee : that a
marnplc 01 sise 5 i. required.
Suppose the measurement.
obtained are ● . <c.11ow.:
197.. 188-, 184” ,205-, and ZOl ‘: and compliance wfth the acceptability criterion
i.
10 be determ%nea.
Line
.—
Information
1
Sample
~
Sum of Z.@.ur.m..t.:
3
Sum of Squared
4
Correction
5
Corrected
6
Variance
(V):
1
Estimate
of Lat Standard
8
Sample
9
Specification
Si. e:
Value
Needed
Explanation
Obta{ned
n
5
Me,,
Factor
975
IX
ureznentn:
(CF):
XX2
190,435
(I X)z/n
Sum of Sqmre.
(SS):
s“X~CF
190,435 - 190,125
310
77.5
Deviation
.:
310/4
8.S.1
fi
-s
I 95
Mean X: ZXln
Limit
(975)2/5
190,125
SS/(n-1)
(upper):
The quantit~
w-X)/c
II
Aecept~iIity
&natant:
k
lZ
Acceptiility
Criteriozx
f2mpare
97515
209
u
10
1.5.9
The lot rneetm the .cceptabiltty
NOTE:
of Calcufatio.s
Speci!icatlon
Unknown
B-1
1.53
w-X)/O
criterion.
with k
mince (U. ~)/s
1.59>
1.s3
[209 - 195)/S .81
S..
Table
B-1
See Par&. B3.3
is ~remt=r than k.
limit L is given. fhen compufe
If ● ■ingle lower spcffieat{on
Iin. 10 -d
com~re
il with k, the lot meet. the =ccept8bility
equal to or greafer than k.
the q~ntilY
~-~)f~
*rii=.iQn.
if (~-Ll/*
in
is
I
!.
M2~-414
11 June 1957
Single Specification
Variability
CUmple
I
!
Unknown
Inforrntiion
J
Sample
z
Sum .3[ Mea. urcme.ta:
3
Sum ef Squared
4
Correction
5
Corrected
Size:
Method
XX
7
Estimate
of b:
8
Sample
(CFh
9
Specification
Standard
2ndmc
‘“t”
b’
13
Acceptability
au
‘ercen’
T3U let rmet. the
lX~CF
Deria:icm
.: fl
Criterion:
310/4
8.81
J-7X5
195
97515
Z09
u
1.59
. (u-x),,
D’*”’
190.435 - 190,1Z5
310
77.5
(upPer):
A21mv=ble Percent
Mu.
(SS):
(975)2/5
190,125
(IX)zln
ZXln
Limit
O~lity
1?,
190,435
1X2
SS/(n-11.
Mean X:
tkpl .nati.n
975
Measurement.:
Sum of Squares
(v):
‘f
Vmlue Ob:.ined
Needed
5
F=ctor
.V.4@I<.
NOTE:
- Standard Detiation
n
6
11
,?
The maximum temperature
of operation for ● certain device is specified ● s 209” F.
2nspection Uvel
IV, normal
inspecA JOI of 40 items is ●ubmilted for inspection.
tion, with AOL = 1% in 10 be u.ed.
From Table- A-2 and B-1 it i. .een that a
sample of .ize 5 is required.
S.ppome the measurements
obtained art ● . follow.:
197., 188-, 184.,205-,
and 201 ‘; and compliance with the acceptability criterion in
to be deter rnitied.
Lime
—
10
Limit-Form
.Z.19%
%
De:.:
M
Compare
●cccptablzsty critarion,
3.32%
Pu vilh
●6nce
M
2.19% < 3.32%
pu is 1.-0 tti
(Z09-195]/8.81
S..
Table
B -5
.%. Table
B-3
See Para.
B6.4
M.
U a sin@. lower specification
limit L is Siven, then compute the quality index OL =
PL rnth
(X-L)/s
i“ line 10andobuLn the ● .timate of lot percent defective p . Compar.
M; the lot meets the acceptability
criterion.
it pL is equal to 0? 1C*S lbn M.
- -- -—--M
I
...
I
TABLE
B-1
Standard Deviatiom Methc.d
MIster Table Far Normal &.d Ti~htened fn. pectlo. for PlaIJs Based on Variability
[Single Specification Limit– Form 1)
Acceptable (
Sample size
code
Gi-
letter
,10
k
B
k
.25
.40
T
kk
.CVCIS (normal
m
k
inspection)
1.50
2.s0
4.00
k
k
k
1.12
.958
m
k
.765
10.00
15.00
T
k
k
.566
.341
.617
.393
.67S
.4s5
.7s5
.516
.82n
.611
.886
.664
.917
.69s
E
7
F
10
t
—
i
—
G
15
2.64
2.53
l-k
34
20
2.69
2.58
2.47
25
2.72
—
2.61
2.50 11.40
!3..26
2.14
1.98
—
1.85
1.72
1.53
1.35
1.14
.936
.71,?
J
30
2.73
2,61
2.51
2.2.9
2,15
2.00
1.86
1.73
1.55
1.36
1.1s
.946
.723
K
35
1.17
.?.65
2,54
1.76
1.57
1.39
1.18
.969
.145
L
40
2.77
—
?.,66
—
2.5s
1.58
1.39
1.18
+ .971
.746
c
5
D
g
,15
+k
-
allty
.—
.65
Unknown
,1
-
L
I
2.00
).15
1,62
1.50
1.33
1,;l 5
.955
.?.24
2.11
1.98
1.04
1.72
1.58
—
1.41
1.23
1.03
2.3?.
2.2o
2.06
1.91
t.79
1,65
1.47
1.30
1.09
2.24
,?,11
1.96
1.8.?
1.69
1,51
1.3)
1.12
I
2.36
2.41
I
2.45
.3.44
2.69
2.58
150
2.96
Z.84
2.13
2.61
zoo
2.97
—
2.85
2.73
2.6.?
.065
.10
-t.15
.25
o
100
L
.814
.874
2.80
2.90
1.01
I .07
2.92
75
1,17
1.24
2.55
N
+
1.34
1.40
2.66
2.71
1.45
—
1.53
2.77
2.83
$
1.65
2.5o
50
Q
2.42
v
k
1.88
2.6o
5.4
P
1
7
--t-
1
2.31
2.18
2.03
2.31’
—
2.18
2.03
2.35
2.22
2.41
1..99
. .
1:76
2,08
1.89
—
1.93
1.80
1.61
1.42
I.ZI
1.00
.774
2.27
2.12
1.98
1.84
1.65
1.46
1.Z4
1.03
.ao4
2.43
2.29
2.14
2.00
1.86
—
1.67
1.48
i.26
1.05
.819
2.47
a.33
7,1!
2.03
1.89
1,70
1.51
1.29
I .07
.841
2.47
2.33
2,1[
2.04
1.89
1,70
1.51
1.29
1.07
.845
.4o i .65
I ,0(
—
AcceptableC alit,
1.50
—
,fVela
Z.50
4.00
6.50
,0.00
.
i
I 5.00
lightened inspectio!
A21AOL wdue8 ye knpercent de-a.
[Irst tunpllq
plan belcw ●rrow, that is, both sample OIZ.Sas well ao k va2ue. When nample sise equdt er e=ceedo lot
,V.V
,tern hth. lot must be inspected.
1:::,
~~
TABLE
23-2
“Standard Deviallm
Method ~E
Maater Table for Reduced lnmc.ectimfor Plana Breed On Varlabilitv Unkmwm
(Single Sp’c.ifi..tl.n
Litnit-F. rm I )
I
I
I
SampIe
Code latter
m
“Ac
Sunple
size
size
.04
I
I
.06S I .10
-L
.15
x.—
k
k
—
—
D
3
E
3
T
4
—
G
5
i
Zoo
H
7
1
10
J
10
K
15
Z.53
Z.4Z
L
Zo
Z.58
—
u
Zo
2.58
N
25
z.61
0
10
P
50
-i-
*
T
Q
75
4,00
6.50
i65i
k
k
k
.165
J+~~
.566
.141
1.12
.958
.765
.566
.141
_—
1.12
.958
,76$
.564
.141
I,lz
.95.9
,165
,566
.341
I
.—
1,45
—.
1,65
1.51
I
—
1.34
—
1.17
1.01
..914
,617
.393
—
1.40
1.Z4
1.07
.874
,675
,455
.955
.755
.536
t
1.$8
i.75
1.62
1.50
1.33
1.15
1.84
1.7Z
.
1.72
1,58
1.41
1.23
1:01
.828
.611
1.50
1.41
1.23
1.03
.828
II
.664
Z.11
Z.)z
Lzo
2.06
1.91
Z.47
z.16
Z.Z4
—
Z.11
—
:.96
Z.47
Z.36
.LZ4
Z.11
1.96
Z.50
2.40
2.Z6
2.14
1.90
2.Z8
—
.?.!5
—
2.00
—
Z.Y5
2.ZZ
Z.08
Z.41
2.27
2.IZ
—
I
k
.—
.958
Z.Z4
Z.11
EEE
Z.50
l.lz
1.9a
—
1.9a
z
t-t
uality Levelo
.40
—.
k
—.
!.84
*
k
-1-d
1.79
1.6S
1.47
1.30
1.09
..986
1.8Z
1.69
1.51
1.11
I.lz
.91?
1.8z
1.69
1.51
1.33
I.lz
.917
.695
1.85 I
I,7Z
1.51
1.35
1.14
.936
.712
1.86
1.73
—
1.55
—-
1,36
.—
.946
.72J
1.91
1.80
1.61
1.4Z
1.15
—
I.zl
1.00
,114
1.98
(.84
——
1.65
1.46
1.24
1.01
.80$
.—
All AQLvm3ues ● re in percent defective.
f2rotdunplln,g plmbelowtrrow.
that it, both mm-qde nize no well •~ kvalue.
~~;;,
e,:,,
,,,m i“ the ,0, lll”,t t., ,mpetted.
.695
—
Whertaemple oize equal, or exceed.
lot
I
Part
DOUBLE
S8.
SAbfPLLNG
PLAN
SPECIFICATION
~
FOR
SPEC337CATZ034
DOUBLE
This part of the Stan-dard describe.
the
procedures
for use with plain for ● double
specification
limit when variability
of the
lot with re.p. ct to the quality cluracteristic
i. unknown and the standard deviation method
is used.
I
Bfl.1 use of Sampling Phm.. TCI determine
whether the lot meets the ●cceptability criterion with respect
to a particular
quality
characteristic
a“d AQL value(.)
the applicable campli”g plan ●ha31 be used in accordanc. with the provisions
of Section A, General
Description
of Sampling
Plans, and
those in this part of the Stamdard.
B9. SEIJ2CTI?JG
THE
SAMPLING
n
PLAN
A sampling
pJa. for each AOZ. value
.hall. be ● elected from Table B-3 or B-4 m
[C.;J”WS:
B9. 1 Determination
of Sample
.Stze Code
ktter.
The .arnple
i..
cone letter .hal;
be selected
imm
Table A-Z in ● ccordance
with paragraph
A7.1.
B9. Z Maater Sampling Table..
The master
satnplmg table. for plum based on variability .“kt-mwn for a double specification
limit
when using the standard
deviation
mctbod
are Tables B-3 and B-4. Table B-3 i. u.ed
10. normal
and tighlened
ir.spection
amd
T=ble B-4 for reduced impectiom
B9. 3 Obtaining Sampling Plan. A sampling
da”
.— consists of a .arrml. ..ze and the assoeiated maximum allowable perceni defective(s).
The sampling plan to be ●pplied i.
inspection
shtil be ob-iaed
from WSter
Table B-3 or B-4.
B9.3.1 Sample Size.
The .unple
#ize o is
tablas correape=ding
show” in the mater
tO each sunple size cod. letter.
B9.3.2 M-.imum
Allowable Percent Defec.
percem
*.
T h.
maximum
allowable
defective
for #ample estinuLe.
of pert.mt
de fe. civ. for the Icxmr. upper, or both .pec.
ificatiori limit. combined, corresponding
to
the sample
.ize
mentioned
ia paragraph
f39.3.10 in shown in the COhmm of the masto the applicable
ter table corresponding
AQL value(s).
U different
AOL, S ● re a.sign=d to each .pe cification limit, de.ignmfe
3XM3’I
the maxfzmIM tiowable
percent de fecfivc by
ML for the lower limit, mad by M
for fhe
upper limft.
If one AOL is asci~e 3 to both
IiAt.
contbi.ed.
designate
the timum
Ulowable
percerd d-f%
by ht. Table B -3
i. ● ntered from 3be 30p for marnul flupection and from the bottom for tisbtaaed fLlWpecffon.
Samp3fng pfuu
for reduced fnspect.ien ● re provided io Table B -4.
B 10.
DRAwU?G
OF SAMPLES
Sample# shall
ance with paragraph
B11.
;:&-.o;&O
be elected
A7.2.
T
in accord-
ACCEPTABILITY
.
B 11.1
Acceptability
Criterion.
The degree
01 Conformaa Ce or a WlA3ity elaaractcria3fc
with re. pect to m doubje mpacification limit
.hafl be judged by the percent of r.onconform% P.tiuct.
The percentage of manconforrn img product i. e.timated by entering Table
B-5 with the quality index and fhe’.ample
.ize.
U
L
X
s
is
ia
is
is
the upper specification
limit,
the lower sp.cificacion
limit,
the sample mea., and
tkm estimate of lot standard deviation.
B 11.3 Pere=nt
Defective
i. the Lat. The
aualitv
.
. of a lot shall be cx~r.a~terms
of the lot perc=nt deiecti~c.
Ita estimate
+33 be de.i~ted
by p~. PUO Or P. me
iadicsten
cmifornunce
with
:::;52ptL
upper .Pe.tllctiorl
limit, PF
w.ilh .e. pee: to fbe lowez .pecifiutio.
lima .
-d
P for both .Pecifiati.n
limiteombimed. The emtimstea p
mid p
r=.pec bedetermined
by wIterins + ● ble B- Y . ‘w’
tively +f.h QL and f)” md the sample ● isc.
The eotinute p Zhmfzbe determined by ●dding
the corresponding
ectinuted
percent defective- pL and p“ found in the tible.
B12.
ACCEPTABILITY
CRITERION
SUMMARY
FOR
OPERATION
SAMPLING
PLANS
B 12.1 be
AOL value for
Lower s’ ecxlncatson Lwm
both Upper
umd.
AND
OF
and
MI L-STD-414
11 JurIe 1957
tdu, the lot meets the ●ccepubi.fityc riteria;
otberwimm, the lot doe. not nwet the ace~.
abf3ity criteria.
U .mither QL or Qv or botb
are me~tiive, then the 101does not meet the
acceptability
criteria.
B 12.1. I Acceptability Criterion. 4 Carapare
the ● stimated lot pe.rcatt delective P = PW +
● llowable
p=rcent
PL with the maximum
d. fective M. 11p in ●qual to or less tfun M,
the lot meets the accepmb{lity
criterion:
if
p is grcatertban
Mor ii eifher Qu or QLor
,then the lot does not meet
both ● re n.@ive
the ●cceptability criterion.
BIZ.Z.2
SurnmaryfOr Opertiianal Sampffrt&
Plan. 3n ca. eg where ● t
erenf AOl. walue
~stablished
le. the upper and lawer .pec ification limit for ● single quality cfuract=r istic, the following
steps sunururi’e
the
procedures
to be US=CL
B 12.1.2 Summary lor Operation of Samplin#
Plan. In cases where a ●m.glc ACfl. value is
~lished
for the .tmer and lower .pccifi cation limit combined for ● .in81e quality
characteristic, the following mtep. ■umma rize the procedures to be used
(1) Deterrninethe
ample
.izecod=
letter from Table A-2 by twin, the lot size
and fnspectimt level.
(1 ) Delerminc the ample size code
letter [rem Table A-2 by “sing the let .i%e
● nd the iriap. ction level.
(2) Select plan from Master Table
B-3 or 8-4.
Oblain the ample
size “ ● nd
the maximum allowable percent defective M.
‘(.?) Select the sampling plan from
Master Table B-3 arB-4.
Obtain the.ampfe
.ize . and the maximum allowable percent
defective
Mu and M’. corr=apondi.g
to the
AOf. va2ues for the upper and lower specification limft., respectively.
(3) Select ● t random the sample .af
“ unit. Imrn the lot: i.sp. ct and r-cord the
mea. ur. merit of the quality characteristic
on each unit O( the amp]=.
of
(3) Select .1 random the ..ntple
fr.rn tie lot; ia. pe.t and =ecord the
meas”remerd
of the quality cfur. cterimtic
on each unit in the .mrIple.
rnesn X
(4) Compute the ●mple
and c.timltc
Of lc.t .tand=rd
dcviatic.n s.
(4) Compute the sample mean X
and estimate . 10I .tamlard deviation s’.
,,
(5) Compute
the quality
QU = (u-X)/.
and QL=
(X. L)/,.
(5) Compute
the quality
Qff = (u-X)1.
and OL = (x- L)/a.
p.,r.n:
B-5.
n unite
indices
(6) Deterrniae
tbe estimsted
lot
percent defective
~ and p~, correspandiag \othe percent defective* shove fhe upper
and below the lower .peciIscaticm
limit-.
A2eodetermi”e
the combin.d percent delec tive p = pu 4 p~.
(6) Determine
the estimated
lot
d. fecfiv. P = PU + PL from Table
(7) lf the e.tirnated lot percent defective p i. equal tc. or 1,.. than the maxim● llowable
ptzcen% defective M, the )ot
um
criterion;
if p is
meet,
the ●cceptability
ur.~t=,
th=n M Or if either W or QL bolhar.
ne~.tive, then the 101doe. not met
the ●cceptability criterion.
B] 2.2 Different AOL Valueo
Lower specification
Limit.
for Upper
ittdice.
(7) 11all tbre=of
the f.dlowin~ corl-
dition.:
(a) ~
%
and
i.
equal
t. 0? 1...
thll
●
~] PL !9 =LNJ81tO 0, h..
t3UII
‘L.
B 12.2.1 Accernability
Crit’eria.5
Gmpare
th. e.tirnated 101 fJC,C.llt dd ectives pL and
PU with the cm? c.pn.ding rntimum
allow.
able p.rcem
defective.
M
compare p = F.L + Pu wfth tke%~#~fa?L
and Mu.
If pf, i. ●qual to or Iesn than htL,
PO i. =qu*: to or le..
than MII. and P im
.@al
to or 1.*s than the larger ‘of ML “and
+S..
*W
Etimple
Example
larger
of ML
(c) p is equal to orlemmthanfbe
● nd btU,
are sati. fied, fh= lot meet. the ●cceptabifhy
criteria;
ofhe=wi. e the lot does mat meet the
acceptability
criteria.
ff either OL or Gff
or both ● re negatiwe, then the lot does not
tne=t tbe acceptability
e=iter ia.
B. 3 {or . cmnplete ●xample of ibis proc.dure.
B.4 lot a cmmpl=te exatnple of thfs procedmre.
42
Z41L-STD-414
Ii June 1$S7
3SXAZ4PLC
I
i
Example
I
I
Double
VariabiNty
spa Mlutino
Ltmtt
and Lower
Zkuiaticm M.thod
Specification.
Limit
Cmmbined
Tbc minimum temperature
of operation for a c=rtAtn device 48 speetfied 8.180- F.
The masimwnt.mprst.re
h 209” F. A lot of 40 item. i- submitted for imopection.
3nmpection Level 3V. normal in.pect(on, wtth AOL. s 1% im to be ..d.
From Tablam
Suppo*e the rne...re.
A-2 and B-3 it is neen that s sample of ●i=e 5 is zequird
197”, 188”, 1M., 205”, md 201 -; ● nd cmnpliuw.
mcntm obtained ● re 8. fof30w.:
with the acceptability criterion i. w b. determined.
E-de
1’
1’
I
of Cdcu3ati0nm
?.bbnamn . Stutdard
AQ L Value far both Upper
0..
E-+
Znforrnatian
Line
—
Needed
1
Sample
2
Sum 01 Measu..
mant.:
3
Sum of Squared
Measurement:
4
Correction
5
Corrected
6
Variance
(V):
7
Estimate
of Lot St&rd
s
Sample
9
Upper
Sise:
Factor
ICF):
SS/(n-
975
SX
310
(SS): XX~C~
190,435-190.125
77.5
1\
Deviation
s:
&
310/4
m
8.81
195
Limit:
U
209
LitnAt:
L
180
Lowe r Specification
II
QtuIity
12
C3udity tid=:
13
Eat. of L9t Percen5
hf.
14
Est.
Z)ef. below
15
Tataf
16
Max.
17
Acceptability
p~ with M
9?5)5
Qu - (U-X)/s
1.59
(zo9-1951/a.nl
OL = &
1.?0
(195-180)/8.81
of Lot Percent
E81. Pe.rcm13 hf.
Nlowable
lot meet.
(975)2/5
190,125
~1.
Specification
Index:
190,435
XX2
(2x)z/n
Sum of Squarca
Mean ~:
Explanation
s
n
10
‘3&
Value Obtained
Percent
Criterion:
the
L)I.
Ab0V8 U:
L
& La&
Da f.:
PL
p = pu + pL
P . Pu +
criterion.
Ante
.%-
Table
B-5
.64%
See Tablm B-5
2.85%
2.19% + .66%
3.32%
3.4
Compare
●cceptability
2.1 9%
%
2.85% < 3.3.2%
P s Pu + PL i. 1=. s t~
See Table
B-3
See Para.
812.1.2 (7)
M.
,..
43
—
m&6w14
11 Jone 1957
EXAMPLE
Exampl*
Example
of cazcU2Mf0m
DOnbla Spcffiuti.=n
Z.imtt
Uakm
Deviation
Vari&i3fty
Different
B-4
AQ3. Value.
- 5tsadard
ior
Upper
and Luwer
Method
Specification
l.imitc
The minimum temparamre
of optra3foa for ● certiin dewice i. .pecified ● - 180- F.
The rnu5mumtempQ=a3ure
ii 209” F. A lot of 40 items in subrnkted for inmpm=3ion.
f.mp=ctic.n L=v=l Iv, normal imW=CCICQI.--I*
ACZL = 1% foI *= upper -d
~~
=
From
Tables A-Z and 23-3 it
2.5% for tha 10uer specification limit is to be used.
Suppcme the measurements
obtained
is ●.en that . sample of sise 5 ia required.
are aa follows:
197. , 188. , 184”. 205”, and ZOI. ; and compliuce
with the acccpt ability criteria i. 10 be determined.
Information
~
Vat..
Needed
Obtain. d
5
1
Sample
z
Sum of Mesmmements:
3
Sum of Squared
4
Correction
5
Corrected
b
Variance
(V):
7
Estimate
of Z.ot Stam&rd
k
Sample Me=
9
Upp=r Specification
Limit:
w
Z09
10
Lower
Limit:
L
,1s0”
11
CluaIity 3ndex:
Q“
lZ
OAity
(ZL = (X. fJ/.
13
Est. of z.&4 Percenf
14
Eat. of f..of Percent Def.
is
Total E.;.
lb
Mu.
Allowfahlc Pereent
Def. •bov~ U:
MU
17
Mu.
Allowable
Def. below
ML
la
Acceptability
Size:
n
975
ZX
Meaour.m.mta:
Factor
(CF):
190.435
XXZ
(SSh
Deviation
s:
P. rcent &f.
Percent
Criteria:
~e
lot meet. tbE
pL<MLsndp<LtL.
m
8.61
fi
97515
195
. (u-X)/o
DA
31OI4
71.5
XXln
Specification
190.435-190,125
310
lX~CF
SS/(n-1)
X
W75)215
190.125
(ZX)2/n
Sum of Squares
index:
Explanation
● hove
U:
~
belsw k.
PL
[209 -195) /6.s1
1.70
(195 -180) /n.81
2..19%
See
Table B-5
.64%
see
Table
2.85S
in Lot,: p . PU ● pL
&
1.s9
9.00%
(s) Comp-rc
PU
2.19%.
@) ;;;p;f
pL
.bf+
< 9.80%
(c) Compare
Wifh ML
p
Z.esn
c 9.80%
●cceptability
criteria.
●be
44
18(s),
3.3.?%
(b); ad
(c)are
B-S
2.19% + .6W
See
Table
B-3
See
T*1.
B-3
See Para.
Blz. z.z(7 )(a)
see Psra.
BIZ. Z.2(7)(bj
S.. Para.
BIZ..2.Z(7)IC)
•ati~fied;
i.-..
PU ~
.15
0.280
O.zo 4
.10
0.119
0.110
0.17 9
0.16 3
0.14 7
0.14 s
0.13 4
0. ;3 5
.06 5
15
Zo
Z5
30
35
40
50
75
I00
150
zoo
G
H
I
J
K
L
M
N
o
P
Q
All AQLandtablcvsluet
0..294
0.250
0.155
10
r
0.Z9 3
0.31 7
0.33 0
“.25
7.15
5.57
5.5B
5.20
3.70
3.72
3.45
Z,68
z.71
1.87
.40
x
0.945
I .00
1.50
15.00
14. IZ
14.ZO
14.75
15.13
15.87
a
10.00
6.5o
4.00
Z.50
—
;htem
insrmcticml
9.81
6.53
4.40
Z.nl
Z.04
1.4Z
0.63 7
9.86
6.57
4.43
z.#9
0.949
1.43
0.63 8
10.63
11.Z3
19.9Z
Zo.oz
ZO.66
21.11
ZZ.00
s.091 11.85[ 16.61 Iz2.86
16.651 Z2.91
‘2’61
“024
I “s’
8.10111.871
[0.32
4.69
3,07
2..?0
—
Z.05
1.53
I.oz
0.68 9
z5.61
12.99 “12..03 Z4.53
6.91
4.87
3.ZO
2,Z9
1.60
1.07
0.7.20
Z.49
1.71
0.789
AcceMabilitv Qualitv Levelt (
0.41 4
0.41 3
0.447
0.467
7.61
5.06
3.91
z,03
1.98
1.17
0.503
0.36 3
13.6311Z.571 17.511 ZL97
5.97
3.97
Z,86
Zoo
’47I
8.9Z
6,17
4.09
Z.95
18.94
2.o5
13.71
9.46
Z.11
6.56
‘0$0
Z1. S7
10.54
ZO.14
33.99
36.90
1.Z9
15.11
Zb.56
I““l 4
ZO.19
ZZ.8b
4.77
—.
4.31
‘Zzo
14.39
16.45
3.26
—
3.0s
Z,17
1.88
0.873
0.566
0.401
1.23
I ..?9
1,29
1.Z9
1.31
1.30
9.80
10.9Z
7.59
M
1.50
8.40
5.83
v
5.50
i~
~
29.45
S1and*rd Devittlon Method
5.35
3.5s
3.3Z
Z.14
1.31
v
1.53
ii-
I.00
t Inorm.1 in! ●ctim
1.z6
0,847
0.079
0.017
0.:51
0.581
0,846
0.544
0.818
0.716
0.5}5
0.388
0.413
0.380
0.165
0.503
M
.40
- i
+
0.422 1.o6
M
.2s
Acceptable ~
0.349
;
M
.15
●re inpercent defective.
O.zo 3
O.zzo
O.zze
0.Z50
0.275
0,264
o.2zn
0.13s
7
E
0.31Z
0.186
0.099
5
D
v
v
v
4
M
c
M
M
.10
3
.065
.04
B
Sample cite
code letter
B-3
Minter Tsble for Norm81 and Tightened tnapcction for Plms Blsed on Variability Unknown
(Double Specification Limit and F.rm2-Single
Specification Limit)
TABLE
-5
-.
I
I
A
a
3
3
4
s
D
E
F
G
0.365
0.365
0.380
I 0.228
0.ZZ8
O<Z50
0.280
Zo
Zo
Z5
30
M.
N
o
0.846
0.946
0..977
0.879
0.789
0.720
0.544
0.544
0.551
0.581
0.503
0.467
0.413
0.363
0,330
Jy:a,
Acceptab =
I .07
1.17
1.Z9
I,zv
1.Z9
1.29
1.11
1.30
1.30
v
1.06
—
1.6o
1.11
,1.9s
,?.00
2.05
“~2.a5
Z.11
“Z.17
Z,17
2,14
1.33
v
, -ii—
I
}.(
t..
.— —
Z..?9
—
Z.49
2.83
2.86
2.95
1.95
—
3.05
3.z6
3.26
3.5s
3.32
t
1.53
—
zi-
.40
..?5
5.20
4.87
3,20
—
3.86
5.97
6.17
6.17
6,56
7.Z9
1.Z9
8.40
9.80
10.9Z
7.59
1.59
7.59
7.59
3.4
3.45
3.91
3.97
4.09
—
4.09
4.31
4.77
4.71
5.15
5.83
S.50
!
--
M
1.50
10
=2
1.00
~
26.94
1.15
10.63
1s.13
21.11
-=l=t+t-
9.46 I 13.11 I 18.94 ] Z5.bl
4-4-4-=
14.39 I 20.19 I Z6.Sb I 33.99
16.45
18,06
first ounpllng PIU bdow ●rrow, that is, both #unple oize a. well m M value. “When cunplo sise equa2@or exceeds lot
e.e~y item in tha lot mumtb. in#pecled,
All AQL and t-ble values ●re {a percent defective.
_l-1-LK
L
0.716
0.349
i. fllfl
0.716
0.349
0.412
0.s03
2
0.
15
K
(
,
10
—
—
—
J
I
7
—
10
-j
1.
I
3
c
7
3
B
H
sample
81;0
ample cite
:xI* Iettsr
23A
Muter Table far Reduced fnvpecclm [m Plan. Bared
o Vsrlablllty thkn.awn
(Double SpecU{cation Limit -d Form 2- StttgteS !clfic atim Limit)
TABLE
,—
TSWO for Eotkmtlq
—
th~ &t
B-5
Pe, CCIIIDefective U#lnS Standard Devl.ilon
TABLE
M#thedl
.——
_
—. _____
1
Thblofor
E!tim.tlng
the tit
B-5-Conthed
Percent D*(ectlve U#lng S;mdard Devlaiion MQ~hod
TABLE
.- .
k!’
EZ
Table for Eotlmatlag tbo bt
B-5-Conllm.wd
Percent Deltctive Usln@ S1-d~?d
TABLE
.,,
Deviation Mathod
-.
,.
. ,.. .
I
i.
.
s
Tmblcfor Eotlmatln[tho
B-5-ContlnueU
lmt PcrcerIt D6fecllve Uc@Stmdard
TABLE
J
Deflation Method
k F
E
“
a
Tatdo for Eattnutlq
tho kt
B-5-Cadimed
Poreant Def*ctlwe UOlag Standard Derlatien ,Mothod
TABLE
.—.
-“
“.
E
. .—
ML-rm-414
11 J5fffa 1957
Pmrt m
C5TZMATZON Or PBOC=
AV~E
REDUCED
A35D TIONTU4CD
B13.
ESITbfATfON
AGE
OF
PR~
AVBR-
The ●verage percent defectiwa. b-cd
for origfnd
= group of let- submitted
inspection.
i. cafled the proceo● voragc.
Originaf imspectimi i. the firm im*pecfiOn Of
●bmttted
~ -~cb?
ety
of p~
from f3M
for ●cceptability a. dfotiaguf.kd
immpec;ie. of product wbfch ti. been remtbmifted after prior re&cftcm. 3%. pro-..
average .fuU be ..timated
from flm r..uft.
of in. peetic.. of samples dr.wmfmrn
a .peelot. for the purified number of precedfq
Of d=~=rdaiag
●.v9rity
FOR
and the ~rremmondtnsedmtid
1c4 +rcud
&fOcfiw
~
& p=,-respectively.
iw mad
from tfm fable.
Tbe ectinuted proceco ● vcrage ~ i* *
~ifhnwfic
meaaef fbe fad3vtdual e.ttrnmted tot perce.t defective- pu’ c.
6tmitarly.
the etiimated
procem ● ● =rage
$L it tbe arithmetic mean of the individual
● ctfaut9d 30t pareemt &facUwa
pL’8.
up.
~.=
AND ~TER3A
=PECTION
B 13.L2 Uoubl.
SpecW. UtImI
Limtc.
The
c &. ●timated Iof percent defecfive ●
.termIned from Table B-5 for the pfaim ba.ed
on the standard deviation method. The qtuf It, imdf... Qu d
0= sti
ba e-vu-f.
and
Tabfe B-5 i- enzered ●epar.tely wlfh ~
the eor--mpmdQL d
the -unP5e ●iae, d
fag ~ and PL us read f mm the t8ble. Th.
eatitrmt.d lot percent defecfive t. p = p .+
PL. The eatimuted
proc. ●S a=rage
p is se
● rifbm.fic
mea. of the individtuf c..tinuted
lot ~rcenf
defectivep’..
of iacp.cfian
d.rin~ the c..r.e
of . cmdr.cf in accordance
with ~rag,.ph
B14.3. AD, 1- sM1 b- iulb
pxocem.
cIuded only once in ●stinuffag
●wr.verqe.
The ..ti_t.
ef Uw prw..
=K= i. d=. i~t=d
by PU -be. eompufed wifh
re. pect to an upper ●pee fficatier. lisnit, by
PL w.h=. c,.mpyte,d w+fh rc.pecf
to ● lower
.P=c,f,.~t*I.mtt. md by p when computed
with re. peet to a double .pecfficatio. fimit.
.-.
D 13.Z.3 S
cfal Cam.
It the qtulity index
OIJ or C3L< a negative ‘numb=.. the. Table
B-5 i. entered bvdimrenardins
the negative
.ip.
f-i---, ‘i. tbi.- a.,
‘h. c.. fi&ated
lc.t percent de fecfive above ftm uppa r limit
or below fbe lo=.
Zimit i. obtafned br mzbtractiq
the PCrcenuge
found i m the” table
from 100%.7
B 1~.1 Ahn.rmA
R.muft..
l%. r.. ult. of
inspection ef product
_ufaetured
under
. ..”diti...
mot” typfcd
of ..IuI
p.odmeficm
pre.3u15 be exeluded frmn the ● .tinnted
ce.. avera~e.
.BIL.
B 13.2
(hnputmtion of the Est5nuted
%0.
. estimated procem- ● =rmean of fhe .atfmafed
atm
t. t e ● r thmetic
‘~
‘h
l~t percent defective.
computed from b
.amptia~ iit.p. ction *..uft.
d the pxecedtms
ten (10) lcIt. .M a. may be othetwf. e decig.
nated. b order to e.tirnate
tbe lot percent
dal.etive,
tba quality Ucea
QU tiler
QL
shaff be cmn~ted
for ● ub lot. Tbom ~e:
C3U = (u-X)/c
md QL= (X. L)/a. @em pus.
Sr*pb 3511.2.)
NORMAL
TIGHTENED,
DUCED IkBP33CTfON
Thts S-*rd
pfam for normal,
iMpactiOn.
B 14.2 -as
Of hmcuon.
m-
esti5fah*d
campfiag
tightened, and reduced
31WWetfon
Mrnuz
AND
D9rtm, tba c0ur9*
●haff
be
tirncttan
fisbtmnd er ‘r.duc8d LrJsp.cficm 1. ~
mrquir9d b •ccor~
wttb pr.sr.~
B 14.3
d
n14.4.
B14.3
Tishtaa8d 311spectioa. TI~btarnd h.
●poetfon ●balf b- fmtitmad whn tha c cti wmpidmd from tfm
matid pro- ●a .nragm
When Form I -Sfngl.
Spectff~tfon
~
1. rm.d for tba acmptabfflty
criterion.
tbe “octl mafe of 101percextl &feetfve pu.or pL 10 mot obta.lmed;fmordertoewtimate the proc.am ● v8r ~s=. it i* n=c=a~=rr to complete paragrapba
B6.2 uuf B6.3 of Form L
7FOraXUnP18. U ~
. -.50-0
●SMPZO SCM SO,PU = 100% - 30.93% = 69.071b,
= 1.60. us~
P1. 9 ~-n
-P*
69.07s + S.sk
. 74*.
52
. ..-
I
XIL-STD414
11 June 19S7
II
I
preceding ten (101 108. (Ot ..&
04h*r rlwn bar of lat. de. i~ted)
1. =crnrduue
with
Kr=zr&pb
BIXZ
i- srestcr
than the AQL,
-d
when more than A c=rta~ number T of
of flx percent
dethem lots have e.timafes
fective
sxceediq
the AQL.
The T vdttbs
● re given in Table B-6 far the procea.
.verage
computed from 5. 10. Or 15 Iots.e
NormmI inspection shall he reinstated if the
● ver-ge
of lots und=r
..tinut.d
preces.
tightened i..prction
is cqud to or 1..8 tkmn
the AQL.
B 14.4 Reduced
Im.pectiom.
Reduced ilI.pection may be inmitumd prc.vid. d that ● ll
of the following conditionare ●atiofied:
I:
I
..
b
estimated lot percent defective is eqtnt
to =ero for a ●pedfied number of conmeeutiwe tot, (gee Table B-?).
●teady
Cad6tfon
c.
PrOdnctiM
is
●t
a
rata.
Normal impaction
●hall he r.in.tated
if any
oaac of the following condition. occ. ra undc r
reduced inspection.
Condition
● .eragc
D.
A lot i. rejected.
Condition E. TM emtimated prc.cem●
is greater tham tbe AQL.
Condition
F.
irreguI~r or delayed.
Production
become.
Condition A. The preceding ten [10)
lot. (or .uch other mmnber cd lm. de. igruted)
and nom
have been under nornul ia.peclio.
has been rejected.
Qther condition.
.. .
Condition
G.
~?
~brrmt
that normal
inspection .hould
be reinstated.
Condition B. The e ctimated percent
defective for each of theme preceding lot. io
1=.. Uthe appUcable
lower limit shown
in Table B-7; or km =ertak
.arnplirIg plan. ,
B 14.5 Sampling P18m. 1.. Tightened Or Reduced lmpecthm.
Sunplu-ig plan. ior tightene d and reduced in.pecticm .re provibd
in
Section B, Part.
1 and U.
MIfA3TD-414
11 Jwm 1SS7
Cuve]
Z.5
10.0 15.0
4
6
8
4
:
9
9
1:
4
4
4
1
5
‘0
1:
4
1
10
4
t49mbar
Of bta
4
i5
5
10
15
5
10
1:
I
1:
15
1;
4
4
4
1:
1!
1:
5
10
I
,
..
L
M
4
6
a
4
6.
999910
4
6
9
44
/
7
:
mm
● re m
9mp31a#
4
4
.:
11
1:
1:
4
a
11
4
a
11
4
a
11
5
4
a
11
4
a
11
5
:
11
4
8
11
4
8
11
4
5
1:
4
a
11
4
e
11
4
8
11
5
4
8
11
4
8
11
5
:
11
5
pluu
prwuad
la thio Staa&rd
5
1s
10
15
10
15
10
15
10
15
10
15
4
8
11
4
4
1:
1:
4
8
11
4
8
11
4
a
11
5
4
s
11
4
8
11
4
8
11
5
-4
a
11
5
far Unse code lctirs
15
10
io
4- — 4-a
“8
11
11
I 10 I
.
15
10
15
10
15
10
15
dAO1.wshm9.
M
..-.
—-
unmlTP514
11 Jrmd 19s7
TAB=
vdtms
of T [or
sUmdard D8dmnua U8fbd
B-6<0nfif=d
TiKhtaud
Impaction
Th. top figure
ia ..ch
ilock refers
t. fbe preced~g
5 10C~. the ~ddfe
preceding
10 let. and the boftom fipre
to the preceding
15 let-.
fi-re
~ ‘e
Ti@encd
ia.pection
i. required
whom tbe numb. r of lnta wltb e~tfmates of percent
5. 10. Or 15 Lets is srester tbmn th= xiveri wdue
defective ●bove tbm AQL from the precediq
of T in lhe table. ad tbe pro.en~ average from them. 10t@ .=.=.da
tba AQf-.
N1 estirnatew
-.
of the tot percent
defective
are c.btained f rem
T8ble
B-5.
—
.002
.03.3
,0s0
.006
.039
.077
.012
.000
.010
.029
.000
.004
.013
.001
.002
.009
,020
,03.1 .043
,002
H
1
.027
,011
.021
.0s2
.050
.089
.113
.306
.40
.054
.087
.146
.169
.2s
.083
.214
.40
,037
.146
.248
.014
,071
.133
.023
.04.s
,2.3s
.396
.017
.111
.?.1s
.005
,040
.10!!
.011
.143
.315
.002
.057
.151
.000
.018
.062
.231
.550
.65
.185
.509
.65
,121
.445
.65
.041
.310
.6.?6
.431
.909
1.00
.36o
..963
I .00
.266
.78s
too
.136
,643
1.00
.003
.317
.81
[11]..
[14]**
.000
.101
.369
[25]**
[45]**
[31]**
●
1,14
2.40
2,50
1.33
2.48
2,50
1.47
Z.50
A
.653
1.39
1.50
.750
1.44
1.50
-..
.84
2,23
2.50
.521
1.31
1.50
.123
1.14
1.s0
.>06
1.80
2.50
tool
I
1.98
4,81
6.50
,A
+
7.74
10.00
A
4.59
6.50
1
Z.49
4.00
A
Z.66
4.00
A
1
10.00
h
A
lz.69
15.00
-+- A
lZ.4>
15.00
&
12.07
15,00
A
7.40
10.00
4.29
6.5o
1
iO.47
15,00
4
Z.24
4.00
,&
i
5.19
10.00
11.51
15.00
L
6.50
&
9.09
15.00
&
6.06
15.00
&
.77
15.00
&
( 9]**
6,06
I0.00
A
=
4.24
10.00
i
.74
9.96
10.00
0.00
4.40
6.S0
1.38
5.96
6.50
[ 7]0.
[IO]**
[lZ]**
1
I
5
s
5
5
5
5
5
5
10
10
10
10
10
10
—
10
10
15
15
15
15
Is
15
15
15
DevIa440n M!thod
I“
::
.
$
-1[IO]**
Slmdtrd
),s0
6.50
&
1.64
3.94
4.00
1.05
3.56
4.00
.11
z.65
4.00
.00
.88
2.49
.00
,10
.es
.044
.74
1.50
[ 9]**
[15]**
[13]*O
[22]**
[ZB]**
T5-
[18]*.
[II]**
Acceptable Ouili!y Level.
I .65 [ 1.0 [ 1,5 I 2,5
●Th=i* mrc no mmpliag plain provided Anth!o Standard for these code Ieltero and AOL vduei.
J
.005
.000
.006
.02s
.000
.003.
,010
v
,000
.003
G
.029
.000
.016
.123
.000
,000
.002
.001
?
●
●
●
F
[18]**
[25]**
●
*
●
●
E
*
●
*
●
●
D
●
●
●
c
●
●
*
●
.40
●
.25
*
I
●
*
.063 1 .10 I .15
*
I
.04
23
sample tll*
code letter
B-7
Llmlt# 01 &#tim~ttd Lut Percent Defective for Reduced Za.pection
TABLE
—.
,:
.008
.033
.058
.011
.038
.ObJ
.016
.045
.065
.026
.054
,065
.032
.058
,065
.039
.064
.065
.044
.065
A
.004
.017
.012
.005
.020
.035
.008
.025
.04
.014
.0)1
.04
.01s
.014
.04
.023
.038
.04
.025
.04
&
K
L
M
N
0
P
Q
.069
.10
&
.064
.10
b
.0s3
.091
.10
.044
.081
.10
.030
.075
.10
.022
.065
.10
.017
.059
.091
.10
B-’f-ConUnued
.296
.40
A
.312
.40
b
.1!38
.25
A
.261
.40
b
.235
.389
.40
.187
.36{
.40
.157
.343
,40
.137
.3Z.9
.40
.40
.177
.25
1
.153
.245
.25
.134
.2)6
.25
.102
.215
.25
.082
.199
.25
.069
.186
.25
.25
.525
.65
A
.501
.65
A
.453
.65 ‘
A
.414
.65
A
.345
.621
.65
.300
.596
.65
.210
.577
..65
.8.?1
1.47
1.50
1,276
1.50
8
b
A
.830
I .00
&
1.Z31
1.50
1.[49
1.50
,
1.082
1.50
1
.959
1.50
b
.799
1.00
.733
1.00
k
.6.91
1.00
A
,507
.989
1.00
.5, ?5 .876
.961
1.49
1.00
1.50
,483
.940
1.00
A
~.59
4.00
1
2.19
2.50
i
3.52
4.00
3.36
4.00
,
3.24
4.00
A
3.01
4.00
A
2.88
4.00
A
4.00
h
2.19
4.0
&
2.13
2.50
,?.01
,?.50
,
1.92
2.50
k
1.76
2.50
1
1.64
2.50
6
1.57
2.50
L
Levels
Acceptable @di}y
.65
2.5
1,0
! 1,5
●xe*pt three in the brackets, 8re in percent defectlvo.
.108
.15
i
.101
.1$
A
.085
.14J
.15
.0?2
.136
.1s
.05?.
.120
.15
.040
.108
.15
.03.?
,099
.15
.1s
5.96
6,50
i
9. N.
10.00
1
&
9:22
Io.oo
5.87
6.50
a
8.98
10.00
&
8.01
10.00
&
8.50
10.00
&
a.z9
I 0.00
h
8.1s
10.00
1
10.0
5.67
6.50
,
S.!iz
6.50
A
5.21
6,50
&
5.08
6,50
4
4,96
6.5b
a
6.5
10
15
1$
15
15
Is
15
14.19
15.00
A
10
10
10
10
10
10
15
5
5
5
5
5
5
5
Numha r
of &to
A
14.07
1s.00
11.00
15.00
L
13.60
15.00
&
13.2s
1S.oo
&
13.03
15.00
A
12.08
15,00
&
15.0
N1
●aih’natem of the lot parcent defectIv* are Obtained from Table B-5.
●ttlrmtd lot P rcsnt defcctivc!from the preccdins S, 10, or 1S leto it
Reduced 6nspectlea IIWY ba Sr@itoted when wary
bdow tha flpr* civm tn the tabl*; rcducod inspection for sampling PIMC mmk.d (**) la fho tlblc raquireo that tha ●atlmtiod
lot po?cent dcfoctlvo 10 eqttafto saro for the number of conteeulive lots Indicated In bracketo. la sddltlon, ●ll other cendltlont
for roduead Inspection, in Pmt 223of Section B. mutt be ostitfi.d.
s
~g
r?
“
~ F
-—___—_
Standard DevlaIkIn M,t~d
—.-
VAf3methe flrot figura In dlraetZom o{ ●rrow and corresponding number of Iotm. fa ●ach block tha top (Igure rofcrc to the
prccedlos 5,10ts, the m5dd2* figure to tho preceding 10”lott, snd the bottom figure to the prteedlng 15 loto.
Ml AQL sad t~blo values,
.065
.04
Sunple OIZR
code letter
TABLE
,.
Limlto of Cctimalcd Lx P~rcetN Delectl}e for Reduced hwpectim
.——
,._
I
m
m
.Ibl
.160
.1s0
.151
100
150
200
0
P
Q
.163
.185
.183
—
.175
.175
,170
.lb8
.191
,191
,197
.la7
.179
.172
.199
.189
,181
.174
,ZOJ
.194
.184
.207
—.
.190
—
.178
.Z08
.Zlo
.198
.IE.5
.189
.183
.201
.182
.192
,Zlz
.203
.193
.181
,185
.z16
.z06
.21b
.215
;,Z03
.Z20
.ZZJ
,ZZ7
,232
.ZJZ
.236
.238
.Z42
.248
.Zbl
.Z80
.108
Z06
.208
.Zll
.Z14
‘.Z19
.Zzo
,22J
.Zzs
.ZZ9
.,215
.248
.23s
,Zzz
.Zb6
,Z94
.319
I .00
L.cvelo (in
.65
,Z53
T
-.
leOudity
.211
.2Z4
.24z
—
z
—
tepll
.197
.202
.214
.15
.190
.19s
.Io
..?Z8
.Z31
—
.Z30
.Z35
.241
.245
“,245
..?49
.251
.255
.262
.Zlb
.Z9S
.Jz)
,)53
1.50
—
ercec
.318
.346
.374
.Z48
.2S3
—
.Z49
.Z5S
,Zbl
.Z66
.?bb
.?70
,27)
.Z17
,Z84
.Z98
—
.
.Zb9
.z71
.Z7b
.Z79
.Z84
.290
.Z91
.Z95
,291
.302
.309
.5Z4
.345
.)73.
,399
30Z
. 30Z
.307
.310
.317
.3Z3
.323
.320
.331
.3)6
.344
.359
,M31
.408
.4JZ
.338
.341
.345
.348
.156
.363
.364
.369.
.372
.371
,386
.403
.4Z5
.45Z
.47Z
.386
)81
.393
.399
.408
.416
.416
.4Z3
.4z6
.43Z
.442
.4b0
.489
.s11
.S28
NOTE: Therm Is s corr*opondlng acccptablllty constud In Tikle 6.1 for ●achvdue
tbmaccc~tabil!ty commnt of Table B-Z In Table B-1 and u,e the corresponding vahe of ~.
of F.
For reduced lnopectlen. find
The MSD msy b, obtalmdby muh’iplylmg the factor F by the diNereace balwoen the uppr spaclflc~tlcm Ilmil U and lower
spee5fictiian limit L
Tha formula lt MSD = F{ U-L).
The MSD s+met m I gulda for the magnitud- of the ●oiimatc of let
otaad~rd deviation whtnu81a[ plmc for th* double specification Ilmh came, bm.td en the eatlmat. of 108ctandard davlatlea of
umbown v~riability.
The estimua of lot otaadard deviation, if it Ic IF-o Ihm the MSD, helps 10 imure, but doe- not uuar MIee,
Ipt acceptability.
L
.lb6
,lb2
75
N
.1613
.112
.166
M
50
40
L
.176
.Ilb
.170
J5
K
.119
.169
.173
30
J
.180
I
.114
H
Z5
15
G
.18J
10
F
.177
7
E
Zo
5
D
.0b5
.I.521
4
c
.04
.18?.
3
Oise
Sample
34
code Imttr
sample tiaa ‘
Mx~14
11 Juno 10S7
APP@Du
B
~efinitkons
,
5!!!!9!
Red
m
x
Sample
X bsr
.
●ix.
~P1.
M==.
● .Ixl.qlc lot.
for
● .i=~le
Arithmetic
lot.
mean Of .mup3m me.surememm
i~~m
E.tinute
cd lot ctandmrd deviation- Standard deviation of ●un ple measurement
[mm a ●insle lot. (See &xmpIe* iaSect40n
33.)
u
Upp=r
●pecffic~tiOm limit.
L
Lower
●pecificalfiOn limit.
k
The
●cceptability
eon. tant @ven
i~ Table.
B- 1 and B-2.
t
Qu
Q ●ub U
Quality
index for u..
with Table
I
I
QL
Q ●ub L
Ouality
index for u..
with Treble B-5.
!
%
p sub U
Sample ● .tirnale
Table B- 1..
of the lot percent defece
p s“b L
Sampl. estimate
Table B-S.
of the 101 percent
‘L
I
I
,,
Definition
P
Total .ampl.
e.timate
M
Maximum ● llowable
~iven in Table.
B-3
B-5.
..
defective
of the lot percent
percent defective
and B-4.
defective
for
above
U from
below
L from
P = PU + P~
.-pie
eatinutea
%
M sub U
Mtimum
allowmblc Pcrceat defective ● bove U given
B-3 and B-4.
(For uoe when differeot AOL valuea
L are specified. ]
ML
M sub L
Maximum Alowable percexaf dcfecfive below L given in TableB-3 and B-4.
(For we when differenl AQL vtiuea for U &
L ● re #pacified. )
P
%
Pf,
p bar
Bamp3e ● intimate of the proceem
estinuted procea ● ●ve rage.
percemf defectivw
p bar
sub U
Tbe estimated proce. m8varage far u
p b-r
●ub L
The eslimatad
procenm sv.rqe
i. Table.
for U and
i.e.,
the
upper specification
limit.
●pacification
Mmft.
for ● 10W* r
T
The maximum number of eattnnted
prece. s sveragam wbkb
BlverI in Table
B-6.
(For u.e in determay ● xceed tb#AQL
mining ●pplication O! ti~hteaed inspection. )
F
A lactez ua.d in d.te rmim.i~ the ~um
(hLSD). The F valu=s are given In Table
>
Greater
<
ham
1’
i
I
I
.x
than
than
sum of
Ml
Standard
B-8.
Deviation
MZL-STD-414
11 JufM2 19s9
SEC’ITON
VARIABILITY
I
UNSNOW7J-3LMJGE
METBOD
Part 1
sZNG LE SPECIFICATION
Cl.
I
I
c
SASIPLUJG
PLAN
FOR
SPECIP3CATZON
LDdIT
UT
CZ.2.2 Accep-ility
Comstit.
The acceptability COa.t-t
k. correspo~w
tithe sunple mi. e mentioned in paragraph
CZ. Z. 1. is
indicated in the column of the master t.ble
corre. poading m the applicable AQL value.
Table C-1 i. enmred lrom the 10P lo. nc.r rn.1
impection
●md from
th. bottom for
tightened inspection. Sampling plans for reduced inspection a*e provided in Treble C-Z.
SINGLE
‘This part d the SUmZ. rd describes
the
prO.y@ur=~
fOr. u*e wilh PlaM for s Si=ule
rep..c1ficati0n knit
whcri variability
O{ cbe
lot with rempecl 10 the qtmlily cbarseteri. tic M u.knowm and the ZWC nmtlmd i. used.
The -cceptability
criteric.ti i# give= in lwo
equivalent form..
Th. mc arc identified
as
Fo,rm 1 d
Form Z.
C3.
use of SUnpliag Plan..
To deterC1.1
mine whether
the. 10C meet,
tbe ACCCptability criterion
wJth respect to a particu.
lar quality characteristic
•~d AQL vaZue.
● hall be treed
the .“pplic~ble ●amplih~ PIin .ccordance
with the provisions
of Section A, General
Demcripciou
of Sampling
pl.m.. b
the... in thi. part of the Sc.ndard.
C3. 1 AccepUbiZity
Criterion.
The degree
of coaormance
of a quazmy characteristic
:imit
with re8pect to ● #ingle specification
●haZl be judged by the quantity (u-X)/R
or
{X- f.)lsi.
:/::1
Cl.2
Drawing
of Sarnp3e..
AN .armples
WT-BY-L&fT
ACCEPTA=ITY
PROZ
CEDURES
WffEN
FORM 1 IS USED
sbdl
-i:
‘iw%”%(ilwz
depending on whether the specification
is = upper or ● lower lirnis. where
be draw. m accordance wltb paragr@iA7.2.
Iimi!
Cl.3
Determination
of Sample
Size Code
Letter.
T he sample
sme cod e letter •hd~
=ected
from Table A-2 in ● ccordance
with par~raph
A7. 1.
U
L
X
~
CZ
3n this Standaqd. K ia the average range of
,.bKrmip
ranges.
32ach d die subSro.p.
consists of 5 mea*u*emenl..
except for tbOa*
plans with ●unple ●ke 3, 4, or 7 in which
● im
19 fh
sum
as i.h
u**
fbe ●kgroup
sanw3e
sise.
Zm wanpufiq
K
338= Ord=r
Of
c=u*t b=
Ihc sample meam=rem=iits
u .-de
rer.-iimd.
Smkgrwpa
af cnumcrmive nn.. urements must ba formed d
the range of
.xh
.ubgroup obtalwd.
X is the ●weraae of
nngea.
tbe individnaZ ●bgroup
SELECT3NG
THE
wHEN FORM
1 ls
SAMPLINO
USED
PLAN
CZ.1
Master
●mplmfi
tal
Samplin~ Tmblec. The matter
C* co r DlaM b- ed on varia blIity u---n
for ~ single ●peef.fieation
Tables
limit wbenuakg
& raag. unfkodaro
C-1 ●nd C-Z.
Tabia
C-1
b .u..d
for
normal ● nd ti~htened inspecfi.m uuf Table C-2
for
reduced
izupoction.
CZ.Z Obtining
the SunptinS
P3an.
The
● X ● -d
.unp3im~ plain ccmsastmO{ . .unple
f
● m ● sociated
accepIAbUiv
Ctaut.
The
.unplimg
plain ia obtain.d
from
Maater
Table C-1 or C-Z.
size
CZ. Z.1 Sam le Si=e. Tbe sample
.homa ,n
table CC4rrm#p0~
~ 1 e nla’ter
.1== e-de Iater.
each ●mple
im the
is fhe
is the
i. the
upper specification
limit.
lower specification
IimIt.
sample mean, and
●verage range of the #ample.
C3. 3 AeceptsbIlltY
Crite Finn. compare
the
q.mtity (u - m
(X- L1
‘Kwithtbe
●bilitv cor.8cant LOrZf (u-XI/X
or (X- “C’%%
L)
equal “to or Creater than k. the lot meats tbe
●.ccptab13icy c rito rloix
u (u-X)/R
or
(X- 2.)1X ia less tbm k or m.’afiva. tbea the
lot deem not met the .c..ptability
e ritoricm.
a it
tO
1Se. Appendix C for definitions of afl cymbolo us id b tbe ●ampllng
uak90wm- raaga mmbod.
%we f+ample
C-1 f.r ● cmIIp3eto ●xunple of tbi. procedure.
al
._ . ..-
pl~o
bac.d
on varIablltty
I
3A1L-m-414
11 June 1957
CL
f3uMM~Y
FOR
OP3IRATION
SNAP LANG PLAN WHEN FORM
USED
8tepm umun.riz.
Th$ following
cedure. fn be followed:
OF
1 LS
c6. 1 AcceptabUity Criteric.n.
The degree
of conformance
of ● qutilty characteristic
with respeet CC.● ●imgle .pecificstimi
limit
.hafl be judged by tbc p.r. mit of notlccmfomnirt~ p.od. ct out. ide the upper er lower
specific aticm limit. The percentage of rmnconforming
product i. estimated by emtering
Table C-5 with the quality iadex and the
#ample ●i*e.
the pro-
(1) Determine
the ●ample .i, c cede letter from Table A-Z byu. iq the 101.ize and
the in. pecti.an level.
(2) Obtain plan from Mater
or C-Z by .elecfin~
the sample
the acceptability
ccm.taat k.
Table
C-1
●ize n and
(3) select *1 random the .;rnpl.
of m
“nit. from the lot: in. pect .nd record the
meamurernenx of the quality charactari.
tic
for ●=ch uait of the sample.
(4) Compute the .;rnple mean X and the
range of the .arnple ~, .md ● l.o
compute the quantity (u- X)IR for am upper
●pe. ificatiomlirnit V or thequamtity (X- L)/R
for . lower specification
limit L.
●vera~e
SELECTING
THE SAMPLING
WHEN FOR64 2 3S USED
c6. ?. Computation
c.f Quality
Index.
The
quality izidex Or, . (U- ZC)CIR hall be com puted “if the sp%cificaticm limit i. an IIppcr
limit U, O= QL = (X- L)c/K if it is a lower
limit L. Tbe q“amitie.,
X ● nd R, ● re the
sample mean and ●verage ran~e of tbe sample,
respectively.
The compmatioa of K i.
●xplairted in paragraph C3.2. The facbar c
is provided in Master Tabl=s
C- 3 an& C-4
corresponding
to the .unple size code letter.
Defective in bt.
C6.3 fhtimate of Percent
The quditv of a 1.s1 hall
be expre.. ed by
PU. the =.timated
percent de fe~tive in the
limit, or
lot ● bov= the upper specification
p.r. =ntd=fectiv= beloby PL. the ● .ti-@d
thc lower ●pccificatiort lirnii. The ●.tima~ed
Percent de f=cti~.
PU O, PL i. mbt~im=d by
.mteri+j Table C-5 with Qu or QL .nd the
●pp. Opri~t= ●AMPlt ●i*e.
(u-X)/R
c.r (X. L)/R
i. equal to or greater thas k, the lot meet.
criteriow
if (u. X)/11 or
the ●cceptability
(X- L)llf i. I.*9 than k or negative, then the
lot doe. not meet the ●cceptability criterion.
(5) ff th= quantity
C5.
CO. f.CfT-BY-LOT
ACCEPTABI w
P%
CEDU3432S WNEN
FOR3A 2 3S USED
PLAN
Ma#ler Samplinj? Table..
The ma. ter
for plana ba. ed o= varisbil ity unka&n
for a single specification
litit
when u.iq
the rang. method ar= Taidec C- 3
● nd C-4 of Part IL
Table C-3 is used for
nc.n’nal and tightened inspection ●nd Table
C-4 for reduced inmpectimi.
C5.1
C6.4 Acceptability
Criterion.
Compare the
e.timated 1m percent defective PU or pL with
the m~imutn
aZlew.hle
perceM
defective
M. U .pU or pL is equml to or le.. Uun M.
if
the lot meet. the’ ●cceptmbitity criterion,
pu or pL is grekter than M or U QU Or QL
i~ negative. then the lot does not meet the
acceptability
criterion.
●amplmx table.
the Sampltng
C5. Z Obtaininz
Pllrl.
Th ●
sampling ptan con. i.t~ of m .UIWI]e .ize and
an aooo~ik.d
maximum
a310w&le percent
ptam ic obtdncd
def ●ctive . The ●amplfq
from Ma.t=r Table C-3 or c-4.
Cl.
SUMMARY OF OPERATTON
OF SAMPLING PLAN WHEN FOR3d 2 IS USED
Tha fellowinK
,tep~
ptwedures
to be fallowed:
●un’unar 3s9
the
(1) Demwime
ihe -ample .ise code lel from Table A-S ~u~inn
the lot dae and
the iriapecttosi Iov@l.
ter
C5. Z.Z Maxd8mtm AIIc.wable Pereent Defective. The madrnwn
allowable percemt de=ive
M for s-pie
eotim.tes corres~ndtied
in
ing 10 tbe sample ●iz= me~tie
paragraph C5.Z.1 i. indicated tn tbe COIUMII
Of the rnmms.r tabte correa pending to the
applicable AfZL value. Table C-3 ii entered
from lb. top f-r ~orrnal iaapectian mad from
the botfom for ti~htened in. pecticm. SunP~
Plaru for reduced inspecticm are pr.a vided in Table C-4.
3See 3cxAmple c-z
tar a complete example
(Z) Obtmi. plan from t.mater Iable C-3
or C-4 by .electirg
the -ample sk= n. the
factor c, and tbe maximum ●llowable pw. ceat defective M.
(3) Select ●t random the sample of n
unit. {ram the 10C inopect and record the
meamm.mem
al the quazity characteristic
on each nut; of the 8sMple.
of thim pru..dur..
62
MI L-sin-414
11 June 1057
(4) timpute the ●unple me-m X 4
av.ra~c
raaSe of the ●ample K.
(7) Uthe ● .timaled
lot pcrcentdelective
PU or PL i. eqtml to or Ie*. thaa the md-
the
mum azlowable
percent
defective
M. 3he lot
meets the acceptability
criterion;
it PU or
pL img.eater than M or U Ou or O’i.%=_~
-i”..
them the lot doe. W1 meet the ● ccept●biliw criterion.
the
q.=lity
“ index
QU =
(5) Comp@=
(U-X)c/K
M the upper speckfieation limit U
iripecified,
or QL = (X- L)CIK i3 the lower
.pccificatirm
limit L ia .pecif ied.
10s m.rc.r..
161Decermirie
the ● .limaled
.-, ———
defective PU or pi. from Table C- 5.-
~PLJl
Example
Single
Limit-Form
and compliance
Line
—
Unknown - Range Method
1
Sample
Site:
.?
Sum 01 Measurements:
3
Sample
627. 650, (R, = 658 - 619 = 39)
538, 650, (Rz = 673 - 638 = 15)
●ccept ability criterion
with the
3nf. rrn.ti..
619,
641,
Needed
n
Mean X:
Obtained
EXP1anatiom
10
I X
647o
XXI.
5
Speckfieatio.
6
The qu~tl~
7
Accep3AZZity
Camsmt:
8
Acceptability
with k
Criterion
The lot doe.
i. to be determined.
Value
4
=
1
The lower .pecifie.tion
limit for electrical
r.miataace of ● certtim ●lectricti comInspection
ponent is 620 ohm..
A lot of 100 item. is submitted for inspection.
Level IV, normal inspection,
tith AOL = .4% i. to be used.
From Tablet A-2 ud
C- 1 it i. ..en that a sample
of size 10 i. required.
Suppose that value. of the’
sample resistances
in the order reading from left to right ● re . . follow-:
643. 651,
67o, 673,
.
of Ca3culati0n*
Specification
Variability
EXarnple
c-1
Limit (LOwer~
L
647
6470/10
37
(39+35)/2
620
(X- L)/It
not meet tbe
.7s0
k
&-
.811
Compmm (X- L)/l!
●cceptability
(647-620)/37
criterion.
.710<
.811
.irIce (X- k.)f~
● &e
Tabla’ C-1
ParaLc3.3
is 1c99 than k.
limit U im give., then compute tb. quantity (u-Xl/X
U ● .imK1e .PP=r .Pecificati..
line 6 ● ad cmmpar= it with k the lot meet. the acceptabUitY criteriom, if (U- rnf~
equal 10 Or greater [ham k.
.-—
kn
i-
I
MIL-ST13-414
11 June 1957
EXAMPLS
c-2
12xample 01 Calculation.
Single Specification
U.knowmi - Rang.
Variability
Ex. mple
Limit-Form
Z
Method
comA lo.ver specification
limit for electrical
re. i.tan.e of ● certain electrical
Zaspection
ponent i. 620 duns.
A 10I of 100 item. i. submitl.d
for inspection.
Level lV. normal in. Dection. wish AQL - .4% i. m be used.
From Table. A-2 mad
Suppo. e lh. v*Iu=. Of the
C- 1 is is seen thal ; sunple
of ●izc 10 i. required.
sample reaiatance.
in the order readimg from left m. right are as follows:
643. 651, 619. 627. 6S8. (R, = 658 - 619 = 39)
670. 673. 641. 638, 650. (R2 = 673 - 638 = 35)
●nd compliance
Line
—
with the acceptability
Inlorrnati.n
Sample
z
Sum of Measurememtm:
3
sample
4
Average
5
Factor
6
Sp=. ific*tiO.
7
Q.a2ity
Zndex
8
‘ct.
bt
9
Max.
10
M,..
Obtained
6470
IX
ZXJ.
Range ~:
XRlne.
of subgroup.
647
6470110
37
(39.3S)12
2.405
c
‘f
Limit
Acceptability
(~we.
):
“f.’
PL
PerceIIt
De f.:
Criterion:
1.76
M
Compare
mat meet the acceptability
See Table
C-?
620
L
C3L = IX- L)CIX
‘ercent
Allowable
The jot doe.
-E:
Value
Needed
m
x:
i. 10 be determined.
10
I
Size:
criterioo
pL with M
criterion.
2.54S
See Table
C-5
1.14%
See Table
C-3
See Para.
C6.4
2.54%>
■ince pL
(647-620)2.405/37
1.14%
is gr=ate.
than M.
U . .ingl.
upper specification
limit u i. Rive., th=. compute the quaii3y frufax QU ~
fU-X)c/3!
in line 7 d
obtain the eotimate of lot percent defe.tive
PU. -mpr=
PU
U p“ ia ●qu~ io or i’z*. ~hn M.
with M: the let meet. the ●cceptability criterion,
M
‘i
[
.996
.932
.87o
I .10
.15
Impec m)
—
med
When sunplt
10,0[
.5s3
.46z
—
15.00
4
x
.364
1
#its equa.loor ●xceed@ let
+6.50
.728
—
4.00
.552
.644
--1-.646
.7z6
.309
—
2.90
.3SB
.449
—
.460
,539
,631
.111
—
.791
—
.807
.34s
.441
.530
.701
.780
.336
,621
.!21
.327
.421
—
.43Z
.510
+.610
.321
.~lj
,310
.105
.216
..?5?.
.189
.184
.116
.178
.s15
.689
.406
.494
.581
.598
.403
—
.490
.577
.360
.~41
.266
.398
.452
.424
.336
,2?2
.Z?b
—
.296
T
15,00
RmIrn Method
.484
.371
.516
.307
.405
.)52
.364
.401
.s03
.654
—
.519
.465
.431
.450
. 50?,
.591
S* well as k value.
,40
.65
1.00
1.50
I
I
Accepmble Oualify Levels (tlgl
.25
AU AC2Lv~ueo ●re in gercent defeciivo.
,“::
tir,t &amplln$ plan below ●rrew, that {s, both sample -lie
a ●, 9wory Item 2a tha lot mnmtbn ln#pected.
Q
P
.063
0’
I
24
1,,06
M
1.)2
.754
—
.1b8
L
I
.746
K
1,16
.616
—
.730
—
,734
1
1,21
.668
.7,?3
H
1.21
.658
.684
G
230
.647
.65o
F
J
.610
.SZ5
E
.498
.565
D
.!325
—
.587
Y-
2.50
-
.s’38
—
v
k
K
ml in pectiml
c
B
sample t 1se
code letter
C-1
Master Ttble far Normat and Tightened Zn$ptctlon for Plans Based an V~riabIllty unknown
(Single Specification Llmlt - rarm I I
TABLE
4s
i$!
#2
. .. ——.
_.
i
+
Q
P
I
1.16
1.17
60
8s
1.11
I.IJ
1.11
1,07
1.08
1.06
I ,0.?
E
1.02
1.o6
1.10
I.oz
1.00
.964
,959
,658
.6.99
.701
.734
—
.768
.7E0
—
.826
.8J9
—
.E85
.899
,962
.E4e
.94.9
.900
.
.791
—
.654
.130
.707
.E43
.904
I .424
1,.3s2
,401
k
4.00
.484
.404
,452
.621
.610
.5s1
.371
.5)0
.521
.494
.490
M
,s11
.s71
5J6
.441
.4J2
.406
.40~
.398
.398
.360
.341
.141.
.266
.27?.
.216
.296
,296
.296
.196
k
6,S0
Raa[e
,34s
. JJ6
.JIJ
.Jlo
.10s
.30$
.276
.2s2
.252
.189
.184
.176
.178
,178
.178
.178
k
10.00
Mtthod
-u-.647
.815
.896
.723
JO
.951
.179
N
;.01
1.05
1.10
,647
.723
.179
—
23
.951
.B35
M
1.01
1.0s
.896
—
1.10
25
,610
.684
.738
.192
L.
.90J
.850
.958
T
9
15
K
.579 I ,50?
,650
.703
,7s5
.650
.s2s
.498 I .43,
.811
10
J
..963
.916
10
1
.569
.565
*
,703
7
33
.614
,502
.581
*
k
2.50
k
1.50
.75s
5
G
.8[[
—
4
;
.861
.61J
1
E
I
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--1--
D
7
.
3
-i-
:ept&l
J
c
EEE
.15
3
I
Sarnpls
●{SC
B
Sample iiaa
code latter
C-2
Mantar Table for Reduced Tnnpeclion for Plan~ Based on VariabLllty Unknown
(Siogle SpeciflcalIon Llmi!-Form
i}
TABLE
:6
-—
.—
xf~14
11 Jfffw 19s?
Parf 1I
DOUBLE
C8.
SAAfPLDfG
PLAN
POR
SPECIFICATION
LtMIT
SPECIFKATION
mmtimum ● llowable ~rcemt
defectively
ML
for the lower Iindt. ad by MU for the upper
limit. If ~
AOL i8 88sinmd to bofh limits
c.mbiaed. designate tbc -urn
aflo.able
percemtdelecfiveby
M. Table C-3 is entered
tram fhe cop for aornul inspection and from
tbe bottma for tAIhtamd inspection.
Sam● re pr. plim8 P1W9
Sor
roduce!ttmpaction
— . .
vialed iii Table G-4.
DOUBLE
This part Of the Sf-rd
describes the
procedures for tue with plain [or ● double
cpecificafioa Iimft when variabttify
Of the
let with respect to tbe quality characteristic
ia u.knc. wm ● nd the range method is umed.
cA.
S-.11..
Tc, determine
-------1 u.. a{
-. ——
..- .. —”.Plan..
.—— .—-—
~hethe r the 8.x meet. tbc .C eept.bility c rite rion *ith rcapeet to a partiastar
quality
char.eteristic
.~d AQL. vtiue(. ), the .ppli be used in accordcabl. ●ampliag F.lao ● U
atxe with the pre. i.imm of Section A, Gen● wJ
eral
De.eription
d
SunplinS
PIMa,
the. e in thi. part of the Staadard.
C9.
SE LECITNG
.N1
A ●unplhg
be .clectcd
10 UOU..
THE
SAMPLING
C1O. DRAW7NG
PLAN
plaa for ● ach AQI. .tiue
from Table C- 3 or C-4 ● m
,
..
...-
. ...
.
.
.
-..
C9. 1 Determination
of Sunple
Size Code
.s.
code letter =hfi
~.
Th ● .unple
b. ● elected from Table A-Z in accord-ee
with paragra~
A7.1.
The
●antple sise
.Orr..pmdiag
●ice
code
for
the lower,
m Is
to
letfer.
qpsr,
67
.
C1l.
;~~OT-~;~O
be ● lected
in
● ccord -
A7. Z.
T
ACCEPTAB1_
Cl 1.1 Acceptability
Criterion.
The degree
of c.nfo~aracteristi.
with re. peel to . doub_fe .~cific. tion limit
hall
be Judg.d by tbc percent ei wnco. ICr.rni.g producL
The per.enta~e
of no.Cwderming product is estimated by entering
Table C-5 with the quafity imd=x ● nd the
‘ample :Ue.
and
Cf 1.3 Percent
Defective
In the Lint. The
qualify of ● lot ●hall be exprew~ed SrImrmof the lot ~rc.nt
dof=cfi.=.
Its •c~~**
W~
be dosipawed
bY P L, PUO 0? P. The ● gtiwta
PU iadic*eD
contmrmca
~tb respect to tbe
UPPG r spockfieatien Mnait. p with resp.ef
to
the lower
.peckfi.atim
lAU.
P fOr
b o t h spaekfieation
limlta combined.
TIM
● p.c -
or botb
sample.
.fmfl
with ~raarapb
b tbh Standard.
R is the >verage
rmge of
rauKc& ~cb
of tie sti#*0Up9
tba ●bsroup
ex’c=pt for those
consimt. of 5 meuurement$.
●is.
3, 4, or 7 in which
pduu dtb ●rnple
●is.
h th= ● ame ● e the
case flu ●ubaro.p
● ~e.
3a computing R, the Order Of
s-pfa
fbe .unple
meamtrernemm ● s nude mat be
ratahad.
subgroup
of co-ecutive
meu urementi
mnot be formed and tbe range of
K ia the ● -erase
etch ●ubgreup obtahed.
●ubgroup ranges.
of the individud
C9. 3.2 Maximum Allowable
Percent DeIe c five. The maximum-t allowable
PC rcrnnt dee.tirnatec
of percent
~tive
for cunple
def ● etiv.
aace
limit,
u im the upper specification
limit,
L ia the lower .peeificalion
c is ● iacfor provided
in Tables C-3
C-4,
x i. fbe ●mple
mean, and
u i- the ●verage range of the sample.
C9. 3 Obtaintng Sampling Plan. A ●sM@in4
plm Comai,ts of ● ●ampfe sise the sl ●octatad maximum
attowablo percent dafac tiw-e(. ). The cunplin3 plan to be ●pplied in
kn#pect&a stmfl be ~btied
from Maater
Table c-3 or c-4.
10 Si=e.
OF SAMPLES
Cf 1.2 timputatioa
of Ouality bdicei.
The
qualify
inchcea Q
{u .Cxl [R and QL=
(X- L)c/R cbdl be !o&uted.
-here
C9. Z hta-tor SamIIlimX Tabla-.
The master
munnlinn tablem [or mlam hmed On variabil ity ~fca~wu for a d~ble
specification
limit
wbeo uming the range rn.tbod ● re Tablea C-3
● nd C-4.
Tsble C-3 is used for norrnaf
and
tightened im.pectiom and Table C-4 for ra duced Lrup.ccfion.
C9.3. I Sun
.bownbiitdl,..
each ●unple
Lf3d3T
—
CIZ. Z.1 A.c=ptabitity
Critdria. 5 timp8re
the estimated lot Per.cenc de fcctive~ Pt. ~
P with the corresponding
maximum aTiow● nd Mu
● lso
8e Ie percent defective
M
compar.
p . pL + Pu with tk e larcer Of ML
● nd Mu.
2f pL ia equal to or 1=6s ~h~ Mb
PU is equal to or lees than b4u. d
P is
equal to or 1=0s than the larger of btL ~
c ritcri=,
Mu. Ihc lot meet8 the *cceplability
otheruase.7be
lot does not meet the scce Pl ability criteria.
33 ● ither QL or OU or both
● re negative,
then the lot does not meet the
aeceptabitity c riteri&
=.cirnatc. p.Laad pU ● baJl be determined by
entering Table C-5. r.mpacti..l~
‘iJb Qt.
● nd Qu ● nd the ●ampl* ● i=..
The =~tim~te
p shall he dew rmined by ●ddin~ the co rres pcmdimg estimated
percent
defective.
PL
amd PU found iii the table.
C12.
ACCEPTAB1~
CRZTER20N
SUMMARY
FOR
0PE2tAlTUN
SAMPLING PLANS
AND
OF
Cl 2.1 O!ie AQt- value for both Upper
b-e
r + Cit,catmm Limit Cmnbmed.
● nd
Cl 2.1.1 Acceptability Criterion. 4 Compare
P . p“ +
che eetimamd lot percent delectlve
● l10-abl*
Prc=nt
PL -ilh
the maximum
dcfcc:ive M. U p is equal to or less than M.
criterion,
if
$h. lot meets the ●cceptability
P i. e,e*t=, th*n MOr if either QU ‘r ‘Lor
both .re negative, Ihenthe Jot does not meet
the ●cceptability criterion.
Cl 2.2.2 “Summary far O~~atic.n -f ~mPliWf
PJan. & ~.ses
m.h.re ● cliffere.t AQL value
~tmblished
(or the upper ●nd k.wcr .Pec ificatio” limit fc.r a sim~ie quality characterthe
istic, the fol Jmnimg steps ●m-.mari=e
procedures
to be used:
C12.1.2 Summary for Operation of Sampliag
Plain In came. where ● .ingle AQL value 1.
=blished
forth. um~er and lower s~ecifi C~t;ori limit cornbin;~
for a ●i=gle quality
.haracleristic.
the following steps summa=i.. lh. procedure.
to be used:
.
ll)”Dctcrminc
the sample si. ecode
letter from T.ble A-2 by using ‘the Jot sic
and the in, pe. tie. level.
(2) Select the sampJitig plan from
Master Table C-3 or C-4. Oblain the ampthe m~mum
le size K.. the factor c. -d
● llowabJe
percent defective.
MU and ML.
corre. pondi=g to AOL VaIUeS fo, the uPP=r
● nd lower Specific atiec. limit.,
respectively.
(1 I Dcternai~e
letter from Table A-2
and inspection Jewel.
(3) Select ● t random lhe ●ample of
from the 10C inspect and record the
measurement
or the quality characteristic
on each unil in the .UTIPIC.
a utit.
(2} Select plan from Maater Table
C-3 or C-4. Obtain the sample ttie n. th=
factor c, and the maximum mfloumble percent defective M.
13)
n unit. from
mea. urem..
or. ● .ch unit
average
IS) -mpt
tbe quality indite.
. IU. X)c/K arid QL, F= (X. L)C/R.
y-fi=nt
●.er.~e
Select m random, the ●ample of
the lot; respect and record tbe
t of the quality characteristic
of the sample.
(4) Compute the sample mean X
rmge of tbe ●ample R.
AOL
4tie
SW
~pk
*PI=
C-3
c.4
va.luet for Upper
OU
for
. campl,ete
(7) 32atl three of the lollowlris
(a) PU is =q-~
~u.
MLl.rger
-. -—..
. .
●xample
cos-
tO Or lEM
tbu
(b) P,. ia aqtml co or I=*w th*m
{c) p is equal toor Jesmtin
of ML and Mu.
● re ●aticfied.
the
fh lot m.mtm tbe accepfAbi21ty
criteria; otherdse
the lot hew not meet the
scc=ptability
criteria.
If either Oz., or QU or
fba. *h. lot dw* tit UI**C
both ● re =gative.
the acceptability
criteria.
a~d
exunpZe
● .d
dbt~ons:
LamIL.
for . =om**t*
X
(6) Determine
the ● .timm~ed lot
percent defective. pU amd pL. corresponding
to the p.r. em defective.
above the upper
and below the lower
specificticw
limitt.
AJSO determine lbe combined percent detectiV= p - ~
+ pL.
● nd
(7) 2f the eotinuted lot percent defective pi. equal to erlem. thui the maximum
d20wable percent defective M. fbe 10Jmeets
the acceptability criterion,
if p ia graatar
lIIM M or U either Ou or QL Or both am
negative, then the lot doe. awt meet tbe acceptability trite rion.
p8cuLcmU0m
{4) Ckmpute the ●ample mea.
rams-k of tbe ●unpJe R.
(5) Compute the qualiJy imdicec QfJ
. (u- X)c/R. and OL =(X-L)CfU.
(6) Determim
the emtimtiad
lot
d= f=ctiv= P * PU + pL frOm T~bl=
C#w.~r Different
the sample ai.e &d.
by using the lot ● i=c
d
tbi.
of Ma
proc.dure.
PrO=~ur*.
MIL-STD4M
llJunelDS7
EXAUPIX
Example
Double
Variability
One AQL
of Calculations
Specification
Unknown
Value for Both Upper
C-3
Ltrnit
- Aver age Rsnge
and
Lower
Method
Specification. Limit
Combined
[or elec:riea2
recisfaace
-f a certaiu electrical
cOrnponeu5 *
The ●peclficstioni
is ●ibmitt.d
for In*petiiar&
fmspecfi..
Uwe2
65o.o ● 30 ohm.. A lot of 100 item.
IV, normal
intpectiea,
wftb AOL
. .4% ii to be used.
From Tuble. A-2 and C-3 it
of size 10 1. required.
Suppose the vafuea of the ●mnp2e
is ● eer. that ● samfle
resistance
in the order reading frm-n left to ri~ht are ● s follows:
643, 651, 619, 627, 65B. (Rl
67o. 673. 64). 630, 65o. (R2
and compliance
with the acceptability
criterion
Obtti~md
Sunpl.
2
sum of Mea. u,. m.clt.:
3
.%mpl.
.
X:
U...
6470
xx
647
XXI.
6470/10
37
4
.?.405
5
(39 + 35)/2
See Table
C-3
680
6
I
Zcxpla.atien
10
1
Sise:
i. m be determined.
V .lu.
Znf.armatiom Ne.ded
*.
. 658 - 619. = 39)
s 673 - 638 c 35)
620
7
fawer
8
Ctudity
Index
Cfu . (U-X)
c/R
2.15
(680 -64Y)z.405/37
9
Ouality
Zndex:
C3L = IX- L)e/11
1.76
(647-620)2.405/37
10
~-t.
Lut p--t
11
Est. of 3A
12
Tota2 Est. Parcant Def. h fak
13
Max. A210wable
14
Acceptab12ify
Specification
of
Pff + PL titb
Percent
Ltmit:
.35s
See Table
C-5
pL
..2.54%
see Tsble
C-5
P = Pu + PL
: 2.89%
D=f. ● b-
u:
w
Def. baleu
L
Percent
Crtterloa:
64
Tbe lot dtm. nut meet
L
tbe
Def.:
M
Carnpare
●cceptabifify
1.14%
p -
crilerlOn.
2.e98
>1.14s
since
p = p“
.s5s
+ 2.54s
SOe Table
C-S
See P*ra.
CIZ.1.Z(7)
+ pL 1~ greater
~
M.
de
—
xm.-sTD-4l4
11 Jute 1957
I
EXAMPLE
~ph
I
of Cakuhuom
Doub3e
I
V.riab33ity
AQL
Different
I
Specfficatlom
Unknown
Values
c+
- ~we
for Upper
LimI1
Range Method
ra~e
and Lwer
Specification
Limit-
The ●pecifi.aticm.
f.r electrical
reaiscance of ● certain electrical cmnpone~t iZn.pectimi 3AV.1
650.0 ● 30 darns. A J*1 of 100 items im ● ubmitted for inspection
IV, rmrmmz impecziou, vifb AQ3. . 2.5$ far the upper and AQL E 1% far tbc lower
specification limit i. Ie be used. From Tablet A-z and C-3 it i. ● ce= that ● .am P1. of size 10 is reauired.
SuPrmse the values of the sample resistances
in the
irder
reading fmm left to right “a-re a. follows:
ZZ.unple
643. 651. 619, 627, 658. (R, = 6S8 - 619 = 39)
670, 673, 641, 638. 650, (Rz = 673 - 638 = 35)
and compliance
Intc.rrnation
Sample
Six.:
I
I
c*iteria
i. co be determined.
Value
Needed
Obtained
10
n
Sum of Me.. urcment.:
I
●cceptability
with the
647o
1X
.%rnplc Mean X:
4
Average
5
Factor
6
Wp=r
specificatio~
Limit:
U
680
7
kwer
Specification
Limit:
L
620
8
0ua2ity index
Qu = (u-X)
9
OuaIity
QL = fX-L).
Z4.nge
IXf.
~:
6470/10
647
3
(39 + 351/2
37
X3tlno. of .ubgroups
See Table
2.405
c
fndex:
C-3
c/R
Z.15
(680-647)2.405137
/R
1.76
(647-620)2.405137
10
~s~. Of ~t
Perce=:
Dcf. =bOv= u:
FU
.35%
See Table
C-5
11
~.t.
p=c.mt
D=f. belOw
PL
2.s4%
See Table
C-5
lZ
Tad
p = PU + PL
2.89%
13
MAX. A130wab1= Percent
Def.
● bove
U: Mu
1.42s
S..
14
-
Def.
below
3A M’
3.23%
See Table
15
Acceptability
‘=f kt
Ems. Per.emt
A330wabla
Del.
Percent
Criteria:
in tit:
fA
criter&,
slats
2.54s
. 3.Z3U
2.898
<7.42s
15(-).
.
.
(b) and (cJ
Table
C- 3
C-3
See Pars.
clz.z.z(7)(d
See Para.
C12.Z. Z(7)lb)
See Pars.
CIZ.Z.Z(7)(C)
.3s% <7.42%
(a) CDmpmre PU
with Mu
(b) Compare PL
with ML
(c) ~t~p~ue
p
The 10t rtmetm ttm ●cceptability
MfJ. pL<M~uldp
<Mu.
.3s% + 2.54%
● re
satisfied;
i.e..
PU <
,______
4
w
C-3
M
T
.40
.65
1.00
1.50
.261
.1561.Z4Z I .350
.230
.210
.lbS
.133
.z3q
2.349
2.335
2.333
2.111
z,j30
35
4b
50
60
85
115
113
230
J
m
L
M
N
0’
P
0.
.Zbl
.244
.169
.13S
2.342
2.339
.539
.564
.53?
.65
.40
.23
—
,ceeptable (3
.q76
.972
.65S
.661
1.06
I.lz
.755
.718
1.16
1.25
1.Z5
1.31
1.z9
1.27
.1.51
.818
.842
.883
.856
.827
1.]0
1.14
.89
.43Z
—
.468
—
.303 .4Z7
.313
.493
.s42
—
.356 .504
.)81
.375
.391
.366
parcant dafactlve.
-t-t
++-
.232
.)60
2.346
-tt-
.240
.147
2.353
30
.5o6
1
,>36
.214
It
.125
Z.358
2s
34
.786
LJ79
15
G
.2s3
2.405
10
r
.136
2.8)0
7
E
.061
.58
2.474
5
D
.ZJ
—
.430
v
.28
z.a34
4
M
3.30
3.14
2.93
Z.zs
1.0s
3.44
2.41
2.37
3.64
Z.b3
3.73
3.90
2.82
2.69
3.q2
3.96
4.44
4.77
5.JZ
5.93
5.50
,?.81
Z,8Z
3.11
3.Z3
3.46
‘3.44
t.sl
Z.50
Z6.94
M
ZE-1
6.60
6.511
I
4.461
6,99
4.76
4.47
1.17
1.s4
7.91
0.11
8,42
s. 50
8.65
9.76
10.79
12,]s
14.47
9.!34
9.89
10.37
10,73
11.10
12.57
11,04
12,24
12.36
12. s9
14.09
I 5.4q
11,s4
2?.90
30.66
19.02
19.88
20.31
21.0$
,?1.63
?.2.26
22.38
z3. zi
23.41
23,79
-L
I4.1O
14.i5
t4.14
15.11
I $.64
16.20
+-
16.55
17.03
17.19
17.40
19.36’ 2%92
21.06
2).s0
33.95
3b,90
40,47
M
1s.00
TI
29.43
31.6q
M
10.00
ZO.Z7 26.S9
\b.45 ‘ 22.S6
lfI.86
M
4.q7
5,17
S.47
5.61
5.85
5.88
5.98
6.76
7.42
8.47
9.90
10.91
.7.59
M
4.00
Rtrme Mcihc.d
.
1$.00
-!Asl.&
4OOI6JOI1OJO
dlty Levelo (N:htemd Inspection)
1.471 2.0.5 lz.q2
1.46
1.58
1.61
1.74
1,60
1,B8
1.98
1.q6
(.95
Z.lo
Z.05
I .9q
1.42
~vv
MM
B
I
.25
1
lIA.,w.
‘“””’---”
4cceptable C mlity Levels (normal in#pectlon]
m-
iiir!t
.10
c
MMM
.06S
G
fa:to?
.04
3—
Ssmple
*11*
B
Sumplc *IS*
cede Icller
TABLE
Mamer Tbbl. fer Nermal .nd Tlthtencd fnsmctionf.r
Plan. B.nedmv..i.hlltt..
(Double Speclficatlon ~lmlt ●ndf;r Form Z-Single ~peciflc”~fion Limit;
————
.. —_.
—
1,
I
I
:
2.4o5
Z.405
z. 379
10
10”
15
I
J
K
05
I
Q
.253
v
Z8
.261
.144
z.349
Z.339
.242
.240
Z.353
Z.J3S
,214
2.358
.564
.504
,391
.356
.493
.537
.366
.350
.506
.506
;755
.75.1
.883
,S56
.827
.S27
.786
.430
.136
.336
.58
.21
.58
l,i’
l.l Z
1.16
1.33
1,29
1.21
l.z7
I,JO
1.14
ML bad table waluec tra in pcrcmt d. f.ctlve.
%deZ3rdt #ampNnszdmb.kw’.rrtmr,
that,,, betb ccmple,l.ea~
30
.214
Z,MB
4
-1-2..530
I
18.06
2.$0
!.93
2.37
2.47
2,82
2.81
2.82
Z.8Z
3.11
).Z3
1.23
3.46
-
M
in33.69
-ii-
10.00
10.13
2>,42
Z3,ZI
21.63
17.19
17.03
15.64
10,
21.05
Z3,79
17.48
15.17
Z3.T9
Z5.9Z
Z7.90
21.90
JO.66
33.95
36,90
40.47
40.47
40.47
17.48
19,30
G
z1.06
Z3.SO.
G-
29,45
3J069
33.69
33.69
40.47
S1S. OqU~C or ,xc.,do
1.Z7
7.54
S.17
4.97
8.42
5.85
3.90
—
3.44
3.30
la.z4
8.50
5.88
3.92
11.10
12.36
8.65
5.98
IZ.S9
IZ. S9
14.09
G
15.49
17.S4
20.Z7
&
8.65
9.16
6.76
S.9.3
10.79
10.79
If?.Js
7,42
7.42
8.47
14.47
2Z.8b
26.94
Z6.94
26.94
26.94
3.96
3.96
4.44
4.77
4.77
—
5.3Z
9.90
weNa* MvsJu*. ‘ WI..SamPle
1.67
1.74
1.98
1.96
1.95
1.95
Z.10
Z.05
2.05
1.99
3.44
16.’5
1.s.86
18.86
18.86
I.1!
1.42
10.92
1.53
2.234
i
1!59
1.910
1.99
7.59
7
N
MM
1.50
IAVCI1
1.910
H
25
,
M
Acmptablo OuaZ{t
I ..?5 I ,40 I .65 I
L
M[hI’l
MIM
.15
7.59
Z.474
M
MM
.10
1.?10
5
L“ZS
*
.065
Ran[a Method
$
$ II
1.910
G
Smnpl* 81SC Samp10
cede letter
● IX*
C-4
Maamr Table #or Redueed Zmpecticmfor Plan, Baoedon VSrlabillty Umkmwn
(Doubl* Speclficalion kltand
Form ?-Single SptcUicttion LlmII]
TABLE
-!5
~$
~
I
I
I
L-...
. ..-
TABLE
C-5
Tabh for EcUmatInI lha Lot Percent Defective USIIIg Rans* Methedl
... ..
—.—
—
—-. —
I
1
i
i
Ttbh
C-5-ConUINed
for E#timatln# tba Let Percent Defective Ualng Rune
TABLE
Method
“
,.”
.
,..
I..
.
,.”
.“
.
,,,*
,,.
.
,..
,,.
. ..
.“
. .
,-
,..
,.*
,.”
,.94
.
.*
*..
,,.
,,..
,..
,,.
..
..
..”
9,.. m “
A.
,.”
,s
,.
.
.
*..I
,,. ,.n *.S
“ ,. .
. ,.= D..
s.. ,.” .
,. ,- !..
,.0
,..
1..
,A ,a
l.. ,.”
*
)..
t.”
,..
a
.
4..
“ ,.- **
.“ ,.9 .s
. .
.,”
.. . “
. . ...
4..
. ..
. .
. .
0,”
6..
.
,,.
,..
*“
,-
,.a ml
9..,= ,-
.
t..
.“
,,.
;,.
..
..
..
.
,.”
.“
..
,.
.- ...
,.. . .
.
.“
.
.,
I
I
,
t3ef@c11veUcla:
C-5-ConUnursl
Tabh for Estimating tbo Let Par.ml
TABLE
Ilmte Method
.
I
—
‘--
TABLE
C-5-Continued
Table fer Eotlmatlng the l-al Percrn! Defective Uolnc Range Method
—-
:!
T*Mo for Estimatlq
Defective U#inS Raa[t Method
C-5-Contlaued
ttm Lot Percm!
TABLE
_—
. . ..
.\.
.
..
ESTIMATION
OF
R=UCED
C 13. fig~MATION
OF
PROCESS
PROCUS
AV~GfZ
AN(3 T1Gf4TENE0
AVER-
Tbe .verag.
percent defective, based
~POa ● group of lot. .ubmttted for c.ri~iii.l
In. pectmn. i. called [be prc.ce. a ● verase.
OrigiM1 im. pectiert imthe fir.t inspection of
. particular
quantity Of product .ubmitted
from
the
le. ●cceptability . . diati~uiah.d
ia. pe. tion of praducl which hambeen re. ub rnisted after prior
rejection.
The pr.acc..
● vera~e
shall be e.timated from the remdtm
drawn from . .pec of im. peetion of ●mple.
Uied numb. t of pr. ceditq lot. for the pur PO.. of delerminiag
.everity of imapection
durimg the .our. e cd ● co=t?.ct in aecordaace
with paragraph
C14.3. Ay lot .bdl
be incitided md, ante (m rt.dnutfri~
chm proc...
avera~c. The e.timate of thepmcc..
average i. de. igriated by p“ wbem cwnpuc.d with
rempect
tc. ● n upper .pecific.tion
limit, by
(JL -b..
..mP.ted
rnth respect to a lower
.p. cifi..tic.n limit, and by p when computed
with respect to ● double .pecifi..t ion Ilmft.
.
C13.1 Abnormal
R.. uft..
Th. ra.ult.
of
ic!. pectitin of product rnamuf. cmred under
ccanditions aot typica3 of u.tmf production
hall
b. excluded from the emtimaled proctm. ● verage.
Cl 3.2 Compufatio.
of tbe EsUnmted
ProCe.. Average.
Th e estmuted pracemm ● vmr .;.
18 the a%hrnetic mean of 4(I. e-hated
lot percent d. fecti.=m
computed from tbe
●ampliag i.. pectioa re. ufto of the precedlmg
ten ( 10) lot. er ● . may be otberwi. e de. ig matad. & order to eatim.t.
the lot p.rcem
defective, the qua3ity hdie..
Q“ andlcw OL
9ball be Coin
● d for aach lot.
Tb...
ua:
Ou = (u-X)C r X and Ot, = (X- L)c/IL
(See
parwraph
Cl 1.2. )
6
C13.7..1 S&l*
Specific&
3An&
Tbe
emilmuea lot percent d ● 1eetlva ●bQ b. d.Iarmin.d
from Tabl. C-S forth #_
ti.d
tuetbod.
T& qdity
M-x
Ou
on the r~c
● bd
k
uood
for
tbae~e
ti
u-r
•~.
tb8 cu. d . tir
●p.cuictiom ulmlL T&l* c-s b tirti
dfb C)uor QL ● nd (h* ●rnfla ●ti=. d ~*
Ific.tlmiMrnft er Q~ ler
AND
CRfTERfA
f=OR
3NSPECTION
corresponding e.limated lot prcent
dcf. cor p . rempecfivel~,
is red
from
Uve p
the ta~)e. Tk
..tirnated
proce..
.ver.~e
%
i~ the -it
f-=*ic M-= Of the individu~
-.titn.ted
lot percent d. fectiva. pu’s. Sim ●.=r8ge
PL
itarly.
tbe estimti.d
proces8
i. fbe srifhmetic mean of the individual estimated lot perceot defective.
pL’..
Spccificatioa
Umit.
The
C13..?.2
Dc.uble
e.timateii lot pe,=.nl
de fcct, ve shall be determi~ed {mm Table C-5 fc.r the Plan. baaed
cm the rmt~. method.
The quality iridice.
OU and OL shall be computed.
Table C-5
is cmter.d #.parately
with Cfu ad
QL ● nd
the .ampfe .izc,
and the c.rrespohdi:g
Pu
PL ● re read from the table.
The ● sti-d
m.ted lot percem defective i. P . PU + P .
● verage
p i. ct+●
Tb.
e.lirnated
proce..
● rithmetic
mea. of the i.divid.af
..tinuted
10I percemt defective.
p,..
C13. Z.3 Special C.. e. If the quality iade.
Ou or 01. i. . aegativ.
amber,
lhen Table
C-5 i. entered bydi. regarding
the negative
.iar..
Howcwer , ii. thi. c-..
the ..timat=d
lot perce.m defective above the uppar limit
or below the lower limit i. obthic.ed by .ub Cr.cting fh~ percentage
lc.und in the table
from 100%.
C14.
NORMAL
TIGHTENED,
“DUCED IkSPECTION
AND
RE-
●u’nplfng
Tbia Standard esmblisbed
P(U
far normal,
tightened.
and reduced
IEmpectk.n.
C14. 1 At Start of fa. pectiom. Normal inspection .hd3 be used ● t the start of ias PeeU& uateoc otb.rwise
dacignated.
C14. Z ZturirIg 3aspection. Qurimgfhe courm
&xctio.
sbdl
be
of iwrnctiim,
normal
Coaiitimms are ●uch
UDd vba. imspoctian
(&85 tibteaed
or reduced iMmcc?ion io not
-itb”
paragrmpfu
r.4dTd
Lm ● ccordume
C14.3 d
C14.4.
Cl 4.3
Tisbtened fxukmcfion. Tishw..d
ia9D0ct10m 91M31 be ttmtituted wbem tbe estj J
td
&t&f
procemi ●verage computed from
the ● stimat.d lot percent defective i- ~
~r
of towauto sero for b ●vclfied
tiv. 10CC(see Table C-?).
prec.di.#
t.. ( 10) lots (or ●uch other aember of lot. de.i~nat.dl
in ● ccmrdaoee .ith
para~raph
Cl 3-Z is greater
than th= AQL,
T of
sod when mere than ● cc.rlaln ~r
theme hats have emtimatea O! the percem
delecctve .xecedisg the AQL. Tba T-values
●r.give.
ln Table c-6 for tbeprocem
●wer,r
age compted
from 5, 10 or 15 101*.8 r40rmal in. p.ctioa
hall
be reiiut.ted
i[ the
● verane
of Iota her
e.tinuted
proces.
Cightea.d im.pecxic.n is ●qtd to or le.. tkn
the AQ t..
1.
COmdItkl
c.
Production
i-
●t ●
●teady rata.
Normal Iaspectlen
one of the following
reduced ia.~ctiOU.
Cmditbm
Iled=ced
inCl 4.4 Reduced
ln9PccUon.
●pecti.a rrmy b. uutitutad providd
that all
of the following conditions ● rc catiafied:
●va
● hall
be reinstated
cooditiea. eccvra
D.
A M
M ‘my
ti.r
k rejected.
condition E. Tbe ● ettmatad procema
age 1. greater
tbao tite ML
irregular
tkmditi..
F.
or delayed.
Prehcttom
Camdittc.aG.
Dtber
become,
Conditioa A. The preceding ten {10)
lot8 (or .uch other number of Iota deaigrmted)
have bee. under norm81 inspection and non.
ha. be.m rejected.
may warrant
b. r.ltwtated.
thmdicioa B. The ecttnu:ed pereemt
defective for each d theme preceding Ietm ile.. than tbe applicable
lower limit #bow.
in Table C-7; or for certain ●ampiius plar.a.
Cl 4.5 SPling PIUIO for Tfuhta.d
or Re dimed LompeCroon. Sam #w
P~
i or tightened -d reduced in@p@ctioa ● re provided in
Sectio. C, Partm 1 aad U.
... ,...
I
Qa
Umt normal
..
.. ..
condition.
w
impaetio.
. bauld
.. .. .
MIL-sTD-414
11 Jme 19s7
TABLE
VA.e.
Sample
code
#ix.
letter
.04
.
B
.
.
●
D
.
E
.
F
,-
.
●
c
G
.065
●
.
Acceptable DIM
.15 .25 .4(
.
.
.
.
.
.
●
●
.
z
4
5
.
●
●
.
.
.
z
>
4
z
4
s
3
4
5
3
5
6
3
b
7
4
6
e
4
6
s
44
77
99
4
6
8
4
6
8
,4
6
9
44
4
3
5
7
3
:
3
b
7
;
7
:
7
4
6
0
4
6
8
4
6
9
:
4
6
8
4
6
8
4
6
8
4
4
:
7
:
;
4
6
a
4
6
a
4
6
9
4
6
9
4
7
9
4
7
9
4
6
a
4
6
9
4
7
9
4
4
:
;1
4
7
0
N
4
7
9
4
7
9
4
7
91
4
7
01
4
7
0,
4
7
10
4
7
9
4
4
4
4
0
:1
:
L
M
Ii
1:1
.4
:1
7
:9
4
7
+9
4
7
10
—
4
7
10
—
4
7
10
—
;
10
—
4
1!
—
:
10
4
1:
—
4
7
JO
—
:
10
—
4
a
11
—
4
8
11
—
of Wm
44
2
4
6
:
9
:8
10
11
3
5
7
4
1
F10
.4
7
10
4
8
11
5
4
‘7
10
4
7
10
4
8
11
5
:7
89
44
67
99
44
78
10
11
:
11
4,4
4
8
—
4
6
9
-3
5
7
15.0
:
2
“3’
10.0
:
8
4
7
10
—
4
7
10
4
7
10
—
4
1:
—
4
7
10
—
4
e
11
4
a
L1
—
4
,?
1:
4
4
3
5
7
:
;
K
23
44
56
!
6.5
.
3
5
Number
‘ectke]
1.0
T -L
●
:
:
J
.
;
H
.1
T?.
.6s
Me3b0d
k.spcction
Sy Lewd
!
1:
3
of T for Ti~ht.ned
.10
Range
C-6
d-
5
10
4
15
10
15
10
15
5
10
15
5
10
:
11
1:
4
8
11
4
8
11
5
4
-8
11
4
8
11
4
8
11
5
:
11
4
8
11
5
:
11
4
8
11
4
8
11
5
11
4
8
11
4
a
11
4
a
11
5
1:
4
8
11
44
88
11
4
8
11
4
8
11
5
11
4
8
11
4
8
11
:
11
4
8
11
4
a
11
4
8
11
1;
-t--t
44
7
10
4
n
1:
11
$
44
7
10
4
78
10,
44
80
11
1:
4
11
$
44
a
11
44
80
11
*
1s
10
15
10
15
10
15
10
15
10
15
10
15
5
10
11
15
uid MLvm3umm.
m
----
MlL%Tn414
11 Juna 10S7
TABLE
m
z
zIT
Vale.
A. ce
d T for Ti@t-.d
‘=%!7
Lmspcuoa
5A ,.1s [ill
ble Ouatit
.15
..?5
.40
.6s
44
77
10
4
10
“4
4
788
10
11
w
4
7
10
:
10
44
laa
11
11
.10
Q-lx
Method
R.-g.
C-6-CooUfoJad
11
11
1.0
1.5
44
f5a
11
11
:
:
11
11
44
a8
II
11
4
a
!1
+
:
11
The S-D
5 lot.,
.- fiiwm in each block refers to the precedim
preceding 10 lots and lhc bottom figure to the pre&ding
I S-lot..
I
I
4
a
11
4
a
11
the middle
1
45
1:
li~rc
10
15
to the
of percent
Tightened
inspection
i. required
when the number of lots with ● .timatem
defective above th= AOL from the precedin~ 5, 10. or 15 lots i. ~rester fhan the given vtiue
of T in the table, and the pr-.e=m averaae from these lat. exceeds the AQL.
Aff estimates
of the lot
percem
defective
are obtained
al
from
Table
C-5.
●
●
●
●
a
[loI**
.000
.009
.025
.002
.015
,037
.004
,021
,044
●
●
●
●
●
[12]**
.000
.003
.011
.001
.006
.017
.001
.010
.0.?2
B
c
D
E
r
G
H
I
1
●
*
.007
.042
.079
.004
.032
.067
.002
.020
.052
[ 8)**
*
●
.000
.015
.014
.014
.101
.199
.028
.110
.230
,042
.151
.24B
.000
.002
.0.?0
.004
.047.
.096
.010
.061
.118
.017
.075
.131
[191** [141**
[JO]**
●
●
4
●
●
*
o
●
.25
.1$
.10
TABLE
C-7
.094
.281
.40
.069
..?52
,40
.04Z
.209
.174
.000
..060
.199
[II]**
[23]**
●
●
●
.40
!
.202
.51b
.65
.16.2
.478
.65
.112
.422
.65
.006
.19z
.466
.000
.008
.158
[17/..
[)1]**
●
●
.b5
.Jsb
.861
I ,00
1.39
?..47
2.s0
1.27
2.42
2.s0
.600
1.34
1.50
.691
1.39
1.50
1,12
2.)4
2.s0
.Z48, .498
.755 1.26
1,00
1.50
.326
..522
I ,00
.5)6
1.94
2.s0
.061
1.37.
,2.30
,00
.40
1.14
2.S7
4.00
b
2.42
4.00
L
2.20
4.00
,
1.41
3.63
4.00
.s3
3.01’
4.00
0.00
1.84
4.00
.00
.35
1.84
[IO}**
[15j**
[28]**
4.0
[ 9]**
[221..
[42]*.
.?.5
[II]**
[18].*
(31)**
●
1.5
Levels
.148
.90
1.50
.040
.449
.90
.000
.104
.50
[13]..
[25].*
[45]**
●
I ,0
Acceptable Oudity
Lot Percent Defective (or f2educcdfn,pectk
●Th-rc ~rc no tunpllng plmo provided In this Standard for the-e code Iettera and A(3L vduos.
.065
,04
code letter
Ssrnple *ize
Llmit# of htimxcd
4.11
6,50
A
4.52
6.50
a
4.27
..50
,
3.27
6.50
A
.?.04
6.06
6.50
12.65
15.00
A
12.43
15.00
A
7.68
I 0.00
A
7.91
10,00
i
12.13
I 5.00
&
11.01
15.00
1
I 5.00
i
9.66
8.45
J5.OO
A
6.06
15.00
,
&
.17
I S.oo
[ 9]**
15,0
1.40
10.00
A
6.30
to.oo
&
4.92
10.00
&
3.s2
10,00
b
.74
9.96
10.00
0.00
4.40
6.50
.19
5.74
b. 50
( 7]**
[121..
10.0
[[O]**
[18]**
6.5
5
5
5
5
5
5
s
s
10
10
10
10
10
Jo
10
10
15
15
15
15
15
Is
15
Is
or z.ato
Number
RWISQMethod
1
.014
.041
.064
.Ozz
.051
.065
/.oz9
.056
.06s
.007
.023
.036
.Olz
.Ozfl
#.04Z
,015
.013
.04
5.5
N
T
.1s”
.093
.146
.078
.139.
.15
.064
.1Z9
.15
.046
,112
.15
.036
.1OZ
.1s
.0Z4
.087
.144
.144
.Z)a
.25
.Izz
.2Z6
.25
.09Z
.z06
.Z5
.190
.Z5
.Z88
.581
.65
.246
.391
.4044A
.z16
.378
.40
.174
.35Z
.40
,509
.94.?
1.00
.857
1.47
1.s0
1.119
1.50
l.o4l
1.50
A
.92i
1.50
b
4:00
i
y
5.01
5.90
6.50
A
3.54
4.00
A
Z.15
2,50
&
13. z7
15.00
19.00
b
11.o~
5
5
10
10
Is
1s
15
15
15
~1 ●btlnmtem of tbe lot percent defective
● re
obtained from T.ble C-5.
Reduc~d Impaction may bo Inotltuted when every emtlmmed lot percent defectlv~ from the preceding 5, 10, or 15 IotmIc
bdew the figure @iven la the labl~ raduced impectlea (or sunpllng plum marked I*.) in tbe table requires that the e8tImated
lot percent defecllve la equa2to -ero, for the number of comecutive Io!* iadlcsted !n br~cket~. in tddltlam. dt other condltiom
for r-ducad lnapection, In Part 221et Sactlom C, mumtbe ● attmii*d.
ref. r# to the
10
14.15
1S.00
9.Z7
10.00
11
5
14.OZ 5
15.00
10
9.15
10.00
AA
8.48
10,00
bd
8.11
10.00
k
RUIIO Method
T#
5.BO
6.5o
l&A
3.46
4.00
1
Z.50
&
1.90
Z.so
b
.?.08
&
5.2Z
6.5o
tt-t-1
6.50
A
3.19
4.00
A
—
1.32
4.00
1
2.99
4.00
b
2.86
4.00
k’
1,87
2<50
A
1,7Z
Z,50
A
1.6,?
2.s0
&
h percent clef, :tke,
.109
1.00
.434
,65
● re
.648
1.00
i
.562
.968
1.09
,389
.636
.65
,326
.6o4
.65
Ipt tholI In the bracketm,
k
,103
1 .149
.140
.332
.40
1.40
2.50
&
2.5
333
.076
El&E!!
.0
It .08
.10
.0)8
.0 z
.1)
.07.6
,069
.10
.020
.062
.09?
.012
.049
.088
,10
Wm. tht (Irml flsu?o In diractlon O( arrow aad corree~adin~
number of Iotn. in e~eh bl~ck tho top (Inure
prccodkng 3 Iota, the mlddlo Npre ‘to tho preceding 10 Iott, and the bottom figure to the precedlal 15 lots.
N]
Q
AQ
.010
.016
.0s9
.004
.010
.033
L
P
,00s
,021
,010
.002
.013
.0Z6
TF
,06S
,04
C-’I-C.mthtued
I
Llmltc of ZZctlm~tedLX Pereent Defective for Reduced fmpectimi
TABLE
.
g$
:!
!,g
-
%
.398
.)92
.384
.J8Z
.318
.371
.369
85
115
175
230
N
0’
P
a
.384
.405
.190
60
.4?.3
.408
M
35
1
.426
.411
.411
30
I
.412
.4[6
.396
15
n
.460
.444
50
15
G
L
10
r
.065
.417
1
E
.04
.402
5
D
40
4
c
K
3
91s*
Slrnple
B
Ienor
.478
,455
.481
.480
.455
,454
.434
.43.?
.41z
.197
.399
.525
.533
.542
.548
.556
.56o
.567
.6OZ
,64z
.804
.756
—
.764
.516
.5)8
.300
.507
.540
.555
.564
,573
,580
.588
.593
.6OO
,637
.677
.846
!801
.78.9
.517
i--l-.490
,464
.442
.421
—
,411
.406
.505
.503
44’I 470I 497
it-
.486
.519
.4’?2
.469
,463
.527
.531
.537
.572
.49?
.503
,509
,542
,416
,480
.486
.517
.427
.434
.441
.441
.454
.457
.463
.49J
.412
.419
.426
.4JZ
.438
.442
.447
,477
.529
695 727 765
I I
442!3
--t-%
’77
:ceptable Ouallty Le !It (in perct
Average Range (hfARl
C-8
.923
.857
.748
.19)
.666
.676
+
.504
.594
.637
.64S
-1-
.6OZ I .656
.608
+
.621
.628 I .684
.6)7 j .694
.642 I .699
.649 I .707
-t-
.68.9
.730
.910 I .985
+
.891
.865
.816
.811
+
de/cctive)
4.00
2.50
*
1.0s6
.958
I
1.180
1,028
I 10.00 115,00
.708 I
.720 I
.129 I
,740
,752
.785 I
.194 I
,s08 ]
I
.908
,923
,934
.949
.830
.618
.96)
I
I 1.004
.843
.879
1.011 I 1.118 I 1.26j
.96S
.907
6.50
NOT&: There h t eorreopoadkg
occepfablllty constant In Table C. I for eqch .aZue of f.
tht ●ccepttbillty comtant of T-ble C-Z in T~ble C- I md u-e the corre~pmtding value or f.
For
reduced hirpection, find
The MAR may ba obtdaod by multlplyin~ the factor f by the difference between the upper .pecificati.an limit u .nd lew. r
speciflcallon Ilmif L. The formuh 1- MAR . lIU-L).
The htAR serveB as a guide for the magnitude Of the average rang, of
Iha ounpla when uaia# plant for the double opecUicatian Ilmit .ca#e, based on the average range of the munpla of .mbm.wn
varlabUity. Tha werap
ruge of the .smple, tl It.ls Ieoo than the 5dAR, helpc to inoure, bd doe- not [utrantee, lot accept.
abiflty.
CO*
$ample #lz*
Vducs Of f for h{dmum
TABLE
,
f
mL-SlW414
.11 June 19s7
APPENDIX
C
mMlmitfO.s
Definition.
Read
SY@.?!
●ike far
sample
m
X bar
x
single
●
lot.
%rnple mean.
Arithmetic
from . .ingle lat.
●mple
meam of
mea..
r.m.rm
Range.
The difference
betweer. the Iarge. t and ●rnalle.t
mea.ur. mests in . .. bgroup.
& this Smitdard, the #ubg.o.p
site <s 5 except for them= plan. in which m . 3. 4: er 7. in
size.
which ea..
the ●ubgroup i. the same a. ths .ampl.
R
Range e: the fir. t subgroup.
Range
R bar
I
I
the
●econd
subgroup.
Aver.~e
ruag..
The arifhn-.etic mean of the rug.
values of
the subgroups ef tbc sample measurcm.nta
[ram ● single lat.
u
L
k
Upper
spec Uication
limit.
faumx
apecificstien
limit.
c
A factor u.ed in determinizi~the
quality index when using the
range method. The c values ● re given is Table.. C-3 and C-4.
The acc.pcability
conctanr given
in Tables
C- 1 nc.d C-Z
Qu
O
●ub
U
Ouafiry
fmdex for “.=
wijh Table
C-5.
QL
Q
●.b
L
Ouafiry
fndex for use with Table
C-5.
Pu
p .ub U
Sample estimate
Table C-5.
of the let percent
defective
above
U from
p
Sample ●.tixnale
Table C-5.
cd the lot percent
defective
below
L from
‘L
●ub
f.
I
Totti SUTIple estimate
P
I
d
M&imum
M
given
%
M,ub.
U
● llowable
in Tablmm C-3
Mtitun
allowable
C-> scuf C-4.
(For
L ● re specified.)
percent
and C-4.
defective
defective
for
p = Pu + PL.
sample
● mtimam.
percent d. fecfive above U gi.em in Tables
use wbem differenf AOL valuca for U and
de f.cti..
blew
f. Siv.m in Tabfe.
~uxn
mflowmble pert..t
C-3 and C-4.
fF~r u.e -ha.
different AQL value. for U ad
f. ● re cp=dfied.)
ML
..tinut. @f the p.ece..
S-pi.
estinmt=d prc.ee..
average.
P
p bar
$U
p bar #ub V
The estimumd
FL
p bar suh L
The
T
of the 101percenl
● stimated
p.rc.m
defective.
i.e..
proce..
..era~e
for UI upper ●pecUication
pro . . . .
● verage
for a lower
.pecific.tion
Cbe
lf-mit.
limit.
um number of emtin’tated proces.
a.er4ea
w~cb
The mmay exceed the AOL given in Table C-6.
(For use in deffr_
WW+fiCafiL= U fi~ht=aod Ampeefloa)
8s
.—.
MIL-STD-414
11 Jffffa 10s?
D
SECTfON
vARIABIIJ’I-s
KNOWN
Part 1
SINGLE
01.
SAMPLfNG
PLAN
FOR
sPEC1 nCATfON
LfhffT
SPEC1fICATION
Com.tant. Th= ●=c=Ptto the SUTIple is.
mentioned in paracraph
DV..2. I, im
i-dicated in the column of the maater tabl*
corre. p.amding to the ●pplicable AOf.. vafue.
Table D-1 i- .ntered from the t.pf. r normal
i.. peetion ● nd from tbe bottom for tightened
im.pection.
Sampling plan. for reduced ic.apectioo ● re provided in Table D-Z.
Dz.2.2
SINGLE
D3.
D1. 1 U.c of Samplinu Plan.. To determine
the ●cceptability
whether
the lot meets
criterion with respect to ● particular qtmtity
chsracteristi.
and ACIL value, the applicable
.ampling
plan shall be umed in accordance
with the prcwi. iom of Sectic. n A. General
Plan.. ● nd lhose in
Description
of S.mpling
thi. psrt of the Standard.
D3.2 timputation.
The folio witas qu~tifY
● ball be compute&
(u-X)1.
or (X- I.)l. . dependins on whether
the .p..fficatiom
limit
i. u upper Or ● 10wer limit, where
A7.2.
U
.L
X
e
Master Sampliq
Table-.
The rzm. t.r
fabJe. Ior planm ba. =d on v8ria bttlcy ~
k? ● ●imsle qeetfkattc$m ltmlt
● re Tables D-1 and D-z.
Tablo D-1 i- omd
(m -rmsl
Ind tightened
tnapectiom and
T&l.
D-z for rod.ced icupectioa.
D4.
8ampffnR PtM.
Tbo Qu81i.a,wd M
pli8* ph. C.nmmtm 01 ● ,unpl*
Tbe
s~moclated
●cceptability
conmtant.
from
k.te
r
samplimg
plan ia ebtahed
D-I
●
Sise.
The ..niph
she
●howa in t e mamter table correspoadhs
AOL.
each ●ampl. ●he code leffer &
lS.a
Appcadis
Z~-~PIe
i. the sample mean. ● nd
is the bnown variability.
SUMMARY
PUR
8mAuNGm..Az4wmz
OPERATION’
N?onu
OF
12s
● nd D-Z.
~pfe
DLL,
Mntlt,
llmit.
btlltv Criterion.
timpar.
the
- L)I. with tba ●cceptqmantity
●bifity coaatant L M (U-X)1.
or (X- L)le i.
tbb. tfmbg=-e~
~
.quf ’te ox sroater
●cc*pfabfflfy crtsertcud If (U-w.
or ~- L)/.
Is 18** tbn k or Decative. tin
tbe lot dOa*
mt mat tbo 8cc*pfAbtltty
c rlterioa.
DZ.1
Table
i- the upper specification
●pecKicatioa
is the low-r
PLAN
●amplms
Obtdmimr
conformance
(x- L.)/..
D1.3 Determination
of Sample Size Cod.
T he m-pie
Letter.
91ZC code,letter
.hdf
~.cted
from Table A-2 tn 8ce.rdmce
with paragraph A7.1.
DZ. Z
ACCEPTAEfl-~
PROWNEN
FORM 1 IS fJSEf#
Criterion.
The dearof a quality characseri. tic
with re. pect to a •in~le specification
limit
hall
be judged by lb. quantity {u-X)/_
or
of
I
D2. SELECTING
THE SAMPLING
wHEN FORM 1 IS USED
WT-BY-~T
CEDURES
D3. 1 Acceptability
●hail
“All -ample.
with para#rmph
Acceptability
●bility comstaut k. corrcapOd@f
This part of the Stand~rd de.tribes
tbe
prOc=<u, =* fer u*= with plan- fOr ● ●in81=
.peciftcac ion limit whe. variability
of the
lot with rcapecl to the quality chbracteri.
tic
Tbc acceptability
criterion
i.
i. known.
givcm in two equivalent form..
The..
are
identified am Form 1 ● nd Form 2.
D1.2 Drawing of Sag.
be dramt i. ●ccarrJa.ce
LIMIT
m i.
fo
[1) Determine [be sample sise coda letter from Table A-Z by u-lr.I Ibc lot ●iM ad
tba tipecftoa
lee:.
D for d= finicia=u al all ●pnbals
D. I fo,
●
COmpfete .sunpf’e
used in tba sunptiQz
Of tti
67
prO=eda.e.
PIUU bned
oavar~U~
I
mL-snb414
11 June 1957
(21 Obtain PI*. from Master Table 33-I
or D-Z by sel=ctitag the ●ample .i%e rI ●nd
the .Cceptabitity
Coti.ta-t k.
●Pecificalion limit. The p.rc.mtag.
ef nomc.nferming
product i’ ● .;imamd b~ ●nfcrTablt D-5 with the quality index.
at random ~ha .unple
ef ❑
(3) Seleti
units from the lot: inspect ● nd record the
tn. amur. merit of the quality characteristic
Ior each unit of the ●ample.
lade-.
The
of Oualilv
D6. Z Computation
quality ic.de= QtI . [U-X) VI. .h.lf be corn.
limit im u. upper
puted if the 8pe; ification
limit U, or C3L = fX-L) v/. if il is s lower
limit L. The quzc.litie..
~ and . . ● re the
..mplc mean and known variability.
respectively.
The laclor
v i. provided in Tables
D-3 and D-4 corre. pc.ading to the .unpfe
size.
[4) Cornput. the .unpl.
me..
X, ●nd
the quantity (u-X)/e
for an
u per specification
limit
U or the quamtity
L)/. for ● lower .peciiicatiaa
limit L
{f-
●lso compute
D6.3 Estimnte of Pert.nt
Defective in Lot.
The quality of ● lot ●hall be exprem. ed by
Pu.
the estimated percent delective in the
lot ● bove the upper .pecificstmn
limit, or
the ●stimated percetit defective below
by P
ih. l-”
owcr specific alior. limit. The citimated
by
percent de~ective PU or pL i. obtaizted
cmte. img Table D-5 with OU or Cfti
(5) lf the quatitity (U-X)/.
O. (x- L)/a
i. equal to or greater lhas k, the lC.I meet.
the acceptability
criterion;
U (u-X)1.
or
(X- L)/W is Icaa :han k c.r eesative, them the
101do=. not meal the acc.ptabillty criserbn.
D5. SELECTING
THE SAMPL3NG
WHEN FORM 2 3S USED
PLAN
D6.4 Acceptability
Criterion.
Compare the”
estimated
101 p=rcent
defective p~ or pL
with th. maximum ●llowable percent de fcc ti. e M. lf pu or pL i’ equal to or le.. than
M, the lot meet. the acceptability criteriotx
if PU or PL is ~reater than M or U QU or
‘L
~S negative. ~h=n th= 10t do= C@ IIWCt
cn. acceptability
crxterior..
D5. I Master Samplirm T. bles. The ma.t.r
m.rnpling tables for plans ba. ed on vari. Iirnil
bilily knc.un (~r ● .ingle specification
● rc Table.
D-3 ●nd D-4 of Part IL Table
D-3 is used {or normal .ad tightened inspection and Table D-4 for reduced inspection.
The
D5. Z Obtainin~ the Samplinff Plan.
sampl.ug plan .onsi. ts c.{ ● ample
.iz.
●nd
maximum ●llowable perccnl
an ●ssociated
defective.
The .amplimg plan is obtained
from Master Table O-3 or D-4.
.137. SUMMARY
SAMPLZNG
USED
FOR
OPERATION
PLAN WNEN
FOffhf
steps summarice
The following
tO be followed:
the
OF
2 IS
Pro-
cedures
D5. Z.1 Sample Sise.
The .ampl.
.i=e ~ i.
.hown in the rnasler table .x. rreaportdine to
each s~mple .i=e code letter,
(1) Dele. rninethe .m’nple size code
cer from TabIe A-Z by ..ing the lot .ise
the in. pecliem level.
D5.2. Z Maximum
Allnr.. able P.rcecIt
De~ereent
fe<tive.
The rnaxirnum ● llowable
corr..
i~ve
M for 9UTIP1. ●.timalc.
poadkmg b tbe sample
●i.e meatlomed i.
r-wr~pb
D5.z. 1 I* irtdicated in the Colwn.
of the mseter
table corrempoadiag
to the
~PP1ic~hle AOL value. Tabl. D. 1 is acte, ed
from tbe t.pfar .armaf inopecfioh and frc.m
tbc bottom let tight.md tip.cuon.
Sunplirig plans for reduced Iamfmctima.are provided io Table D-4.
~T-BY-WT
CEDURES
(3) S4ect
st ramdom tbe .unple
of n
umits from the 10G irs. pect and record the
nma.ur.nmnt
01 the qualhty charutari9tic
on each umit of tbe ●empl..
ACCEPTABILITY
PROWNEN FORM Z IS USED 3
EXamPI.
D-2
far
.
complete
exunple
tbe sample
[5) Compute
the
( U- X}v/U ● . upper
Db. 1 Acceptability Criterion.
The de~ree
of con>ormae.ce c.f ● quality eha~aeterimtic
.pecifi. atio~ limit
with respect m ● .iagi.
.hdl
be judpd
by the prc=a
of ~~conformimg producl nutside tbe upper Or lm.er
‘S=.
and
(2) Obtaia plmr. from Mater
Table D-3
or D-4 by ●electing lhe ●unple ●i=e U. fbe
df.wable
perfbctor ., ●nd the mulmum
cent defeefiwe M.
(4) Compute
DE.
141-
;F%%%$;
%ai%
me-
X.
quality
index f2u .
t
cificatimn
limit
U
= (FL)v/.
If ● ,-*
i, .peeified.,
16) Determine the ●mtimsted lot prcasd
defective PU or pL fram Table D-5.
of thl.
precedure.
88
-——
MUA7D-414
11 Juoa 1SS7
(7) U the emthrmtcd lot percent de f.c UW* pU or pL im eqtml W or Ie*a ttmo tbe
maximum atlowable
percent defective
M,
cricerla~
the lot meata thm ●ccaptabiii.~
u ‘u h ‘rnesattve,
“
“ ““”=’
‘- let M
“ ad
‘f ‘4Z
QL
thea the
deem
the =ccopMbUitY
criterion.
EXAMPLE
&Ample
D-1
of Ca3ctiiiam
SiaCle Spec51ictii0a L%iitVariabiIlfy
Example
Information
Lint
—
Sample
2
Known V.riabitity:
3
Sum af Mes..rcmcnt.:
4
Sample
Sise:
Mm.
X:
630,000
ZXln
The Quantity:
I
7
Acceptability
CoLI. taat:
8
Acceptability
with k
Criter-
I
3.000
IX
b
NOTE:
—
Expluulion
Value Obtained
.
Speeificatioo
I
i- to be determined.
n
5
The lot does
Ne.ded
criterion
io
1
I
..
t(cw-n
60,500; 68,00(h 59.000; 65.500;
61 ,000; 69.000;
S6.000; 64.500;
with the acce?tabilitv
and rompliame
I
1
The ●pecif ied minimum yield point for certain ●t4el c~-ttags is 50,000 psi. A lot
of 500 item. im wubmicted for inspection.
lo bpection Level IV. normal Ia.poction.
The variability
. i. knowm te be 3000 p-i.
From
with AOL . 1.5S i. to be u..d.
SUPW9C
fhe
Table.
A-Z and D-1 it i- seen that ● mample of ●kc iO io re.autred.
yield point. of the ●unple specimen,
● re:
6Z,500;
6z.000;
I
Form
63.000
Llmlc (Luwer):
58,000
L
1.67
(X- L)le
mot meet
6J,000110
1.70
See T-ble
D- I
1.67 c 1.70
see Para.
D>.3
k
Compare
the =eceptabi3ity
(X- L)/.
critmriom, dnce
(X-L)!.
If ● ●ksie upper specUiCatiOn ltrrdt u i. SWen. tbeh compute
b d
compu~
it with k the 10C meet. the .cceptabiiify
lbequal to or greater tbui k.
I
I
I
89
(63,000-5.5.000)/3000
is le..
th=
~
tbe quaatlfy (U-X)1.
crit=rio.
if ( u-X)k
tm
i.
54flL-sl’13-414
11 Jumd 1957
E~LE
D-2
of Cafcuhtfonm
fkampfe
Single Specification
VariabUity
Example
L4mit - Form
2
Known
The specified mimimum yield poiuf f-r certain .teel casting. . . .in S8.000 psi. A lot
or 500 item. is submitted ror inspection.
inspection Level Iv, normal lnspectlon,
with AQL = 1.5% is to be u.ed.
The variability
e is known to be 3000 psi. From
Table,
A-2 and D-1 it is . ..cI that ● sample of ●ize 10 i. required.
.SuPpa. e the
are:
yield points of the sample mpecimen.
62.500; 60.500: 68,000; 59.000; 65,500:
62,000; 61 ,000; 69,000; 58.000; 64,500;
with the ●cceptability
and compliance
sample size:
2
Know. Variability:
3
sun-l of Mr.a.urerncIll’:
4
sample Me-
5
Factor,
b
sp=cific aliOn ~mi,
7
Ouality fnder:
9
10
‘m’”
‘f
n
3.000
c
6>0.000
xx
1.054
ltiwe r):
‘“1
‘L
Max. A1l.awabl, Percem Def.:
Critcrian:
(63.000-58.000)1
3,000
!.76
OL : (X- L)v/o
‘Crcent
Acceptability
with M
S8.000
f-
M
Compare
pL
The lot d~es not rn. e$ the ●ccepf.abifity criterion,
~E
630,000/10
63.000
TXln
v
“
Explanation
10
I
X:
is m be determined.
Value Obtaimed
biforr?mtirm Needed
Line
—
8
criterion
.054
3.927.
Se.
3.63%
See Table
D-3
S=. Par..
D6.4
3.92% a 3.63%
since PL is great=r
Table D-5
than M.
ff . sin
1. upper
.pecific.tion
Iii-nit
ff i. given.
the.
compute
the qu~lity index Qu =
defective PU. compare PU
(U. XIV . m lme 7 and ebtain the sstimale -f $he perceml
if pu i. ●qual 10.0. 1.*S than Mwith W. the 1.s rn. et. the ●cceptability criterion
F-
90
I
-------
. .
..-
.-
,’
1.64
8
2.7?
2.7?
2.81
2.88
1
8
10
14
x
5.,
M
N
‘E
15
11
6
2,77
2.12
2.59
2.96
2.97
27
37
.063
2.92
19
2..94
10
.10
.?.80
20
1=r~
2.63
7
2,12
6
J“
o
2.58
6
.?,69
5
2.5s
1
4
2.63
49
4
3
—
k
H
—
—
n
2.58
F
k
.06S
3
—
n
.04
G’
F
E
D
c
B
Sample 91*c
code letter
.
.10
k
2.65
16
2,71
42
I
1
I
I
2.30
2.62
34
.29
2.62
2.57
2)-
45
2.S4
1?
2.49
2.45
10
12
2.4s
2.3s
1
‘?
2.37
6
5,.,4
4
1
I
4
2,14
.25
I
I
t
I
I
2,41
31
~o
2.48
Z.4J
25
49
Z.41
2.35
2.31
2.29
2.26
2.25
19
13
II
9
8
?
62.2,
I
I
I
I
I
I
,
[
Acceptable Oua21ty Levalo (tightened lnopectlon)
.15
2.72
31
2.69
2.59
11
22
2.54
9
2.54
8
2.49
6
2.s0
2.46.
S
-1
2.39
4
1
.1s
[
[nklnklnkl
++”
a
ccepttble Ouallty Level? (norma2 Inopaction]
2.05
2.la
12
2.33
2,34
40
%4
.65
2.29
2.21
27
21
2.21
2.16
10
14
2,13
2.13
9
8
6Z.0*
5
.40
TABLE D-1
Matter Table for Normal and Tlghtenad Inspection for Planr Baoed on Varlablllty Known
(Single Specification Lkmlt-Form
1)
I
I
I
I
I
I
,
I
1,25
1.99
1.96
59
44
30
23
26
13
i ,00
2.18
2,11
2.14
2.12
2.o7
2.03
11 “2,01
10
8
?.‘“ 1,95
5
ak
,65
’
I
1.s6
1.s0
3
7
9
E
H
1
IS
13
11
9
7
2,50
4.00
1.70
1.69
1.67
I
I
t---
1.65 t
1.61
1.57
Acceptable O
El
61
42
32
22
10
1.56
1.53
1.51
1.49
1.45
1,48
48
6.50
1.51
I
I
1.29
1.29
I.Z~
10.00
109
82
55
1.11
1.15
1.13
1.11
1.01
.991
.9,9
,
I
t
]
Ill
[
I
I
I
1
I
,
When S~ptO
1.07
1.07
1.05
.964
,942
,924
.906
.877
.197
.,.28
k]ak
],
I
I
I
I
I
,I
147
Ill
75
27
24
..20
lb
12
8
,
.045
.841
.8I9
.737
.719
.706
.685
.649
.S84
.,,,
15.00
I
“1
I
I
3
I
I
I
site equa20or ●xctads tot
15.00
127
95
64
24
21
17
14
11
7
n
10.00
d
z
~~
*
?1
;.
=s
=-b-t=-,
20
lZI
Is
12
9
6
,
6.5o
!ty Lavelo (tightened Incpeclhm)
93
1.51
1.46
36
J,42
25
1.38
1.35
1.34
1.31
1.28
1.20
,.,,
1.38
70
1
I
Vlvlvlvl
kink
20
18
Is
13
10
8
5
4
n
.—
4<00
31ty Level# (normal Inmpeetim)
AQL VdUS* ●?E In Bercent dafectlve.
at cunplkag plm baZow●rrow, that ln, both aunple site *8 well amk value,
item in
nzuat be kmpected.
idol
1.50
1.28
1.17
1.09
v
5“ 1.$9
4
3
z
Z.50
Acceptable I
k
1.89
?1
2.04
65
Q
1.89
54
2.03
49
P
1.86
36
2.00
31
o
1.84
28
1.97
25
N
3.79
39
1.93
17
M
1.75
Is
[.09
14
L,
1.75
1.88
12
14
1.10
10
1.62
6
1.68
1.53
4
B
1.44
1.33
,?
J
1.25
v
z
1.72
K
I
1.50
nk
12
1.S6
l--
1.83
II
f
I!fi::v,r,
AI
——
—
I
--+-H%-
1,42
2
D
v
k
1.36
I
n
l==
I .00
2
c
B
Sample ●Ic*
code Ietlar
TABLE D-1-Conl[nud
Maoler Table [or Normal and Ti~htenid Znopectionfor PlarJI Based On Variablllty l(nown
(Single Speclflc.tlon Limit-Form
II
. ---
2.12
11
P
2.77
2.58
6
0
15
2.59
6
N
I
2.55
4
M
Q
2.ss
4
L
k
132.’
8
K
J’
}
.04
914
I
I
39
1
16
2.65
I
17
2.s4
2.49
la
2.59
11
Z.J8
7
2.50
2.37
6
2.49
b
7
2.34
5
2.46
2.34
5
5
Y..3O
2.19
3
4
2.19
k
3
n
2.46
r
k
.10
5
m
.065
a
1
34
G
r
E
D
c
25
Sample aico
coda Inttmr
D-2
*
2.23
2.25
2.26
2.35
‘k
7
a
13
z.41
2.23
6
19
2.14
2.07
3
4
2.07
1.94
1
z
knk
I
I
21
2.21
2.21
2.13
8
14
2.08
b
Z.13
2.0%
b
9
2.05
1.91
3
s
1.91
1.01
3
z
.25
n
.40
knk
II
.b5
I
1
1.b9
,.581,
1.42
1.S.6
z
3
1.3b
10
5
[.99
l.aa
I
II
II
b
1.86
1.7a
-=-H-i
=-l-=-i
3
z
Z
I
4*
F1
R
—
n
.15
ble Quality Levelo—
Msomr ~nbte for Reduced Zn8pectionfmr Plant Baiedon Variability bon
(Sinlle SpecUicaIlon Limit- Form 1)
TABLE
.
I
z
Q
P
o
N
M
1.79
1.84
28
1.?2
1.70
19
12
10
1.60
1.60
a
L
S
1.62
b
41.53
t.5j
K
J
4
9
53
1.44
1.33
a
G
E
.1
1.2s
k
a
n
1.00
TABLE
D-2-ConUnued
I
I
II
I
1
I
1.39
1.28
1.17
1.09
k
1.53
1.61
1.65
22
32
1.51
11
13
1.49
1.49
1.45
9
9
7
5,1.39
5
4
1
2
n
1.50
I
I
I
I
!
1.35
1.42
1.46
\s
25
36
1.34
1.31
10
13
1.31
10
1.21
1.24
42
1.15
29
18
1.13
1.11
12
15
1.11
11
1.01
9
8
1.28
.991
.919
.8.35
.755
k
6
5
3
3
n
51.ZO
I
!
4.0
.991
1.20
1.11
1.01
.936
k
“
6
5
4
3
2
m
2.50
Acecptable C2uaIityLevelt
..—
I
I
49
33
21
17
14
14
11
1
1
5
4
J
n
k
1.03
.995
.942
.9?.4
.906
.906
.877
.797
.797
.1?.8
.641
.573
6.5
Table {m Reduced kicpectbn f.? I?lan. Breed On Variability IGI.Wm
(Sin@Speciflcatlon
Limit -F.atm 1)
F
E
D,
c
B
‘Smple Siso
code letter
Masltr
:.
56
18
2.4
20
16
16
!2
8
0
6
.803
.770
.719
.706
,685
,685
.649
,584
.584
,515
k
=--l
n
I
1
:8
:s
.
kUL-sm-414
llJums 106?
Psrt n
DOUBLE
DE. sAM’PU?JG
PLAN
sPECIF3CAT10N
_
FOR
SP3ZC3SXATZON
the lover
Itrnlt. M4 by MU for tb= UPWr
limit. u one AOZ. i- ●ssigned to bath l~ltc
combined. demipte
tbe maximum A31.wable
p-rcerd defective by M. Table D. 3 is entered
tipeczton
and from
from the zop for uornuz
tbe bosom for ttghtened imopectdon. Sampli.s plans for redoced imcpeczion sre prOvided in Table D-4.
DO CfBCE
This part Of the Standard describma the
procedures f.r use with pftis for ● double
Specific-tiom
limit when variabttlty
of the
lot =ith reopact to the qtmfky c~rscteristic
i. known.
DE. 1 U.* Of SUnplimc Plan,.
TO determine
w%the r the lot meets the ●cceptability cri qu~i~
le.-ion with ?=*PCCX co ● XrtiCtIISr
characleri~
tic and AOL v’azuels). the applicable ●ampliag plan shall bc u.ed in accordance with the prwimic.nm
cd .$ection A, Gea eral DeacriptiOm
of SkrqdiW
Plmns,
md
those in this part of the Standard.
I
I
D9. SELECTWG
A sampling
.h.11 be selected
[0110-s:
THE
fMkfPLfNG
Lfb4ZT
D1O.
● nce
D1l.
DRAWING
Samples #ball
with parasraph
#.&-T-Y~O
...”
plan for esch AQI. .ake
from Tab)e D-3 or D-4 ●
.
..:
Table
D9. i Determination
Of S=mple
Sise
Code
Letter.
T he ●ample ● ma cade letter .bfi
b~.cte.d
[ram Treble A-Z in mecordamce
with paragraph
A7. 1.
--
U
L
“
X
.
D9. > Obtaining .sunpli.g
P1_
A ●unpliag
● 2*, d
M ● s80plaa Celia, mt, 01 ● ●mple
.dated maximum
aflowsble ~rc=m
defecPIti be ●pp3Aed Jo
tively).
The ●uf@ins
inspection
shall be ebtahed
from 3dmcter
Table D-3 or D-4.
m ito
.of
.unpte
.8Unut.*
percent
th4 Imr.
nppe?. 0rb04b cp*ctfication limits co~ta.d.
eerr*mpOndbs
fa
●ize memfiomed in parasrmpb
tb. sample
D9.3. 1. i. #ho_
in the cdunm of the W18mter
~Iv*
dafeectwe
for
for
table
eorreaponding
co tba
wdte(s].
K dKferemtAQLos
applicable
be selected
A7. Z.
T
In accord-
ACC~PTABIIXl%’
product
La estimated
D-5 wAzh Z& quality
by enterkg
M-x.
D 11.2 Computation of Quality lndice ■ . The
. (U-xwi e and OL=
qua3ity iadices
Q
(X- L)v/c. ●ball be ~omputed, where
D9. Z Master SamPlinE Table..
The maater
SUnpl-es
ier
w bs. ed on wuiabi3Itit
● r=
ity known for ● double cpecific-tti
T=bleD-3 and D-4. Table D-3 11 u~ed for
.O rmal amd tightened izupection ud
Tmblc
D-4 for reduced inspect.ion.
D9.3. 1 Sun
1. Si.e.
The ●unple
●i.e
#how.
=~ t e master
ZAb3e. eorrecpondlag
each ●unple
●txe code letter -d
AOL.
SWLES
D! 1.1 Accepi.bility
criterion.
Tbe degree
r.cleri~ tic
et conformance
al ● qutiltY c
with respect
to a do~le
sF&c Ification limit
al ~con.ihll
be judged .by tbe perce~
The ~TCeIIUSS Of Wafarmiog product.
PLAN
.IJaforzniq
I
OF
AQ3.
m
aa~isad
w
●xb speckficatlon Umlt. demtsuua th8 -tmmm tile-able
percent defective by ULIOZ
es
is
iis
is
ia
the upper specification limit,
limit,
the 10wer ●peeificmion
a facsor providsd in Table* D- 3 ~d
tk .unple
mean. and
zbe ksowm wariabifizy.
D-4.
nlL-s’nk414
11 JuIIe 1957
t, tbe 10I doe. rat meet tb. ●ce.pl ability .rit. ria. Zf either OL O* O“ or both
ar. ae*.U.e,
UMrI the 10; &e.
03%rpe.t the
●ccep3abUtty criteria.
athrwi.
Pi
+b
*=
s-Am
.Uew*Ie
‘P~z~ti
delceuve M. 25 p u equaf to or lea- 3baa U
ff
the Id meeb the ●ccep3abUIty crUeri~
p ic ‘re=ter
tbm M or if Of) or Of. or both
ml
meet
the
.,* Itapfive.
Umn the lot &es
acceptabffity criteriam
D12.1. Z Suna~ryef
OP erati.n of Sunplia
Plan. la caoe. where a .ingle AOLvtiue
~
~bliohed
for tbe upper and lower ●pacification limit cornbim.d (or a ●fwle quality
characterimtlc.
the tolZowinS steps 8umma.
ri. e th.. procedtwe.
to be u.ed:
(1) Determine
the sunple ●ise code
letter from Table A-2 by u.ing the lot .ize
and the in. pectioa level.
..
: D12.Z. Z summaryc.f operation ef sPlan. Za em=. wtmre ● diflereot AOL
-d
lower t~c.
~ctabliched
f., the “p-r
Aficatiom limit for a •in~le qtmii17 character .tcp.
. urnnmrime
imtic, tbe ;dfowtbe
prmcedurem fn be u.ed:
(1) Determlae
letter from Table A-Z
d
in.peetio.
level.
the ●unple ●k. code
by uefa, the 105.&e
Table
(Z) Select plan fr.am Mater
D-3 or D-4.
Obtti
tbe .unpla si.e n. the
factor ., and the rruximurn allowable perced defective M.
{Z] Select tbe san-tpliag plan front
Mate.
Table D-3 or D-4. Obtaio tb. ample
.ise tI .ad the I.cter
., eorre.podirq
to the lar~erof
lb. two AQLva3ue..
dal.
o
the maximum .U.Ywable percerit delecgive.
●nd M
corresponding
to the AOL
va
‘Y ue. for 1# e apper and lower specificatiea
limit.,
respectively.
of
(3) .%], ct ● l ra=dem the .am~le
n unit. from the lot; in. pect and record the
m... ttmeatat of tbe quality characcerimtic
on ●.cb unit of the sample.
of
13) Select at random the ●mple
n unit. from tbe 10C irIap. ct ●md record the
mcaauremcm
of the quality characteristic
on each unit in the .arrtple.
= (U-x)vl.
percent
D-5.
(4) COmpute the .unple
mean X.
(s) compute the quality
ad QL . (X. L)v/..
indicem Qu
lot
(6) Determine
the ●.tinmxed
defective
p . pu + pL from TabIe
(7) M tbe e. f.inuted lot percent defective p i. ●qual to er le.. than the maxi.
mum allowable p.rceas defective M. tbe lot
me. t. tbe acceptability criterion:
if p is
sreater than M or if Qu or OL o, both ● xe
=S~~V~.
tfI*n *let doa - not meet ~e
mccapc-bility criterion.
DIz. z
&w.r
Dlff8remt
AOL Values
.Sp.eUi.aUOO
LiInlL
for Upper
and
compute
tie .8mpIe
(5) Compute the q~ty
= (U- fov/. and CZL = (X- L)v/&,.
mean
. .
x.
indiee.
QU
@t
(6) Determine
the ●.tImued
p“ mud pL, correspond p.rceat
de fectl.es
ins to tha pa rc.af d. f.ctivec tie
tb. upper
and b.lmw the lower .pecific.tkm
limit..
Afmo d.te rmine th. combined percent de f.c tive p = p“ + p~
.
(7) u all three of tbe fallowing
cc,n-
i’ equaf
tbma
diuolta :
l.)
~u
to or 1...
%.
(b) pL i. mquaf 1. or lR.8
D1 2-2; 1 Aceap4abflUy
Crit9ria. 5 COirtfu*e
the ●stdnuted 1ot pmrc~t defeetivem m.. h
the cerro@omd4ng
PU dth
~
-a..=bI= Perta=t
de f==ttvew M
d
Mfj alao
=Omi=r.
P . Pfi + PU wittt k
larger d ML
mmdMu. lf pL sequmt taarle*attmm
ML. P
ic 9qtmf to or Ie*m tbul Mu. ad
p i. q A
to or lam than the larger of ML aad Mu,
criterk
the lot meat.
tbe ●ecepbility
—---
(4)
ffun
Mu
larger
(CJ p b equaf
of ML and Mu,
ts Or Ie*#fzlamthe
u. satiaficd, th. lot umato the ~C~tdiii~
criterk
other+se.
the lot does MC meet the
“’=~
or both am
“’’”’A’*
aesativ~
m..t tbe acc.ptiifiiy
tbeo ‘*’
*
criterb
lot%::%
.
bn~14
11*2ES7
EXAMP=
D-S
fsxanlpze of Cdcufat,ioms
DOEbh
sp4c3d&az10a ZAm2t
varhbmfy
Dm. AC3L Vahie for Seth Upper
E.mtple
@
XmOwm
&w.r
SpeeUiea320a
2AMA1 Combined
mitdmnun yield 3,0311u[m cemd.
steel rutimzN are
The ●peclfie.d maximum ad
67.000 p. i and 58,000 psi, rucpceUvel y. A lot of 500 items is ●tbmitted for impec tloa.
3nop.ct30n
&val
ZV. aornd
insPct3aa,
W3UI AQL
= 1.5% 1- to be ..4.
T&
?abka A-2 ●nd D-> it i. seem fzut a
variability
c is &o-n
to be 3,000 psi. Frati
.unpl.
of ●i.e 10 i. required.
SuPpu. e the yi.ld point. of the ●ample specimens
● re:
6z, SOO; 60,500; 68.000; s9,000; 65.500;
6z.000; 61 ,000; 69.000: 58.000; 64.500;
●nd compliance
lnIornutio.
Lb.
—
I
with the ●cceptability
criteriom
V. I.e
Needed
is to b, determined.
Obtaim.d
Explanation,
1
Sample
?.
Know.
3
Sum of Meaaurem6ats:
4
Sample
5
Factor,
6
Upper
7
Zmwer Specific=cion
8
QuaIity
Index:
Qu = fU-X)V/.
1.41
(67,000-61,000)1.054/3,000
9
Quality
Lufex:
Z3L . (~- Z.).1.
l.?b
(63,000-58.000)1.054/3.000
Size:
n
10
Variability:
Mean X:
3,000
o
ZX
630,000
sXln
63, o0O
v
630,000/10
1.054
Specification
Untie:
U
67,000
Limiti
L
56,OOO
10
Est. of Lot Percen:
Def. Above
11
12tc. of &t
D*I.
J2
TelaJ ~*t.
Pu + P~
See Table
D-3
pu
7.93%
See Table
D-5
IA P&
1.92%
See Table
D-5
U:
..:
PerccnI
P=r=e=t
D-f-
Max.
14
AcceotablI1tv
C.ite rioa:
pu + “pL with M
A310w~ble Percent
●
~
~~
P -
7.93% + 3.92%
11.85%
13
The 3ot doe
Below
not met
D.[.:
M
cmn~r=
.
Seo T*1c
3.63S
.n .
the ●ccepzcbiflty
11.85% > 3.63%
criterion.
da..
p = pu
See Para.
D-3
D13.4
+ PL io sreater
97
------
.. .
-—
than ~
um=slv-414
11 Jnne 19S7
EXAMPLK
Exampte
ml=
D-4
Cafcutatimu
of
sp0dfka3A9n
V.rkatduty
AQL. Vti.ss
Difiere.t
ZAmtt
KaOwt!
for Upp.r
&
lmwer
SpeeUicDtinm ZAmlt.
● re
The .pecified
maximum and minintum yield p0&39 for cer3mim oteel ca.tl~o
psi -d
58,000 psi. reapectivdy.
A lot d S00 item, is submitted for inspeeknspctinn with ML
= 1%. for the uPP8r aad
UO..
znspctko.
*CI
IV, uarnuf
The vari.bilicy
. is
AOZ. . 2.5% for the lower tipecificuiom
lkmit im m. be u..d.
Frern
Table.
A-Z ●d
D.> it i. ....
that ● .unple
cd ais.
kcuaw. m be 3.000 pi.
11 c~rre. poridir..g to the s.rnple
.ise code letter, 1, ●nd the AQL value Of 2.S% i.
specimen● re:
required.
S.ppc.. e the yield Pc.itis d the ●mple
67.000
6Z.500; 60.500:
64.000; 59,000; 65.500:
6Z.000; 61.000; 60.631; 68.000; 62.000; 63,000
with the ●cceptability
and cmnplisnce
Information
Lime
—
Size-:
criteria
Value
Needed
1. to be determined.
Expl-ation
Obtained
11
n
I
Sample
~
Kn~wn Variability:
3
Sum .f Me...
4
.%rnple Mean X:
5,
Factc. r:
6
UPPe r Specific atiort Lirnic
7
faw.
8
Quslity
Index
au
= (u-X)v/.
1.07
(67,000-61,648)1.049/3,000
9
Ou-lity
htdex:
QL
= (X- L)*/a
1.28
(61.648 -SB.000)l.0491J.
=.~
‘t
10
rernen:.:
67.9,131
Ix
678.131/11
61,64.9
XXIC.
See Table
1.049
v
r Speci[ieatiea
‘f
3,000
o
Limit:
u
67,000
L
58,000
D-3
u:
Pu
3.07%
See Table
D-5
Percent Def. Selow b
pL
10.01%
See T-ble
D-5
13.10%
3.07% + 10.03%
‘“’cent
11
E.1. of bt
17.
T.atal Cat. Percent
Pz.
Def” -’e
Del. h
bt:
p = pu +
11
Mu.
Allowabi.
Pe r..mt
Del. Abo.e
14
-
A31.wable
Pe rcest
De[. B=lmu k
15
Acceptabilit~
Criteriw
(al Compare
U:
(b] Compare
with ML
(c) Cemoare
with “ML
%
2.59%
Se.
Tabl.
D-3
‘L
s.60%
See Table
D-3
PLI
with Mu
The 10: dins. not meet
fied; i.e.. pu ●64U. pL > Mb
oOO
3.07s
~ 2.59s
-
PI.
10.05% > 5.60%
0
13.10% >5.609
the mccep~bUity
●nd p wM~
crIterl..
.tnce
15(a), (b) -
see Par*.
DIZ..Z. Z(7)(a)
see Para.
1312.Z, Z(7)lb)
s.. P.**.
D12. Z. Z17)(C)
(c)
● re
Dot ●*-
08
,:
-.
-.. .—
I
IJ
1
I
l!
,.
a
I
TABLE
D-fl;
J!LJ__
—,.
When ●ample ●Is* equdo or ●xe*sd*
Table for Normti ●nd Tightened Ioapectlon ~or Plain Bamadon Known Vtriabllity
(Doubla 5pec{flcatlon Llmlt and Form Z-Single Specification Llmlt]
AU AQ L id tabl~ who
● m In pmcaat defective.
● firm sunpllq
plan balow arrow. that Id, bath mmpsa 01*4 as well as M valua.
I:la.,
@v*r, ‘Mm ,. tba 10, rnu,tb. SrIlpocied.
Q
P
o
N
M
L
K
J
1
n
a
r
E
D
c
B
ImpI* -I*E
ode letter
—.
Matter
..—
lot
..—.
.—.
T
v
9 2.s9 1.061 10 ),63 1.054 II
1
6,48 I .007
6.46 1.00s 109
61 4.35 1.008 70
81 4.34 1.006 93
I.ooq
1.007
9 7..00 1.010 54 2,s2
5 2.00 1.008 11 ‘1.82
P
Q
A33ML
,~c::it
6.75 1.011
42 4.s5 1,012 48
3 2.12 1.o16 31 2.9~ 1.014
o
ct..
7 19.46
82
I ,004
9.73 1.003 I Z7 14.02
. . well .S M WIZ..
I
I
~
1.15s
v
1
19.90
I 47 19.84
[11
?5 20.48
56 20,90
30 21.77
31 Z2,51
21 u;i)
24 23,13
20 23,43
1.003
1.00s
1.001
1.009
1.013
1,011
1.019
1.022
1,026
16 23.96 1.033
12 24.88 I .04s
f5 2b.b4 1.0b9
6 28.64 1.095
4 31.01 1.155
v
M
4 33.67
m
13,00
When *ample ●IS6 Cqualc or •xceod~ lot
15.00
1.00s
1<008
1.010
1.016
1.019
1.022
1.025
1,031
95 14.09
9.76 1,006
64 14.s8
49 14.81
3~ 1S.61
39 10.93 1.018
Z4 16.23
21 16.71
17 17.03
14 17.36 1,038
Z1 16.z7
5s 10.17 1.Ooq
1.080’
5 Zo.ao 1,118
4 22.91 1.IJ5
z] 11.5b 1.023
42 I,).40 1.012
v
3 Z4.2Z 1.225
v
64
10.00
11 I 7.88 1.049
n
10.00
6.50
I
I
I
Accepluble Qu4Zlty Zmvela (tichtened 10spQcll.onl
4.00
hd tabla vaheo ●rt 18 percmt defective.
sampling plan bet.- .rrc$w, that f., both .unp,e
v-ry item In the 101muot bs hmpecled.
1.50
I
6.9S 1.014
32 4.68 1.016 36
2a 3.0! 1.OIE
s 2.19 1.02!
N
2.50
7.34 1.021
z?. 4.98 1.024 25
M
I
7.80 l.OZb
18 5,29 1.0,?9 Zo
1.038 1! 1.54 1.03s
—
—
1 2.3s 1.031 19 3.2$ 1,027
4 2.51
L
20 11.57 1.o26
1.72 1,029
1$ 5.34 1.035 18
1.045
14 3.43 1.038
la I l,n8 1.029
z 2.49
8,13 1.035
13 5.50 1.041 15
1.045
15 12.04 1.03s
K
3.61
9 12.88 1.061
6 13,s9 1,095
5 15,21 1.118
3 15.60 1.ZZ5
I 2.51 1.049
Iz
v
v
3 {1.14 1.ZZ5
M
6,50
12 12.35 1.04s
n
J
e.13 1.041
8.43 1.054
8.62 1.069
B.9Z l.lia
5,60 1.049 13
9 5.68 1.061 10
s }.b@ 1.069
1 2.’bZ 1.000
54
B
7 5,83 1.080
6 1.77 1.095
b 2.s7 1.093
G
5
5 6.05 1.110
4
*
1.155
4 2.s8
r
9.97 1.155
4
1
1.U5
3 2.76
E
4 6.99 1.155
v
9.27 1.414
M
3 10.79 1..?Z5
n
3 1.56 1.225
v
2
he
4.00
6
n
2.50
Acceptable Quality Level# [normal In#pectio,
v
?. 6.11 1.414
Mv
t Z.23
1.414
D-3-Con(lnued
?. 3.90 1.414
m
1.s0
D
v
“
1 .?.13 1.414
v
m M
1.00
TABLE
,.
Tcble for Normal and TI$ht~ned hmpectlon for Plma Baaed on Known VarlabIllty
(Doubl. Specllic8tl.m Umit -nd 5’orm Z-Single Speci[icztlm Limit)
c
B
mpl* 01:
oda ldtt
MmIar
...
.04
I
.065
[
.10
D-4
I
●s
well
.1s
●s
Acceptable (lualhy
AU AOL Ad Iabh VdUCi i?o in PO?CQ84dafactlvc.
I US* flrol mmPlkIs Plan hlOW ●rrow, that I*, both mnv.le slsa
{DISC, ●T*?F Itim k~ha lot mutt ba inspected,
Q
?
o
1!
M
L
2(
k
J
i
H
a
r
E
D
c
B
mph Dim
ode letter
TABLE
I
.25
M vahie.
Levels
.40
I
.&<
When mmplo tlse ●quala o? azewdc lot
I
Matter Table for Reduced Znopectlonfar Plan@ Based on Known Varhbllliy
fDmhlo Specillcmion Limit and Form 2–Single Specllicatl.m Limit)
. .. ——.
—
1.0699
1.05 4
1.04 s
1.87
3.81
5.77
l.be
3.68
3.63
L61
3.26
3.05
4
4
b
a
8
10
1z
19
28
1
J
K
L,
M
N
0
P
0
1.01 8
1.02 7
1.0699
1.095
1.155
1.15s
32
22
13
11
1
$
5
4
1.ZZ5
3.85
3
H
3
1.414
3.00
2
1
a
1.414
G
1
v
v
3.90
M
1
n
1.06
k
12
D
~.
B
Ssmplo BI*9
cod- lqtt@r
TABLE
D-4-Continued
4.68
4.98
5.58
5.6o
5.b8
5.68
5.0)
6.05
6.05
ACCI
1.016
I.O1O
1S.61
14.81
1,018 31
I.olz
10.93
10.40
—
I.oz 1 .?9
1.014
7.34
6.95
7.5
36
1.02 4
1.01 6
49
1.0,?$ Z4
16.71
1,029 z!
11..58
1.035 “18
8.13
15
i
1.031
17,05
17
1,035
12.04
15
1.041
8.13
13
4Z
1.038
17.36
14
1,045
12.35
IZ
1.05i
8.43
10
i
1.o38
17.lb
1.045 14
IZ.35
Iz
1.054
8.43
10
56
M
Zo
16
16
1z
1.049
17.88
11
1.061
12.88
9
1.069
5
8
8
1.080
19.46
6
ZO.80 ).11.3
8.62
?
5
4
8
1.095
1.118
1.155
1.080
11.89
4
7 I 19.46
6
1.118
8.92
15.Z1
4
lZ.91
1.Z25 i
13..59 1,095
5
1.155
9.97
1.ZZ3
15.bO
3
IJ.67
1.225
?.0.90
21.77
23.13
+
23.43
Z3.96
z3.96
24.08
t4.64
zi.b4
28.64
)l.O1
1.009
1,013
1.022
1.026
1.033
1.033
1.045
1.0$9
1.069
1.095
1.155
F
T
1.Z?.5
17.74
t
1.116b
)
1.2z5
10.79
II
J
“
1.414
T
9.27
M
2,50
.9.92
5
4
3
2
n
1.04 1
1.04 9
1.061
1.061
1.080
1.118
1.118
1.1s5
1.225
7.5b
6.99
1.414
v
v
6.11
M
1.50
.Mmter Tsb2e for Redue.d Zn*p.ctl.n lor PlarM Bated on Known Vsrisbllity
(Doub18 Specillcmtion Umit and Form Z-Single Specl{~cItiOn Umit]
.-. .
.
1
.
——
–-—
——-
D-5
TabIc for CotlmstInS the lat Percentage Defective for Plans Bared on tiowa Varllbilityl
TABLE
.
——
__
1,
Part Ill
ESTIMATION
OF PROCESS AVDLAOE
REDuCED
AND TIGNTENW
D 13.
~:S#fATfON
OF
PROCESS
AVER-
Th. ● ve rage percent defecti*e. baoed
UPOn A 8r0.P 0[ 10U ●tbmitmd for or~imal
in. pecticm, i. called Sbc proceaa average.
OrlgirIal inspection is the fir-t Inope.tion Of
● prticular
quantity 01 product .ubmitted
from the
[or .eceptahslity ● . di.tfngui.hed
in. pectian of product which ba. b=cm re. ub rnirted
after
prior
rajectimm.
Th. procea.
shall be ..tinuted
frc. rn tbe re. ult.
of i.. pe. tion of wampl. mdrawn from . ●peeifi.d
murnber of preceding
lot. for the pur-
●.eragc
pose of decermis.img severity cd inspection
during lhe tour. e of ● contract in accordance
with paragraph
D14. J. Any Iot. .htil be included OUZY once io e.timatitig
tbe proce. a
● ver average.
The estimate of the prec...
●t?. is designated by $u what computed with
limit, by
r.. pect to ● n upper ●pecific.tion
PL wb=n cOmp~t=d rnth r=~p=ct tO ● 10w=r
specification
Iirnit, and by p when cmnput=d
with re. pect W. a dc.uble .pecificaciOm Iimit.
D13.1
Abtmrrr,a) Remult,.
Th. re. ult. 0[
irmpectior. of product
manufactured
umdcr
conditions not typical cd tmual production.
shall be excluded from the estitrmted
pre cemm’ average.
A34D CRfTER3A
1NSPECTION
!. with Q
or QL 4
muted Y et perce,att
D13.?.. I SiI@.
Sp.cifieatlon
Z.lml% 6
The
estimated
1ot percent
dof ecu-e ●bal-1 b
deCennined
frarn Table D. 5 ter the plum hawed
O. bnowa varbbi3ity.
Tbe q-am3ityiadex Q“
hall
be us.d far tbe ea.. of aocJppr .pec iiic.tiom limit c,r QLlor
the c.. e of a 10X.
●pecifi..ticm
limit.
Table D-5 ii entered
6Wbem Form
the corr.
spondin~
.mti-
defective
Pu 0. P L. ?*spectively,
is read from #he ~bIe.
The
●verage pu i. the arithe.tinuted
proces.
metic m-u.
of the Itidi.idual e.timated lot
the e.ti percent defective. Pu’ ●. Sinaihrly.
nuted procems average p is the arithmetic
meof tbeiadividdemt~atcd
lot percemt
de fect%ve. PL’..
D13. Z.Z Double Specification
lAmit.
Tbe
e.cim.ced lot percent dciectzve ●hall be .determim.d from Table D-5 for the pluI. bm. ed
on variability
b.swa.
The quality Indic.s
0
and QL shall b. computed. Table D-5 ienY ered separately
with QU and OL ad- the
carre.pomding
pu snd pLare
read frOm the
The e.timtied
ict percemt defective
fable.
is p = pU + pL. The e.tirnat.d pro . . . . a.er ●ge p i. th= ●rithmetic rn.a.mof the individual
=atimsced lot percent defective.
p’..
D13. Z.3 Special Case.
U the quazity index
0,, or Q, ,s a nt~atm.e number. them Table
DY5 i..~~ter=d
by-di. regarding
the negative
si~n. However. io thi. case the e.timated iot
●bove the upper limit or
P. TC.nt defective
below the Jow.r limit i* obtained by ●ubtract ~~~~
Per==at=ge
found in the table from
AL
D1 3.2
Ccmputatiem d the Esf.inuted prcaverce. a Avers e. Th ● e.tmuted proce..
●ge M the ●r~thrnetic mean of tbe estimated
from
the
10t pe rcem def ●ctive computed
.unpling
itt*pecti.ma re.. tit. of the preceding
tea (10) low or S* may be .alhenvi. e d.miS ❑ated. In order to estimate the lot percerat
dsf.cti.e,
the quality kdicem Ou &\.ar
QL
●lmfl be computed for each lot. Theme ● re:
(3u . (U-X)WI.
and QL = (X- LWIO.
(S8.
paragraph
D] I. Z.)
~31
TXGZiTENED,
‘“ %%%dWPECITC)N
AND
RE-
This S$azidard e.tabli. ha. wampling
pl*rsh for normal,
tightened,
and reduced
i-peetioa.
D14. 1 At Start
of Inspection.
Normal in.pectiom SW
b. wed ● t the ●tart of inapec.
UOa IU13C.*Secberwim
de#$gm4ted.
D14.Z
OuriaS fn.xctiou
During the co.r ● e
uumction
shall be
of In9puctia,
-rmal
used when taapeecio.
cmaditioo. ● re much
tbt t6sht.nod O. redncad iaapection
is not
rqufred
fn accordance
with prmS.aphs
D14.3 and D14.4.
D1 4.3 Tight=imd 31Wpecttoa. Tiuhtermd tnSpectltl. .W1
be in. ututed wb. n the emti naat.d
proce. m ●verage
computed from’<he
crltariO=,
~h= a~tis~di=utia
d.tmit ti a-cd (0? Czu ue*ptabi3~ty
defective pzz or pL i. ❑ m ebtaiaed,
10 order to emtinmte the procems
●veraga, it ia aecea.~y
to eornpiete paragraphs D6. Z d
D6. S af hrm
2.
‘ra, .m~e.
ifQ . -.50and O = 1.60,thenpu
= 100IL - 30.854% = 69. J46%. pL = %4g%
~
P “ 69.146% + &S
. 74.6z6&.
rnste
Of
lot
~_~l.
percent
..-—
----
MUAID-414
11 Jftfld 10s7
!’
prece4iag
[e. (1OJ Iot# (.r much other smmwith
ber of lma demig=atedl in ●ccordmce
paragraph
D1 3.2 i. greaur
thaa the AQL.
and when more thao ● certAn number T Of
these 10ta ‘have ●stimmen of the percent
deiective exceeding ctaeADL. Tb* T-value.
are SiWeaI in Table D-b when tbe pr.acua
average is computed from 5, 10. or 15 lots. 8
Normal inspection still be reimtmted if the
.stinnted
pro . . . . ..erage
of Iota under
tightemed iiwpectio.
i, equaf tc.c.,lem. than
the AQ L.
Iesm than
i- Table
Caufitiom
●tcD4y rak.
c.
loumr limit
Pr0dmct50n
is
Nonnsf
impecthm *baff be retostate4
eondftiom
occurm
one of tbe foIlowing
redueed tic wctlon:
Condition
D14.4
Reduced fnsp=ctior..
Reduce4 bcpectien may be instituted provided that all
of the following cOndiliOn. ● re ■atisf ied:
D.
cbown
●
t
●
U my
tiad~r
A Iot-ic rejected.
. ..erage
fkradiiinm E. The estiunkd
i. ~re.ter
tbn the AQL.
irregular
Comditiom F.
or delay=d.
P.oductiom
plwJce~-
be=om.a
Dthe r ccmditiom
u
COtisti.n
G.
that normti inspection should
may wtarrwt
be reinstated.
Condition A. The preceding tea (10)
lots designated)
lc.ts (or such other mmnberof
have be.- under r.c.rrnsl i.. pecti.m -d
no.e
has been rejected.
D1 4.5 Sarnplin~ Plans for Tightened or Reduced k,C.~=CtLOIl.
S~PIIDS
Pl~S fOr *lghl e~ed and reduced inspection ● re provided in
Section D, Parts I and 11
Condition B. The e.linuted
percent
lots is
defective for ●ach of these preceding
I
10s
..
the ●pplicable
D-7.
I
TABLE
v.iu.
mof
D-U
T for Ti+t.oed
k+spsctbon
—
Sample
code
size
Acceptable
letter
.15
.25
.
●
●
●
●
●
.
.
●
3
5
6
3
5
6
3
5
7
:
7
.
3
●
3
4
b
3
.
:
:
4
6
a
4
b
9
4
7
9
—
4
7
9
4
6
9
4
7
9
4
7
10
4
.
.
.
●
c
●
.
●
D
●
●
●
F
.
.
.
G
H
1
J
K
L
I
2
4
5
3
4
6
3
5
7
3
6
7
:
8
3
3
3
:
:
:
4
6
8
4
6
8
4
6
8
;
4
7
9
●
3
4
b
3
4
6
3
5
7
3
5
7
:
7
4
6
8
4
6
8
4
‘1
,9
4
7
9
4
7
10
4
7
la
3
5
b
3
5
7
3
b
7
3
6
8
4
6
a
2
9
4
7
9
4
7
9
4
7
10
4
7
10
4
7
10
3
5
7
4
6
a
4
b
8
4
6
b
8
4
6
9
4
7
99
4
7
4
4
7
7
9 I.101
:
8
4
4
4
b
b
b
:
a 181819119101
:
8
4
b
8
9
9
9
9
10
10
10
10
4
b
a
4
6
q
4
6
99
4
7
9
4
7
9
4
7
10
4
7
10
4
7
10
;
10
44
88
11
11
t
4
7
9
4
4
4
4
4
4
4
1:
1:
1:
1:
1:
1!
l.:
I
I
44d
1:
,.5
—
.
B
.
i.e
—
●
.10
●
(in percent deft!,
1.0
1.5
2.5
●-o
.65
.065
.
tavels
.40
.J-t
E
OustIty
!
4
4
7
7
10110
444444
77
:1:1:
II
●
4
7
10
—
4
8
11
—
4
8
11
4
8
11
—
4
a
11
—
4
8
11
—
4
8
11
—
4
a
II
●
15.0
*
w
445
88
11
11
10
445
88
II
11
-++-
10
445
88
11
11
10
445
en
11
11
10
445
88
11
11
10
u
.There
are
no .antplimg
plMM provided
15
15
15
1s
-l-J-15
44=
a
445
88
11
11
+E
44’5
4
8
8
8
11
11 .11
—
Nu13160r
of bm
7F
10.0
10
Is
10’
15
in this Standard fer these code letters 8nd AOL.a3nOS.
I&
—
hfnATD-414
11 June 1951
TABLE
VAM.,
Sample
code
P
Q
I
●L.
letter
Accepmkle
.04
.065
4
7
10
4
7
10
4
1
10
4
7
10
v ●riab.bMc7 ~
D4-CmtJmd
of T for Tl@umd
Ouatlty
Lavelo
f519~Cti00
(in PC rcemt ttefe
.15
.25
.40
.b5
I .0
1.5
2.5
4.0
4
7
10
4
4
4
4
4
4
4
1
10
If<
1:
i!
17
4“
8
lJ
4
s
11
4
8
11
4
s
11
4
8
11
.4
.10
.4
1:
1:
4
1:
J:
.4
1;
1:
4
1:
The top rigure in cacb block refer.
to tbe precedi~
5 lot.,
15 lots.
preceding
10 lot. ●nd the bottom figure to the precedi~~
4445
888
11
11
10
11
the rniddlc figure
15
m the
Tightemed i.. pectiom i. rquir.d
wbem the aurnber af lotm with .stirn.tea of percent
defective ●bove the AQL from the preceding 5, 10, or 15 Iotm i. greater thaa the Eiven value
Of T iu tbe t.ble, and the proceos ●verage from th.. e lat. e=c=ed. th= AOL.
N]
estinutea
of the lot p.rcemt
de fectiws
● re
I
107
Obtaimed from
Table D-5.
I
4
:
I
~
●
*
●
●
*
*
*
●
●
●
c
D
E
●There
—
2(
● re
,028
,064
,09b
+
.051
.10’9
.1S
plant provided
.014
.036
.056
no aampllng
.008
.021
.033
.038
.092
.140
OZJ
0s8
090
.011
.011
.051
.006
.016
.030
J
4,453
6.5o
A
4.o45
6.342
6.50
1.3Z5
5.958
6.50
z.q37
5.69?
6.50
I
7.s02
10.00
A
1.093
10.00
J
6.114
9.806
10.00
5.154
9.330
I 0,00
4.386
8.049
10.00
1
1
5.009
6.50
A
4.909
b.50
A
2.758
3.987
4.00
2.89!
,4.00
A
4.719
6.5o
A
Z,643
J.94z
4.00
1
8.205
10.00
A
8.05s
10.00
a
1,786
10.00
i
5
5
10
1$
Is
5
5
10
10
12.848
15.00
A
12,693
15.00
A
~
12.427
15.00
5
5
[’015
5
10
10’
-L
12.054
I 5.00
&
11.470
15.00
A
1$
15
Is
IS
10.436 5
15.0010
b
1$
9.419
15.00
A
I 5.00
1.714
14.z91
I 5.00
*
15.0
V. fIablllI~ Known
TF
Z.40J
3.8JI
4.00
t.166
3.698
4.00
I
1.645
4.496
6.50
and AQL va5ue#.
1.641
2.449
2.50
1.562
2.412
2.50
1.461
Z.J59
2.50
1.326
z.Z17
2.50
%
1.1)6
Z.141
2.50
1.560
3.250
4.00
1.225
2.9z4
4.00
.631
1.64J
2.50
.046
1.880
2.50
.769
Z.354
3.850
.369
I,Z48
2.145
far lhe. e :ode letter,
.540
.908
1.00
.910
1.4z7
1.50
.85J
1.J94
1.50
.316
.892
1.00
.298
.549,
.b5
.15.9
.J13
.40
—
.171
.JZ6
.40
.3!7
.564
.b5
.718
1.346
1.50
.451
.252
.508
.65
.142
.298
.40
—
.847
,.00
.
.677
1.Z70
1.s0
.375
,773
,.00
,ZZ3
.418
.65
.103
.252
.382
.53J
I,IJ9
1.50
.Jz Z
.718
.00
.147
.385
.6OZ
.078
.Z17.
.347
in lhh Standard
,09 I
.18B
.25
.08Z
,177
.2s
.070
,164
.244
—
.030
.081
.129
018
0s1
082
.011
.011
.051
.004
.014
.025
I
,057
.147
.227
.02.?
.0b7
.114
013
041
071
.004
.017
.033
.002
.009
.018
.311
.874
1.194
.178
.5Z8
.867
.09n
.309
.5.22
,16b
.62Z
1.124
.086
.)57
.669
.045
.197
.384
.027
.222
.558
.011
.109
.290
.003
.050
.144
l-l .-1.0Z6
.093
.167
53”
.010
,052
.110
.005
.025
.056
.013
.049
.090
.001
.008
.01.9
.001
.004
.010
G
.002
.021
.064
.001
.009
.029
*
.021
.100
.204
●
.021
.2, ?2
.558 !
.
J
.011
.109
,209
.
*
—
C1. &litv Levels
1.0
●
●
.
●
.b5
Acceptable
,40
●
●
●
,,?5
007
027
055
4
●
J-
*
●
.
*
●
35
●
,15
,10
.065
code letter
.04
Sample size
D.7
Llmlto o{ Estimated Lot PerceIII D. f.c!Ivr ior Reduced Inspection
TABLE
*r
~~
II
1
,.
5
.277.
.392.
.40
.299
.41Z‘
b
.(41
.241
.2s
.1s0
.249
.25
.705
.994
1.00
m
All A(3L ●nd tsble vduec ~r; In percent defective.
*
.316
.40
b
A
A
.191
.25
h
3.Z7Z
4,00
1,959
2.50
.435
.635
.b5
1.113
1.50
i
.Z51
.38Z
.40
.017 .030 .049 .080 .146
.03Z ,054 ,086 .134 .232
.15
.04 .06S .10
?.25
—
10.0
1 .0
*
5.546
6,5o
5.310
6.50
5.131
b.io
A
8.0z2
10.00
A
8.516
10.00
A
8.3Z8
ko.oo
h
14.173
15.00
A
14.034
I S,oo
&
13.801
I 5.00
&
-
5
5
5
s
5
5
10
10
15
15
14
15
15
—
10
10
10
3u-
-1-
13.588
15.00
1
13-238
I S.00
A
1115
13,017
I+5.03
of I/As
Numb-r
AN entknmteoof the lot percent defective
● re
Obtained lrom ‘Table D-5.
Rw!uc813 impectkon may b- tnalituled when every emtlmaled lot percent defective from the preceding 5, 10, or 15 lot- in
bdow the flsure glvon In the table. fn addition, III c.ther conditiom for reduced impection, In Part 323of Sectloa D, must bc
dtiltfled.
bUmethe flrot fl#ure In dlrectlon of arrow and correepondin~ number of 10M. In each block the top (Igura reform to the
precedlm[ 5 lott. the middle figure to the preceding IO lots. and Ihe bottom figure 10 the preceding 15 lots.
*
N
T
3.093
4.00
1.821
2.50
ha,
I,o1O
1.415
1.50
.6zl
.959
I .00
.383
.608
.65
.211
.557
.40
.120
.Z14
.Z5
6.S
V~rIabIllty Knows
T
---1I
-1_
z.96Q
4.00
b
1.732
Z.406
2.50
.501
.934
I ,00
.348
.586
.65
—
.934
1.440
1.50
4.0
.191
.344
.40
.
.107
,203
.Z5
.
La C19
2.5
.-.
we u“alftv
.40
.,
Lat Percent Defective lor Reduced fnnpectim
D-7-Conllnued
“X
Llmlto of thtimited
TABLE
_——
=H
.
baL-sTD-414
11 June 1957
APPENDIX
D
Defhiflmu
Sz@!s!!
Def intt.io.s
Read
n
Sunple
x
.
X
bar
for + ●ingle lot.
site
S-pie
rnemn. Arithmetic
8 tingle lot.
mean of
● unple
rneawaremento
from
fbowa variability.
The predetermined
variability
of the quaf bow.
ify cbaract.ristic
which vill be u.ed rntb the .ariabifify
●cceptabfltfy plus.
Sigma
u
Upper specification
Iimtit.
1.
Lawmr ■pectficatian
limit.
k
The .ceeptabi3ity
v
A factor tw.d in determining
the quality
the bnowLI variability
acceptability
plan,
giv== in T~b10. D-3 -d
D-4.
constant
givem in Table.
Q“
Q
,ub U
Quality
Index for use with Table
D-5.
QL
O
.ub L
C3uality Index for use with Table
D-5.
D. 1 and D-z.
indices when ua ing
The v vafues., ● re
m
p sub U
Sample
estinute
.Table D-5.
0[
the Iot percent
defective
●bove
U front
PL
p ●ub 1.
Sample escinute
Table D-5.
of the lot percent
@ef.ctive
below
L fr.am
P
Total ●unple
M“
Maxdmum dfowable
given in T@bles D-3
Mu
M ●.b
‘L
M ●ub L
u
P
p bar
P“
p bar ●ub U
‘L
p bo
●ub L
Tbe ●mfimuod pw..s.
.Verq.
[*.
The estimated
average
for a lower
exceed
=1-
>
Greater
lor sample
defective below
Maximum ●llow.blcpercent
D-3 and D-4.
(For usawhen
different Mf)
L ●re ●~edfted.
Tbe maximum
Less
defective
than
tbM
process
eatimatea
applic~t~a
L.eom than.
Greater
than.
110
.-
1. @em
value.
defective,
ia Table.
U =d
for
i. e., the
-n upper Spectficstlom
●pecf3icatlon
unlit.
Umit.
pr.xeoa
●veragewhich
of emttnuted
given in Table D-6.
{For u.e indetnr Of ti8bt=n=d i=~p=ctiOa. )
number
tbe AQL
SLunof
.—.——
p = p“ + PL.
Maxfmum allowable percent defective ●bove U ~ivem h Table.
D-3 and D-4.
IForuce
when different AQf- v81uec for W and
L ● re spactfjed. )
may
<
percent
and D-4.
Sunpfe
ewtdnnte
Of the procemw merceut
amfimated procema average.
T
I
emfirnsfe .af tbe 101percent defective
----
----
I I
-.
,FOM d.m# thb lhn,
lFOM k-,
DEPARTMENT
Ih”
It”. )
n
OF THE NAVY
111111
No PGE?AOe
wscE!EEAmv
1S UAILEO
1947MC
UNITED
OFFKIAL
●ENALTV
●krJNE5
FOm ●RIv ATC USC E.100
BUSINE:SNOR~,P;~M,M,fi[&,
rlnsl CLAW
POSfAGE
WILL BE PAID BY THE DEPARTMENT
OF THE NAVY
Co@xuanding Officer
Naval Ordcmce Station
StandardizationlDocumen
Indian
had
, KO
20660
tatiop
Divieion
(Code
524
STATU
I
,.
DDa??”1426
. . ..
--?r
NOTICE OF
CANCELLATION
NOT MEASUREMENT
SENSITIVE
MIL-STD-414
NOTICE 2
2 February 1999
MILITARY STANDARD
SAMPLING PROCEDURES AND TABLES
FOR INSPECTION BY VARIABLES
FOR PERCENT DEFECTIVE
MIL-STD-414, dated 11 June 1957, and Notice 1, dated 8 May 1968, are hereby
cancelled. Future acquisitions should refer to an acceptable non-Government standard on
sampling procedures and tables for inspection by variables for percent defective such as the
American National Standards Institute (ANSI)/American Society for Quality Control (ASQC)
Z1.9-1993, ASampling Procedures and Tables for Inspection by Variables for Percent
Nonconforming.@
(DoD activities may obtain copies of ANSI/ASQC Z1.9-1993 from the Standardization
Document Order Desk, 700 Robbins Avenue, Building 4D, Philadelphia, PA 19111-5094. The
private sector and other Government agencies may purchase copies from the American Society
for Quality Control, 611 East Wisconsin Avenue, Milwaukee, WI 53202-4606.)
Custodians:
Army - AR
Navy - OS
Air Force - 10
Preparing activity:
Navy - OS
AMSC N/A
AREA QCIC
DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited.
NOTICE OF
CANCELLATION
NOT MEASUREMENT
SENSITIVE
MIL-STD-414
NOTICE 2
2 February 1999
MILITARY STANDARD
SAMPLING PROCEDURES AND TABLES
FOR INSPECTION BY VARIABLES
FOR PERCENT DEFECTIVE
MIL-STD-414, dated 11 June 1957, and Notice 1, dated 8 May 1968, are hereby
cancelled. Future acquisitions should refer to an acceptable non-Government standard on
sampling procedures and tables for inspection by variables for percent defective such as the
American National Standards Institute (ANSI)/American Society for Quality Control (ASQC)
Z1.9-1993, ASampling Procedures and Tables for Inspection by Variables for Percent
Nonconforming.@
(DoD activities may obtain copies of ANSI/ASQC Z1.9-1993 from the Standardization
Document Order Desk, 700 Robbins Avenue, Building 4D, Philadelphia, PA 19111-5094. The
private sector and other Government agencies may purchase copies from the American Society
for Quality Control, 611 East Wisconsin Avenue, Milwaukee, WI 53202-4606.)
Custodians:
Army - AR
Navy - OS
Air Force - 10
Preparing activity:
Navy - OS
AMSC N/A
AREA QCIC
DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited.