Qualiba Conlrod
aiaiklC:
XCE): variale thal, denole the, slle of lhe syler
ine t
al
S al inslask E. Tf Lhe systen Pails
hen X[l)=o otlerwife xCt)=1
XC:) =1, Vi ¬Cok f
Rll=P
o)
tine
ak
acbioning
Sis
that
(we vppse
MTTE:Mean
before the
of
durabion of fucbioning
int malluncElon
MTTE
KU)dE
E is delihed by
S is
&is
AL
tand
RCL)
We
hene
malunclo1ed
fonceionig
PlE)
AE
funclion
of
tmal
lhe valjo
the
At
is
MTTE=
K[t)=y>babilky »l malfunceiont hau
exprenedtg in
is
C
-6
Da:ore:
b
bime
MTBI (Meana D veperalle entit
(hallunckions
Mean time
YConsecueive
tine
onlojtJ.
exP(-[tntidu)
suppose
Conslad
bebueen
behrea l alfonckon
b/w lwo
y
tine blu Ehe malfuaclian
Ehe CK-) A"eAovel
tine vneil the Vtk yenovabion
the
KEhafruckiog
M) nvater of non delece ched conpeteuk oe meué L.|
WCU) num ber ot can poneaks ak Eine-t t hvins delele
sincet=o
bne t not haty
avl
Umberobconpoteads
n
-
Ngle) 3
Ce (W-1) Vepair
gin
d efeds
componendts had Lheir1t
duation ak
delece.
tshichi
duvobion ak uhiel
ebhelr
theiruyVepal
pas
i coamponesks
deleck
ave
s
conpatesk
whd i
duveion al
Cor bhe Pirt bame
-
VepairS o
ME7 1
o
the K
delece.
RCl)=
xi)
P
RCE) s r
a
N
.delect -K)
ACt)- P{ XIE) =1
N
pAbr}
system)
vepvajle
lon-
discvee systes
dherde: AC)=N
Omponents _inCe
1, VieCo»tJf=
=
iYed
aMantelablilé:
Theasuves tke Capa b\te o S to be Yepaived
.
MCE)= P(<<S is rpor Dn (»fJz7)
Lovk)>1).
MCE)= 1- PSis nat vepaivd
on
dan CoJ77).
MCt) = a1
M
d'scvde sysleas: M,CI E L
MuCl)=
of
MTTE)
dunkion
the
meashure
that
Con side Df a vaviable
Puackiing of ø
ieparttian forcbion of DS
Desilyol delect:
VCE)= d
GCe)dt
he
F(l)=P{Dfetf
1-l),
= eE 2
pobabiliaor
bh 1s deleek
MTTF= /VUdv--Jvd
dxevoke syder: MTTP= ~4
6t ini iol deled ()
Kakvo
A
lu
VE 77
(lbv
o
defecked
nok
gis
everl A E e
77.
+sk
bluELE
ad
ect
B:
.del
event
<e
p(2/A): ppbblila f evesk x s is delseled,hal
b/u
At Sepsan,cndition
it is nol deleded do o
Kalio
>7
depebion
Ct)=
PEla) = AAR)
PA
Ce)=
R-R. lat)
AE XRIlt)
dE
Rt)= Cxe-.
dis cyele Sycless; C-MCl)-NM1ol)
Depend abilikg afler vepairi
.discvete systeas
RuCl) = Aull)
N
altervesboorobin
delecl
MUTx: average time Until
MUT =
MUT=
ult=
Pudvpote: if thealovasl
La
Coe VefaC
dhll)
+6
dE
R'ult)=epltanlo) du
ull)=NatAllt+sl)
uE)AE
MTTR: Mean Time
Repeir
MTTR-/C1-Mv)dv
discvele syat en
MTTR=
tis dekined by:
on
t
blee
yepaired
donCat)7
is
S
delecdd
Conditian thol'S°is
ec
i s t =toA
MCE: 1- exrl-{ly)d
lrepairakian
u
yalia
TR=
then: MCt)= -EEL MT
Sppse
that
AC)=
ta
doesn"E hevea
E
delec bfu o
ASecdiz probeb:1'y thal
Calastro phique
leeAssoioti
S
is lormed obn compotert
S
Cof fa biiey
de/ect ofone
the
bl
Klt) We prpose
of theyest. Wes
ion
allecl the Pvtck
Compoes
Sens
hen lal
ia
ave
compoteabs
he
R:t))
does'E
rallel Assocation
syskem
Ehe
o
Puncbian
pYpse th tke campotenks ave dekeckecd-
tke
cohen the all
Survit
-RCt) = T(1-Rell
RIU=-(-RCU) LAGESTTON
UTTLISATTON DETAMTKEA
DES RE CHAN GES:
NDelinion naximua duvabon of suppla
delelivcnen t j
L
! Valio of
MTBF
:Vayiable
e< numberol deledst 77
Vaberofmax'mun defecks during
-V
PYbf.bili
deleds duving
non-breaMig =
ol
Ay:probabililkg
ere will be no
more
Me lhenmed cel Expreuons
=tprebitey
bhan
ht70
Dess a m e b e r s t Form } Bz0
:pavameLer
paronek
of scale 7 o
er 6fposikion-0
S< + %
bReporbin kuekton:
Fll=-e
zo F-1
Kenk For the cae, oibvtion
KP
onentia) ds
Parbeulor cae o We:bull
ATB
MTBE
Ralio 6f instontaniows deleckevinn Al) E
-Fl)
wrth t
B-
7
70
LAtenprrlakion:
slprces
ndependesk
P = ) KU)=e
t. che cko
EXUS: need Systemt
P
1 5 f e ,5 :labizve
3eY;
3
Corrosi on
donat'h
of plasbc debrnabion
S: P(t) is symaetric, ditkvibubion is
ecl oYma72
d Expecbabio
E ) =Y+1f[H
euler FvaCti'on
MTBF e
t?
A-
4 w)
ariance: v(t)= q2T(Hdis per sion:
B
=t
RCe)=E*
L)-(
o = + (olo5)"|
B
A
8X4C,
Kemor
the pannete- B i's wi thovt dianenSion
g
Tne payaneler i n ine units)
b/ E=a
i's, tofelgurvvd
re
2
0
T
h
e
-if
E= r
the
ak
beqbn
-
The delecls
iF Y= 0 orin
of time
le
bekre
preent
decbs aye
The
CCE)
e
Oviginof Eiu e00
70
t
7A The S cde perame ter 1
vace Cl) wilh
la ie vaiks/
=FI
(tIABy E.e
devide qvea
Vemains vndenjed.
is mellplied by 5
Cuvve
wil
5
to:
Y
=ayes
V=
Y-LLny
BXC
X=lole-
C-Rlag
Preporak ion ol Given
2t--t3 /
ifN7F)- Ne5o,
.iNelo F)=-o3
N+o1
hd
uith
Esthe e s
the axts Lat
h e st-line d
A w A hi te
line
lo ind P wedvav ,shin
ne gives B.
a
Qualik ConErol
Nome nclalue
SL omps
A Fieldassembly of pawer bailers
C- Clectric boilers
Hcaling boilers sleel plake o r Cast iran secliotol
HV-Pealing baler salely volves
healerstwoler
ined
EsL
poloble
HUW-
M- Minia -uve boilevs
N- Nucler power plont Componens
NPT
Compoten parbiolsr
1
NA
NVPP
in Sulakion asSembly
Solel valves
Yesuve pipig
stc pvessure VeSse ls.
Ke
plo
inhovted
RP is3skant
Rtp- Rehforted thevmosel ploclic Corvesion
eqUi pmen
S-Power bolers
U,VE,y3 - Pvessuve Vessels
UP Kupkuve disc devices
UM- Miaiotuve pressuve Vesels
UV- PressuVe Ve sselsalels vol ves
UV3-Hgh presure Vessel salelyva/ves
V- Boile r salely valves
mx +b
M=
b=
S
the mean
=
-1/1
Sanple
bion L j
obSerw
in lhe sayfe
bhe Aumbe of obsevation
=
i=l).
standord devielion ob
X)x* a
=[7)
axK
-
MeonBr) Chorts:
LC
VcL
=
C
X
slalis lie
Sanduvd deviabion: A
avound the mean
of dola dispevsion
Lhak meas uwes lhe aar
a
lovgesl anddala.
by the
The, dilerene
of
Delintion3 Range: Smalles
obsevrva tions in Sel
where
R-a
LPS Ce)
C
2=
x'+y2
=
Sulsbial qvalilycanbol
MolEipy b
aox+01x+
Polynomial Kegesion g
nol
at-6)=
2ax + 7b+ (nt-
Cirele of bestl
uheve
= = the avevage o! gample means
Z
6
SLandovd novmal ovioble (2 brg5-4Y713
Fo 93. 71%. Canlidence)
slandovd devialion ol lhe distribolion
=
oSanple means Compuled as 6/V
=Somple
Populalion (prcess) Sland. deviel
=
VCL
LCL
size
=
whev
+AeR
- ArR
K
=
avevoge Vange o
A= faclor
o
Samples
bbined bronbelle
ARonge (P)Chavkse
CL = R
LCL P P
&p3 ave obloined Frm
D,
volues lo
wheve
tole
A P-ChortS: A conlol chorl thot moni tors Lhe proporlion
or
delecls in a sample
UCL
P +7 6r
LCl
=
where)
P
where
P-zp
deleckiv
=
the Sanple proporbion
deviolion ol lhe slerdard
Lhe Sslandayd
6p preporeion
ddecbive.
-P)
AC-Chaytsz A control chorl used tomottor the 1e 92
of deleces pev Unit
7 VE
UCl = c
ocess (apolilil:
Cp
zT
C
LCL
=Sralie jL =
-1SL
PYoCess width
Cr E process copo bilikg indexr
inlerpvetolion (pz1 process is minimoll apable
o
bic
7 u not copoble
P E l D11
pocess ex Cecds mnimal
PzL
Capo bilit
al the mean:
ceatered
a precess whch i nol
CP
min USL-A
A
CP
36
AE Ue mean
o
F Lhe process
associoted
ol
lily
que
level
A
hih
Sir Sgma qvalita
de/eckie parts Permilliot3.Y
Ximately
with appro
or chancc o
pvobebi1:
shous
thal
Lhe
lol.
OC curE Aavnph
ol dekects in the
ovious
GCCplinga lot given
preporlians
SUes
S m o l . defecls Lhok Con
Gye
uillig
.#OL: The
of the 7
in
Upper
deleclive(LtpD): The
lolerale.
lolerente
peytcnl
Lot
o
A
deleclive items
casUmes
aye willin
o
pvaprlion
expected
The
qualilg(A0a):
Under he
Avevage oulgoing
evstdCusbaner
to
lhe
Pac prob.ofocc.03
uill be pacsed
lhal
defeceive ilcms
Ao0=P-PM)
Soopliag plan
sanygleSiZe ChoStn
eso
=Lle
isel u
0
