A COMPARATIVE ANALYSIS OP VISUAL LAYOUT
TECHNIQUES A S A P P L I E D TO MEDIUM S I Z E J O B MACHINE SHOPS
A
THESIS
Presented
to
the F a c u l t y o f the D i v i s i o n o f Graduate
Georgia Institute of
In Partial
Technology
Fulfillment
of the Requirements f o r
Master of Science in I n d u s t r i a l
the Degree
Engineering
by
Earle I s r a e l Denenberg
June
Studies
195^
A COMPARATIVE ANALYSIS OP VISUAL LAYOUT
TECHNIQUES A S A P P L I E D TO MEDIUM S I Z E J O B MACHINE SHOPS
Approved:
7^
XP—
Date Approved by Chairman; A / / ^ y
—
3/\/S>.S<&
ii
A CKNOWLEDGMENTS
F o r his guidance and a i d in p e r f o r m i n g t h i s
study,
I w i s h t o t h a n k my t h e s i s a d v i s o r , P r o f e s s o r W i l l i a m N «
Cox, J r .
I also wish to acknowledge the
statistical
assistance rendered by D r . Joseph J . Moder, the
c r i t i c i s m s offered by the rest of the reading
constructive
committee,
and the help p r o v i d e d by D r . Joseph E , Moore on p s y c h o l ­
ogical
aspectso
F i n a l l y , I w i s h t o r e c o g n i z e my w i f e ,
Doralee, not only for her c l e r i c a l a i d , but f o r
t e c h n i c a l a s s i s t a n c e as w e l l «
her
iii
TABLE OF CONTENTS
Page
ii
. . . iv
v
vi
ACKNOWLEDGMENTS
LIST OF TABLES
LIST OF ILLUSTRATIONS.......
ABSTRACT
Chapter
I. N
I TRODUCTO
IN
1
Srta
emof
entRof
hrechProbe
lm
A
eta
eseta
II. LITERATURE SEARCH.
k
III. JOB SHOP DEFINED. *
li|
IV. EXPERM
I ENTAL PROCEDURE
17
V. EVALUATO
I N AND RESULTS
28
Q
u
a
n
ttiitta
ttiiv
e
Analytsiss
Q
u
a
n
a
v
e
Resul
Qual
Analytsiss
Qualiittati
ativ
ve
e Resul
VI. CONCLUSO
I NS
38
VII. RECOMMENDATO
I NS.
i|0
APPENDX
I
A. A
CM
ON
D
E
NA
SN
EC
D
FOR
M
OEFRSTHEPRO
AM
ESR
C
IDANCOS
O
CE
I TY
O
F
E
C
H
I
A
L
E
N
G
N
I
E
P
O
E
D
E
FOR STANDARDZ
IN
I G LAYOUT NOMENCLATURE
B. EQUP
IMENT LIST - GV
I EN CONDT
IO
I NS
l\$
C. PROCEDURE DATA
±
i9
D. DATA EVALUATO
I N SURVEY AND COMPUTATO
I NS
59
E. SAMPLE CALCULATO
I NS
76
Bibliography
•««••«....
... o • ....<,
o o o 81
0
IV
LIST
OF
TABLES
TABLE
PAGE
1 •
MACHINERY
INDUS TRY
2.
PLANT
3.
COST A N A L Y S I S . . . . •
II.
TIME
5.
FLEXIBILITY
6.
DECISION
7.
SUMMATION
8.
STATISTICAL
.
LAYOUT COMPARISON
•
C H A R T . . . . . . . .
2
O••<»••
11
O
ELEMENT..
«
30
*..
THEORY EVALUATION.
OF DATA
EVALUATION.«
TABULATION
29
31
«.
33
« • . . « .• O.
36
36
V
L I S T OP ILLUSTRATIONS
Figure
Page
1.
Sketch of Machine Shop . . . . . . • • . < . . .
2.
Rough S k e t c h o f F l o o r P l a n and P r e l i m i n a r y
E q u i p m e n t and F a c i l i t y A r e a s • • • < • < ,
••••«••
22
3.
Method I - D r a f t i n g
21+
ij..
Method I I
- Templets
5.
Method I I I
- Models
6
Method I V - Templets and M
0
»•
»
18
«,
25
»••••••••
o
d
e
l
s
.
o..
26
•
27
v i
ABSTRACT
V i s u a l
i n
l a y o u t
a p p l i c a t i o n
t o
l a r g e
e n t e r p r i s e s
w h i l e
t e c h n i q u e s .
The
w h i c h
s e v e r a l
b e s t
o r
o f
t h e
s a t i s f y
t e c h n i q u e s
s c a l e
s m a l l e r
p u r p o s e
t h e
o r
g e n e r a l l y
m a s s
o f
t h i s
r e q u i r e m e n t s
h a v e
t h e s i s
o f
o f
i s
t o
t y p i c a l
l i m i t e d
t y p e s
s e l d o m
o f
u s e d
s u c h
d e t e r m i n e
s c i e n t i f i c
a
b e e n
p r o d u c t i o n
e n t e r p r i s e s
t e c h n i q u e s
l a y o u t
w o u l d
j o b
s h o p
l a y o u t
m a c h i n e
s h o p
was
r e - l a y o u t .
S p e c i f i c a l l y ,
s e l e c t e d
a s
t h e
a
a r e a
medium
o f
s t u d y
t h e
medium
s i z e
j o b
s h o p ,
a c c o r d a n c e
w i t h
t h e
d e f i n i t i o n .
p e r s o n n e l ,
a r r a n g e d
a n d
b y
e a c h
t e m p l e t s
f i r s t
a n d
t e c h n i q u e
m e t h o d s
i n
t e c h n i q u e s .
i n i t i a l
q u e n t
t y p i c a l
o f
f o u r
s h o p
The
was
a s s u m e d
d u p l i c a t e d
p r o v i d e
a
u s i n g
b a s i s
p r o v i d e d
a
s t a n d a r d
s e q u e n c e
t o
m i n i m i z e
l e a r n i n g
s h o p
t e c h n i q u e s :
f o l l o w i n g
o p e r a t i o n s
(1)
c o s t
c r i t e r i a
f o r
o f
t h e
l a b o r
w e r e
t h e
p r o c e d u r e
f o r
o f
m a t e r i a l s ,
o f
was
m o d e l s ,
b y
t h e
o t h e r
o f
t h e
d u r i n g
c o n s i d e r e d
e v a l u a t i o n
a n d
shop
c o m p a r i s o n
l a y o u t
o r d e r
t h e
o f
r e c o r d
i n
c o n d i t i o n s
o b t a i n e d
d e t a i l e d
l a y o u t s
o f
o f
e a c h
i n
t e m p l e t s ,
l a y o u t
w e l l
d e f i n i n g
s e l e c t e d
f a c i l i t i e s ,
f i n a l
e n t e r p r i s e
A f t e r
m e t h o d s - - d r a f t i n g ,
m o d e l s .
t o
t r a d e s .
W i t h
a n d
t y p e
A
The
j o b
a
t h i s
w o r k i n g
e q u i p m e n t ,
was
t u r n
m e t a l
j o b
s i n c e
t h e
s p a c e ,
s m a l l e r
s i z e
r e p r e s e n t s
i n
h a v e
t h e
t h e
s u b s e ­
e f f e c t s .
s i g n i f i c a n t
l a y o u t
(2)
t i m e
vii
I
required to accomplish layout,
i n terms o f a d d i t i o n a l
(3) f l e x i b i l i t y o f t h e
labor cost and time f o r
layout
re-arrangement,
(!+) e d u c a t i o n a l l e v e l r e q u i r e d t o p e r f o r m t h e l a y o u t ,
(5)
mental a b i l i t y required by the layout technician,
(6)
p e r c e p t i o n and u t i l i z a t i o n
technician,
a n d (7)
a t t a i n e d by the layout
d e c i s i o n i n f l u e n c e on management•
a n d (3) w e r e e v a l u a t e d q u a n t i t a t i v e l y ;
were a n a l y z e d s t a t i s t i c a l l y
naires distributed
Factors
space
(1),
the remaining
(2),
factors
from data obtained by question­
to Industrial
engineering
graduate
students and p r o f e s s o r s .
W i t h i n the scope o f t h i s p r o b l e m , the conclusions
t a i n e d d i d n o t s p e c i f y a n y one p a r t i c u l a r
universal application
to
technique
job shop o p e r a t i o n s .
ob­
for
Instead,
it
was d e t e r m i n e d t h a t t h e m o d e l t e c h n i q u e was b e s t c h o i c e w h e r e
t i m e l i m i t a t i o n was t h e g o v e r n i n g f a c t o r , w h i l e t h e
t e c h n i q u e was p r e f e r r e d w h e r e c a p i t a l
minimized.
templet
I n v e s t m e n t had t o be
Where time l i m i t a t i o n and c a p i t a l
are o f approximately equal importance, the
expenditure
statistical
a n a l y s i s designates the model technique as p r e f e r a b l e .
One r e c o m m e n d a t i o n i s p r o p o s e d as t h e r e s u l t
r e v i e w o f the space p e r c e p t i o n d a t a .
The r e s u l t s
review tend to indicate that the q u a l i t a t i v e
of
of
the
this
evaluation of
this f a c t o r is acceptable; however, the development of a
quantitative
e v a l u a t i o n , in accordance with the procedure
g e s t e d , would e s t a b l i s h the f a c t o r more d e f i n i t e l y .
suggested t h a t the f a c t o r o f space p e r c e p t i o n and
It
sug­
is
utilization
b e
d e f i n e d
f e e t
o n
t h e
m o r e
a c c u r a t e l y
e v a l u a t i o n .
i n
o r d e r
t o
q u a n t i f y
i t s
1
CHAPTER
I
INTRODUCTION
Statement o f t h e p r o b l e m . - " I n d u s t r y has been constantly
exposed to discussions o f research on t h e applications
of visual layout techniques and their
r e l a t i v e merits as
applied to large scale o r production type
activities
0
Attempts t o apply s c i e n t i f i c layout procedures to the
a
s m a l l e r i n d u s t r i a l a c t i v i t i e s and j o b type shops
have
g e n e r a l l y been neglected o r discouraged u s u a l l y because o f
preconceived opinions o f impracticability and excessive
expense.
I t is the purpose o f this paper t o present a
comparative analysis o f representative visual plant
techniques as applied to a job shop.
shop has been chosen as t h e s p e c i f i c
this research.
layout
A medium s i z e machine
design l i m i t a t i o n f o r
Theobjective o f the investigation is to
determine t h e most e f f e c t i v e method o f l a y o u t f o r a t y p i c a l
machine shop.
A r e a o f r e s e a r c h . - - S i n c e l a y o u t i n t h e j o b shop has g e n e r a l l y
received only casual attention from the industrial
engineering
p o i n t o f v i e w , a n a t t e m p t w i l l be made t o show t h a t a t l e a s t
a
T h e 1951 U n i t e d S t a t e s Bureau o f Census r e p o r t s
t h a t e a c h o f 2 1 6 , 0 0 0 m a n u f a c t u r i n g e n t e r p r i s e s (90 p e r c e n t
o f t h e t o t a l ) employ 100 persons o r l e s s , w h i l e t h e r e m a i n i n g
2l±,000 e s t a b l i s h m e n t s e a c h e m p l o y m o r e t h a n 1 0 0 e m p l o y e e s .
M a n u f a c t u r i n g e n t e r p r i s e s o f l e s s t h a n 100 employees a r e
usually classified as the smaller businesses.
2
one
o f
p r o v e
the
s e v e r a l
f e a s i b l e
shopo
To
p r o b l e m
s e l e c t e d
C h a p t e r
t w e n t y
I I ,
t o
t h e
The
m e d i u m ,
a n d
v a r i a b l e s
o f
s t u d y .
s i z e
j o b
w i t h
a
S t a t e s
t r a d e
w h i c h
e n t e r
j o b
m a c h i n e
B a s e d
i n
a
i n t o
j o b
a
s h o p
was
d e f i n i t i o n s
w o u l d
e m p l o y
m a c h i n e
t o o l s
n u m b e r i n g
the
T a b l e
s h o w n
t h e
m a c h i n e r y
i n d u s t r y
a
a s
i n t o
1 .
i n
w h o l e
i n
f r o m
f r o m
1 . ,
M a c h i n e r y
D i s t r i b u t i o n
Number
o f
E s t a b l i s h ­
o f
n o t
c l a s s i f y
d e t a i l
the
B u r e a u
( e x c l u d i n g
e m p l o y e e
d o e s
f i n e
b e t w e e n
H o w e v e r ,
s t a t i s t i c s ,
T a b l e
C e n s u s ( 1 )
s e p a r a t i o n
s h o p s .
d i v i d e d
o f
s u f f i c i e n t l y
f o l l o w i n g
E m p l o y e e s
o n
w o u l d
s h o p
B u r e a u
i n t o
d e f i n i t e
l a r g e
i s
l a y o u t
a p p l i c a t i o n
s i z e
t h e
m a c h i n e r y )
f o r
p l a n t
s e v e n t y - f i v e .
s h o p
make
v i s u a l
medium
p e r s o n s
U n i t e d
m a c h i n e
a c t u a l l y
a r e a
a
medium
f i f t y
to
many
t h i s ,
t h e
o f
s a t i s f a c t o r y
t h e
a s
f o r
t w e n t y - f i v e
t h e
and
l i m i t
s u c h
m e t h o d s
s m a l l ,
h a s
to
to
p r e p a r e d
s h o w
how
e l e c t r i c a l
groups©
I n d u s t r y
Number
o f
E m p l o y e e s
m e n t s
1-9
10-1+9
50-99
100-1+99
500-999
1000+
T o t a l
Number
3 3 , 8 8 3
1 2 8 , 6 5 7
9 3 , 6 2 9
1 , 6 9 6
3 7 0 , ^ 8
322
226,li+8
290
6 9 2 , 5 5 8
1 7 , 9 0 6
1 , 5 4 5 , 3 2 3
3
THE MACHINERY INDUSTRY IS THEN BROKEN DOWN INTO
SEVERAL CATEGORIES, ONE OF WHICH IS THE MACHINE SHOPS.
OF THE TOTAL MACHINERY INDUSTRY, THE MACHINE SHOP DIVISION
HAS 3»H2 ESTABLISHMENTS AND 58,160 EMPLOYEES, OR 17 PER
CENT AND 3«$ P©R CENT, RESPECTIVELY. THE RATIO OF ESTABLISH­
MENTS TO EMPLOYEES IS FOUND TO BE SIGNIFICANTLY HIGHER THAN
IN THE OTHER CATEGORIES, INDICATING THAT MORE SHOPS WITH FEW
MEN PREVAIL IN THE MACHINE SHOP TRADE THAN IN ALLIED MACHINERY
ESTABLISHMENTS. THIS WOULD LEAD TO A GENERAL CONCLUSION THAT
MACHINE SHOP ACTIVITIES PREDOMINATE IN THE 1-100 EMPLOYEE
CLASS ALMOST EXCLUSIVELY, WHICH THEREFORE ESTABLISHES THE
AREA OF MACHINE SHOP PRACTICE.
CHAPTER
LITERATURE
The
II
SEARCH
subject of s c i e n t i f i c plant layout is
rela­
t i v e l y new to t h e f i e l d o f i n d u s t r i a l e n g i n e e r i n g .
Its
a p p e a r a n c e became e v i d e n t d u r i n g t h e s e c o n d q u a r t e r
of
the t w e n t i e t h
century.
Practically
all
the
pertinent
l i t e r a t u r e u n c o v e r e d was c i t e d i n c a s e h i s t o r i e s
forty
selected periodicals,
o f some
which excluded s e v e r a l books
w r i t t e n during the past eight y e a r s .
exceptions, the reference material
W i t h one o r
two
dealt only with
layout in production type enterprises
plant
o f medium and
large
s i z e w i t h 100 o r m o r e e m p l o y e e s *
The p r o b l e m s e n c o u n t e r e d t h i r t y t o f o r t y
years ago
l a y i n g out a p l a n t are c l o s e l y a l l i e d to the problems
present day i n d u s t r y .
with advancing
W i t h t h e a d v e n t o f mass p r o d u c t i o n ,
the introduction
of
However, the methods o f s o l v i n g
problems have changed s i g n i f i c a n t l y
o f the automobile
these
technology.
synonymous w i t h
In the early part o f
the
t w e n t i e t h c e n t u r y , a change s t a r t e d to take place in
the
layout procedures of factories.
for
machinery tapped from a central
N o l o n g e r was p o w e r
line shaft;
no l o n g e r
machines and benches permanently p o s i t i o n e d ( 2 ) .
ing knowledge and i n t e l l i g e n t a p p l i c a t i o n
in
The
of safety
m o t i o n and time s t u d i e s , and economic p l a n n i n g ,
to
were
increas­
procedures,
mention
5
ONLY A FEW FACTORS, INCREASED THE IMPORTANCE OF BETTER
LAYOUT PLANNING TECHNIQUES.
THE DEVELOPMENT OF PRODUCT AND PROCESS PLANNING,
WHICH WAS EVIDENCED BETWEEN 1920-1930, MEANT THAT THERE
COULD EVOLVE MORE THAN ONE OR TWO SOUND LAYOUTS FOR A NEW
OR REMODELED FACTORY.(3) IN THE EARLIER DAYS OF THE SMALL
JOB SHOP, THE LAYOUT WAS USUALLY left to THE EXPERIENCED
JUDGMENT OF THE SHOP OWNER. THE OWNER, WHO HAD THE ABILITY
AND INCLINATION TO EXPRESS HIS THOUGHTS ON PAPER IN THE FORM
OF ROUGH SKETCHES, WAS SIGNIFICANTLY MORE EFFICIENT IN HIS
PLANNING THAN THOSE WHO COULD NOT DRAW OR THOSE WHO HAD A
LIMITED KNOWLEDGE OF MACHINE SHOP PRACTICE.
AS SHOPS GREW INTO FACTORIES, IT ALSO BECAME INCREAS­
INGLY IMPORTANT TO APPLY SOUND JUDGMENT AND TECHNICAL
KNOWLEDGE IN THE INITIAL PLANNING STAGE. PROCESS CHARTS AND
FLOW DIAGRAMS FIRST APPEARED SOMETIME DURING THIS TRANSITION
PERIOD; HOWEVER, NO DEFINITE DATE COULD BE ESTABLISHED AS
TO WHEN THESE CHARTS AND DIAGRAMS WERE INITIATED. UNDOUBT­
EDLY, SOME SHOP OWNERS HAD CONCEIVED CRUDE VARIATIONS OF
THESE METHODS WHICH THEY ADOPTED TO THEIR OWN NEEDS LONG
BEFORE THESE METHODS BECAME KNOWN AS INDUSTRIAL PLANNING.
NOW THAT INDUSTRY HAD SOME UNDERSTANDING OF WHAT WAS
NEEDED TO EQUIP THE FACTORIES, THE LACK OF AN EFFICIENT
METHOD OF PLANNING THE PLACEMENT OF MACHINES, MEN AND
EQUIPMENT BECAME MORE APPARENT. TRIAL AND ERROR METHODS
WERE VERY COSTLY. DRAWINGS WERE TEDIOUS, TIME CONSUMING,
6
and consequently, expensive.
templets and more r e c e n t l y ,
answered part of the
G r a d u a l l y , the use o f
cardboard
three dimensional models have
challenge.
The purpose o f these a i d s to p l a n n i n g i s n o t
only
to help layout personnel with t h e i r problems, but also
f a c i l i t a t e the use o f the r e s u l t s o f t h e i r e f f o r t s
to
in
c o n v i n c i n g management t h a t a d o p t i o n o f the p r o p o s e d method
is d e s i r a b l e .
In industry,
when new l a y o u t s a r e p r o p o s e d ,
o r when p r e s e n t l a y o u t s a r e t o be a l t e r e d , management
u s u a l l y has t o make t h e f i n a l d e c i s i o n f o r a c c e p t a n c e
re jection
0
V i s u a l l a y o u t techniques emanate from
several
basic methods:
I•
Drawings
A.
B.
II•
plan view
drafting
1.
Blueprints
2.
Whiteprints
Isometric
drawings
Templets--two
dimensional
A.
Block
templets
B#
Contour
C.
V a r i a t i o n s o f c o n t o u r t e m p l e t s made o f
templets
plastic or photosensitive
III.
Models--three
dimensional
A.
Block models
B.
Contour models
C.
P r o t o t y p e models
film
or
7
The d r a w i n g t e c h n i q u e as o u t l i n e d above is
explanatory.
self-
T e m p l e t s e x i s t m a i n l y i n two t y p e s .
The
f i r s t is the b l o c k templet which is n o t h i n g more t h a n a
r e c t a n g u l a r piece o f cardboard cut to the o v e r a l l
dimensions.
it
differs
contour
plan
The o t h e r t y p e is t h e two d i m e n s i o n a l
from the former In that
it
templet;
is cut to the
(with overruns of moving parts)
general
o f the machine or
implement and u s u a l l y has a p l a n v i e w d r a w i n g p r i n t e d
on
it.(5)
A v a r i a t i o n o f the templet that is becoming
increas­
ingly popular consists of one-eighth inch transparent
plastic
p h o t o g r a p h i c a l l y p r i n t e d on one s i d e w i t h the
templet of a particular
in the p l a s t i c
machine.
Small magnets imbedded
serve to hold the templet to a metal
layout board,(6)
Scale models are also found in comparable types
those o f the templets.
to
I n one c a s e , the s i m p l e wooden
b l o c k is u s e d , w h i c h g i v e s no i n d i c a t i o n
C o n t o u r models do n o t d i s p l a y a l l
of contour at
the features o f
all.
the
m a c h i n e b u t m e r e l y p r e s e n t t h e g e n e r a l s h a p e , so t h a t
p i e c e can be r e a d i l y i d e n t i f i e d .
of several different materials
of the machinery.
P r o t o t y p e models are
to produce a detailed
Sometimes b a l s a wood is
carved to the desired accuracy.
Colored s t r i n g is
throughout the p l a n t «
cast
replica
painstakingly
used w i t h t e m p l e t s as w e l l as models to i l l u s t r a t e
flow of materials
the
often
the
8
R e c e n t l y , three dimensional models have been
combined w i t h templets
in i n d u s t r i a l planning work*
The
model shows t h e a c t u a l m a c h i n e i n t h r e e d i m e n s i o n s
the templet which Is placed under the model
table travel, projections,
T h e u s e o f a l/V
= l
although variations
f
and necessary
indicates
clearances•(7)
g r i d has been u s e d i n most
I n s c a l e f r o m 1/32"
while
t o 1" = l
instances,
1
have
been encountered.
The r e p r o d u c t i o n o f l a y o u t s f o r p u r p o s e s o f
display,
f o r r e c o r d s , and f o r o t h e r m u l t i - c o p y uses has d e v e l o p e d
w i t h t h e i n c r e a s e d demands f o r b e t t e r l a y o u t
The f o r e m o s t m e t h o d o f r e p r o d u c t i o n
graphy.
techniques.
i s b y means o f p h o t o ­
Photostats are used e f f e c t i v e l y
in
conjunction
w i t h templets, e s p e c i a l l y w i t h the magnetic p l a s t i c
and the photographic n e g a t i v e t e m p l e t . ( 8 )
processes similar
of blueprints
White prints
to o z a l i d are f r e q u e n t l y employed
or photostats.
the necessity of any a d d i t i o n a l
times, photographs are taken directly
model or t e m p l e t .
master p r i n t . ( 9 )
preparation.
Often­
o f the l a y o u t , be
U s u a l l y , small sections
it
o f the l a y o u t
are pieced together to form a
then
the
Once the l a y o u t has b e e n r e p r o d u c e d ,
The p r i n t s produced p r o v i d e a n e a t ,
are
single
can t h e n be d i s m a n t l e d a n d t h e components r e u s e d f o r
planning.
repro­
templets
photographed separately to reduce d i s t o r t i o n ,
several pictures
or
instead
Direct, clear, uniform
d u c t i o n s may be o b t a i n e d i n t h i s manner f r o m
without
templet
it
future
compact
9
r e c o r d o f w h a t a c t i o n was f i n a l l y
taken or o f what
c o u r s e s c o u l d be f o l l o w e d sometime i n t h e
Several efficient
possible
future.
methods have been found f o r
filing
l a r g e and space-consuming l a y o u t s when t h e y a r e n o t i n u s e .
Templets are sometimes s t o r e d v e r t i c a l l y
on sheets
four by eight foot plywood double-hung similar
to
of
windows.
To o b t a i n a l a y o u t o f a c e r t a i n p o r t i o n o f a p l a n t ,
the
c o u n t e r - b a l a n c e d b o a r d i s m e r e l y p u l l e d down o u t o f
its
filing
position.(10)
Models are u s u a l l y stored in sections
of specially built cabinets.
in
drawers
They are a l s o s t o r e d by making
them i n t o a d i s p l a y complete w i t h a t r a n s p a r e n t s h e l l
the building and a r e p l i c a
provide an a t t r a c t i v e
o f the surrounding areas
exhiblt
was t h e s i g n i f i c a n t
chemical industries
and models.(11)
to
0
One o f t h e c o n c l u s i o n s r e a c h e d a f t e r
case h i s t o r i e s
of
the r e v i e w o f
r o l e p l a y e d by the
i n the use o f t h r e e dimensional
Construction of p i l o t plant or
drawings
unit
operations, which required detailed layout of piping,
tanks,
a n d o t h e r p r o c e s s i n g a p p a r a t u s , was a i d e d i m m e a s u r a b l y b y
f i r s t building
in miniature.
to r e a l i z e the merits
Other industries
o f models as w e l l as
were soon
templets.
The e x t e n s i v e use o f models i n t h e a u t o m o t i v e
Is r e c o g n i z e d by the i n t r i c a t e
their
layouts.
detail
incorporated
industry
in
The C h r y s l e r C o r p o r a t i o n b u i l d s models
moving p a r t s , while a t y p i c a l
with
l a y o u t o f t h e F o r d Company
1 0
d e p i c t s
s u c h
d e t a i l s
c o l u m n s . ( 1 2 ) ( 1 3 )
o f
p l a n t
i s
l a y o u t
The
i n
c l a t u r e ,
f o r m
s u c h
e f f o r t
t o
a n d
t o o l s ,
t h e
o f
p r o p o s e d
m o u n t e d
e x a m p l e s
i n d u s t r i e s
a n d
t h e
A m e r i c a n
s m a l l
o n
w a l l s
e x e m p l i f y
the
s i z e
g e n e r a l l y
s h o p
t h e
w o r k
g o a l s
t h e
t o
a n d
s t a t u s
w h i c h
a n d
a r e
p r o d u c t i o n
l a r g e l y
t h r o u g h
w h i m s ,
o f
k e y
c a t i o n
o f
f o r m a l
I n
the
i t
b
c a n
be
a
t h e
n e x t
some
T h e
o f
t o
t h a t
the
d i v i d i n g
m o o t
p o i n t ;
c h a p t e r
a b b r e v i a t e d
t i m e
h a d
the
p r o d u c t i o n
p r o c e s s
t o
o f
e n d o r s e d
s h o p ,
b y
m u c h
t h e
t h e
o f
h a s
b e e n
t e c h n i q u e s .
same
m a n n e r
d e c a d e s
and
w h i c h
v i r t u e
l a y o u t
s e v e r a l
b y
p r o p o s a l .
v a r i a b i l i t y , ^
j u d g m e n t
t h a n
s h o p
t h i s
n o t
j o b
v i s u a l
i n
p l a n n e d
t h e
a n
t h e
s e a r c h ,
t o d a y
r a t h e r
f o l l o w i n g
N o t e
o n
M e c h a n i c a l
c o d e ,
A t
nomen­
a g o
o f t e n ,
-
p e r s o n a l
s c i e n t i f i c
a p p l i ­
t e c h n i q u e s .
p r e s e n t e d
a l t h o u g h
w e r e
o f
a f o r e - m e n t i o n e d
r e s p e c t
p r e p a r e d
p e r s o n s ;
p r i s e s ,
(11+)
t h e
w i t h
r e l i a n c e
a p p l i e d
i s
t h e
e x t r e m e
s h o p s
t e c h n i q u e s
p a p e r .
f r o m
A .
p r o c e d u r e ,
A s s o c i a t i o n
l i t e r a t u r e
d i s r e g a r d e d
l a y o u t s
m o d e l
A p p e n d i x
i n c l u d i n g
t h e
l a y o u t
S o c i e t y
a n d
S t a n d a r d s
s i g n i f i c a n t l y
l o t
A m e r i c a n
i n
s t a n d a r d s
T h r o u g h o u t
s t a n d a r d i z e
t e m p l e t
a p p e a r s
l a y o u t
d i f f e r s
a
w h i c h
w r i t i n g ,
a s
s w i t c h e s
p r e c e d i n g
a n
E n g i n e e r s
Job
a c t u a l
a i m e d .
I n
a n y
a s
w i l l
c h a r t ,
t h e
f o r
l a r g e
s c a l e
d r a w i n g
b l o c k
b e t w e e n
u s e d
s e v e r a l
p r o d u c t i o n
w i t h
the
i s
n o t
c h a r a c t e r i s t i c s
d e f i n i t i o n
a v o i d
a n d
s e t
a m b i g u i t y .
l a y o u t
t y p e
r e s u l t s
p r o d u c t i o n
t h e
t o
o r
o f
t e c h n i q u e
t e m p l e t
h o w e v e r ,
be
c o n c e n s u s
c o m p a r i s o n
t h e
l i n e
a
o f
e n t e r ­
t h i s
i n c l u d e d ,
a r e
j o b
s i m i l a r .
s h o p s
f o r t h
i n
Block Templet
Table 2.
Plant Layout Comparison Chart
2-Dimension
Templet
3-Dimension
Templet
Combination of
2 and 3 Dimen­
sion Templet
Cost
Low f i r s t c o s t .
C a n be made b y
inexperienced
personnel.
Requires services
of a f a i r l y skil­
led draftsman with
a knowledge o f
machine t o o l s .
F i r s t cost con­
siderably higher
than for block
templet.
Requires skilled
model maker i f
made s p e c i a l .
Most models n o t
yet available
commercially.
Cost o f models in
q u a n t i t y not a p ­
preciably higher
t h a n good 2 dimen­
sion templets.
I n i t i a l cost of this
method combines the
cost o f 2 dimension
templets with 3
dimension models.
Engineering Value
V e r y p o o r . Does
not permit good
visualization
of layout or
effective ar­
rangements .
Good. This type of
templet in the
hands o f a p r o ­
f i c i e n t engineer
permits very ef­
fective layouts.
Does n o t p e r m i t
easy i n t e r p r e t a ­
t i o n o f the l a y ­
out by non-tech­
nical personnel.
G o o d . Makes f a s t ­
er development
of equipment a r ­
rangements f o r
effective lay­
outs . Helps
to ' s e l l ' the
layout.
Best.
Combines a l l
the merits o f 2
dimension templet
and 3 dimension
model.
Table 2 .
B l o c k Templet
P l a n t Layout Comparison Chart
2-Dimension
Templet
(Continued)
3-Dimension
Templet
Combination o f
2 and 3 Dimen­
s i o n Templet
Advantages
Can be made
q u i c k l y at very
low c o s t .
Gives a very a c ­
curate layout
and r e d u c e s time
r e q u i r e d t o make
f i n a l drawings.
Clearly indica­
tes actual f l o o r
areas required.
S e r v e s as a p e r ­
manent t e m p l e t
when p r o p e r l y
made.
Greatly
reduces p o s s i ­
b i l i t y of errors
as compared t o
block templets.
Aids v i s u a l i z a ­
t i o n o f layouts
by n o n - t e c h n i ­
cal personnel.
V a r i o u s schemes
c a n be p h o t o ­
g r a p h e d f o r com­
parison studies.
Models c a n be
used i n d e f i n i t e ­
ly.
Permits h i g h l y a c ­
curate layouts to
be made q u i c k l y
w i t h c o m p l e t e engin­
eering d e t a i l s .
Gives f u l l v i s u a l ­
ization of layout.
Only one s e t o f
models necessary
t o make any number
of layouts.
Re­
d u c e s l a y o u t and
drafting c o s t .
Disadvantages
Does n o t p r o v i d e
for accuracy of
layout, effective
arrangements or
economical u t i l ­
ization of floor
space.
Increases
d r a f t i n g time and
cost of engineer­
ing drawings.
Cost i s c o n s i d e r ­
a b l y h i g h e r than
block templets.
Does n o t p r o v i d e
ease o f p e r c e p t ­
i b i l i t y inherent
in models. Re­
quires engineers
to carry mental­
l y a l l planning
Does n o t c a r r y the
engineering i n f o r ­
mation provided
by the 2 dimen­
sion templet.
Does n o t show
machine c l e a r ­
ances r e q u i r e d
for operations
or s e r v i c e s .
In-
Highest i n i t i a l
o f any m e t h o d .
cost
Table 2 .
B l o c k Templet
P l a n t Layout Comparison Chart
2-Dimension
Templet
3-Dimension
Templet
Disadvantages
Posters discrepa n c i e s and e r r o r s .
Increases o v e r a l l
layout c o s t .
(Continued)
in the t h i r d
dimension.
f
(Con d)
creases
time.
drafting
Combination o f
2 and 3 Dimen­
s i o n Templet
Ik
CHAPTER
JOB SHOP
A specific
III
DEFINED
d e f i n i t i o n o f t h e term " j o b shop" has
not been a v a i l a b l e to i n d u s t r y .
I n s t e a d , i n d u s t r y has
included i n the scope o f t h i s term a n y t h i n g from a model
shop t o s o m e t h i n g s h o r t o f t h e macs p r o d u c t i o n t y p e
enter­
prises characterized by the automobile i n d u s t r i e s .
The
General E l e c t r i c Company, I n p l a n n i n g i t s
Engineering
L a b o r a t o r i e s , set f o r t h the following c r i t e r i a which
for
r e a s o n s o f common v i e w p o i n t s a t i s f y t h e d e f i n i t i o n o f
small job
shops.(15)
lo
Short order jobs—work o f u s u a l l y eight hours or
2.
Number o f employees r a n g i n g f r o m s i x t o
3.
Number o f machine t o o l s r a n g i n g f r o m t w e l v e
twenty-five,
less.
ten,
to
C o l v i n a n d S t a n l e y l i m i t t h e s m a l l j o b shop to one
employing less than twenty-five persons which, they suggest,
reflects
t h e common o p i n i o n , ( 1 6 )
It
is n o t a b l e t h a t o n l y m e t a l working or machine
shops a r e c i t e d f o r d e f i n i t i o n .
T h e m o s t common o f n o n -
metal trades in the job shop c a t e g o r y is the
industry.
one
printing
The small job p r i n t i n g shop u s u a l l y employs f r o m
to t h r e e workers and has two or t h r e e p r e s s e s .
shops, however, have several c h a r a c t e r i s t i c s
which
All
will
job
15
d i s t i n g u i s h them from the p r o d u c t i o n t y p e o f
LO
Within a particular industry,
enterprise:
job shops
will
p e r f o r m more jobs o f l e s s q u a n t i t y t h a n p r o ­
duction shops
2.
e
J o b shops have a s p e c i f i c o r d e r q u a n t i t y
is r u n i n one s e t - u p .
which
The job is u s u a l l y
a-kind and is seldom repeated e x a c t l y .
one-of-
Production
shops may s e t up f o r s h o r t q u a n t i t y runs t o
customer schedules.
fulfill
R e t o o l i n g w o u l d be r e q u i r e d
f o r each p e r i o d when a c e r t a i n q u a n t i t y is t o
be
3«
delivered.
J o b shops tend t o employ m u l t i - s k i l l e d workers as
differentiated
from the production type
industry
w h i c h employs p e r s o n s who a r e t r a i n e d t o o p e r a t e
a s p e c i f i c t y p e o f m a c h i n e , such as a type o f
punch press or t u r r e t l a t h e .
J o b shop p e r s o n n e l
can be c l a s s i f i e d i n two c a t e g o r i e s — t h e mechanic
and the a s s i s t a n t mechanic
(or trainee), the
d i f f e r e n c e being t h a t t h e mechanic has mastered
the use o f a l l equipment associated w i t h t h e trade«
4
#
A v a r i e t y o f work w i l l e v e n t u a l l y confront the job
shop whereas t h e p r o d u c t i o n s h o p , even t h o u g h
may h a v e t o r e t o o l f o r d i f f e r e n t
jobs,
It
will
e s s e n t i a l l y b e c o n c e r n e d w i t h t h e same g e n e r a l
type o f manufacture i t has a l r e a d y experienced.
This requires
the use o f universal type tools
in
16
the job shop and c o n v e r s e l y ,
would predominately u t i l i z e
the production
special
shop
purpose
machinery*
5.
J o b shop o p e r a t i o n s
employ fewer workers
s m a l l , medium, and l a r g e class
in
the
establishments
c o m p a r e d t o t h e same c l a s s i f i c a t i o n s
in
as
production
type shops*
6.
Mass p r o d u c t i o n
t e c h n i q u e s a r e l e s s common a n d
l e s s o f t e n o b s e r v e d i n a job shop t h a n in
t i o n shops p r i m a r i l y
production.
because o f smaller
Assembly operations
observed intermingled
are
produc­
quantity
usually
with fabrication
operations
i n j o b shopsO
The q u a l i f i c a t i o n s
arid f o r
above are q u a l i t a t i v e
that reason are d i f f i c u l t to measure.
definitions
in
nature
These
a r e b y no means r i g i d , b u t a r e i n t e n d e d
to
s e r v e as t h e c r i t e r i a o f a job shop f o r t h e p u r p o s e
of
this
research.
17
CHAPTER IV
EXPERIMENTAL PROCEDURE
The methods o f i l l u s t r a t i n g l a y o u t s have expanded
to o f f e r
s e v e r a l a l t e r n a t i v e c h o i c e s as new m a t e r i a l s
t o o l s have b e e n d e v e l o p e d .
from f o u r b a s i c t y p e s :
m o d e l s , and
However, a l l
(1) drafting,
templets
and m o d e l s .
techniques
(2) templets,
These f o u r
(3)
repre­
j o b machine s h o p p r o b l e m .
I d e a l l y , a l a y o u t c o u l d be d e s c r i b e d a s most
if
evolve
fundamental
p r o c e d u r e s have b e e n s e l e c t e d f o r a p p l i c a t i o n t o a
sentative
t h e b u i l d i n g were d e s i g n e d a r o u n d t h e f i n a l
fortunately,
i n d u s t r i a l planning
c o n f i n e d to s t r u c t u r e s already
efficient
product.
today is almost wholly
In order t o simulate
t y p i c a l p r o b l e m o f a medium s i z e j o b s h o p , a b u i l d i n g
by e i g h t y f e e t
(columns t h i r t y f e e t
w a l l s , and s i x t e e n f e e t
Figure 1.
on c e n t e r s )
sixty
foot
was a r b i t r a r i l y c h o s e n .
dimensions o f d o o r s , overhead c l e a r a n c e s ,
By a p p l y i n g e a c h l a y o u t t e c h n i q u e
approximate
etc.
to a
standardized
c o n d i t i o n s in each c a s e , a comparison
can be made on the b a s i s
of time,
f a c t o r s as e x p l a i n e d i n Chapter V ,
the f i r s t
a
i n from e i g h t
shows a s k e t c h o f the b u i l d i n g w i t h
problem with i d e n t i c a l
Un­
in existence or buildings
h o u s i n g the p r e s e n t a c t i v i t i e s .
feet
and
c o s t , and s e v e r a l
other
The l a y o u t r e s u l t i n g from
method p e r f o r m e d becomes the o b j e c t i v e l a y o u t
for
19
each other method in t u r n ,
to f a c i l i t a t e comparison.
each method were used to o b t a i n a l a y o u t
different
If
from
t h a t o f each o t h e r m e t h o d , c o m p a r i s o n would be h i n d e r e d by
the i n t r o d u c t i o n
of this additional
In addition
thirty-five
variable.
to the selected b u i l d i n g
miscellaneous
p r o d u c t i o n machines and
three persons were chosen to s a t i s f y
definition.
To f u r t h e r
dimensions,
the medium s i z e job
supplement the given
Appendix B summarizes a l l
twentyshop
conditions,
equipment, f a c i l i t i e s , and
services
i n c l u d e d i n the procedure o f each m e t h o d .
Two p r e m i s e s w e r e m a d e b e f o r e t h e p r o c e d u r e w a s
started.
F i r s t , i f any person technically
techniques were to f o l l o w
this text,
trained
in
the procedures as o u t l i n e d
regardless
o f the degree o f experience.
time t a k e n t o d e t e r m i n e w h i c h move i s
b e t h e same r e g a r d l e s s
neglig­
Second,
t o be made n e x t
o f the method used.
r e q u i r e d t o make the move p h y s i c a l l y ,
known to
in
the time r a t i o o f methods would remain the same,
o r t h e time d i f f e r e n t i a l w o u l d be so s m a l l as t o be
ible,
layout
the
will
The time
however, is
definitely
vary.
The methods used a r e as
follows:
Method I.
Drafting
(modified block templets
II.
Templets
(contour)
III.
IV.
Models
(prototype)
Templets and Models
III.
drafted)
superimposed)
(combination of I I .
and
20
Method I I was a r b i t r a r i l y p e r f o r m e d f i r s t
the s t a n d a r d l a y o u t ;
to develop
Method IV was n e x t a p p l i e d t o a v o i d
t h e n e c e s s i t y o f d u p l i c a t i n g e v e r y move common t o b o t h
m e t h o d s ; Methods I I I and I f o l l o w e d .
was made t o p e r f o r m e a c h method a t
the
A deliberate
same p a c e .
effort
Every
move p e r f o r m e d In Method I I was r e c o r d e d and t i m e d t o
nearest minute.
Any e r r o r s
made i n Method I I were a l s o
r e c o r d e d and f o l l o w e d as the
other methods.
s t a n d a r d p r o c e d u r e by the
This was done i n o r d e r t o c o n t r o l
carry-over learning
effect
the
o f one method t o the
B e f o r e any move was made, the
time r e q u i r e d
the
other.
to
0
deliberate
where a p i e c e o f equipment s h o u l d be p l a c e d was r e c o r d e d ,
t h i s time b e i n g e x a c t l y the
was u s e d f i r s t .
A p p e n d i x C shows t h e o r i g i n a l
and t i m e d a t a w i t h " t h i n k "
added t o " a c t "
same i r r e s p e c t i v e
o f w h i c h method
operation
t i m e s l i s t e d under Method I I
t i m e s o f e a c h method t o e s t a b l i s h
but
total
times f o r each method.
The g i v e n c o n d i t i o n s o f e x i s t i n g b u i l d i n g ,
required,
and equipment were s u r v e y e d f i r s t .
facilities
Methods I ,
II,
and IV r e q u i r e d r o u g h s k e t c h e s w i t h d i m e n s i o n s t o b e made from
c
P r a c t i c e e f f e c t s were i n v e s t i g a t e d from the p s y c h o l ­
o g i c a l viewpoint to determine t h e i r importance i n t h i s
application.
A s t u d y o f r e c a l l , r e m i n i s c e n s e , r e t e n t i o n and
memory on i n d i v i d u a l d i f f e r e n c e s , d i s t r i b u t i o n o f p r a c t i c e ,
and whole o r p a r t l e a r n i n g r e v e a l e d l i t t l e e f f e c t on t h i s s t u d y
b e c a u s e ( 1 ) a r e l a t i v e l y s m a l l amount o f r e p e t i t i o n was
p e r f o r m e d , ( 2 ) e a c h t r i a l was r e p e a t e d b y a d i f f e r e n t m e t h o d ,
and ( 3 ) s u f f i c i e n t c o n t r o l was r e t a i n e d o v e r the s t i m u l i ,
p r o c e d u r e , and r e s p o n s e t o n e g a t e t h e p r a c t i c e e f f e c t s • ( 1 7 ) ( 1 8 )
21
manufacturers
1
c a t a l o g s o r from the
Templets drawn i n I n d i a
existing
i n k from t h e s e
equipment.
sketches
followed
the p r o p o s e d A m e r i c a n S o c i e t y o f M e c h a n i c a l E n g i n e e r s
s t a n d a r d s as o u t l i n e d i n A p p e n d i x A .
however, to include a l l
the
It
was n o t
i n f o r m a t i o n on t h e
b e c a u s e o f t h e v a r i e t y and s i n g u l a r i t y
necessary,
templets
o f the machine
F o l l o w i n g normal l a y o u t p r o c e d u r e , r e g a r d l e s s
of
t e c h n i q u e a p p l i e d , a s k e t c h was made o f the b u i l d i n g
p l a n , n o t i n g e x i t s and o b s t r u c t i o n s .
It
is at
this
tools.
the
floor
point
t h a t t h e g e n e r a l a r e a s o f e a c h s e r v i c e o r f a c i l i t y were
determined.
the r i g h t
For e x a m p l e , due t o t h e
half
o f the b u i l d i n g ,
i n e r y and f a b r i c a t i o n
travel
o f crane over
the l o c a t i o n o f heavy mach­
s h o u l d be w i t h i n t h i s a r e a ;
the
supply
room s h o u l d be c l o s e t o t h e r e c e i v i n g d o o r , whereas t h e
should be c l o s e t o the f r o n t
entrance
working a r e a .
sketch, a pre-grouping of
machines
I n making t h e
as w e l l as n e a r
office
the
the
i n e a c h a r e a was r o u g h l y drawn as shown i n F i g u r e 2 . ^
No a t t e m p t w i l l be made t o d e f e n d t h e a c t u a l
ment o f equipment and f a c i l i t i e s
although reasonable
arrange­
layout
t o l e r a n c e s were o b s e r v e d .
d
I n t h i s c a s e , equipment was l a i d o u t a c c o r d i n g t o
a p a t t e r n d e v e l o p e d by t h e a u t h o r a t t h e machine shop o f
t h e G e o r g i a I n s t i t u t e o f T e c h n o l o g y E n g i n e e r i n g Experiment
Station.(19)
The l a t h e s , m i l l i n g m a c h i n e s , and b e n c h e s
were f o u n d t o be c l o s e l y r e l a t e d b y c o l l e c t i n g i n f o r m a t i o n
from p a s t work o r d e r s
( S e e A p p e n d i x B ) . This d i f f e r s from
t h e c o n v e n t i o n a l c o l o n y t y p e l a y o u t u s u a l l y employed b e c a u s e
o f s o - c a l l e d u n p r e d i c t a b l e p r o d u c t and p r o c e s s v a r i a t i o n .
0
22
P i g .
2
tfOUGH 5K£fCH Of ftOOtf PLAN ANP PtffUMlNARV
PQU/PM£AiT AND FACILITY AREAS
23
After
t h e b u i l d i n g o u t l i n e was e s t a b l i s h e d ,
p r o d u c t i o n e q u i p m e n t was p l o t t e d
previously assigned.
under the influence
in the general
the
areas
Rearrangement o f the equipment
of process flow, materials
a i s l e space, and similar layout f a c t o r s .
followed
handling,
The supply and
t o o l r o o m f o l l o w e d I n m u c h t h e same p r o c e d u r e a s d i d
men's l a v a t o r y and the o f f i c e s .
Machinery units l e f t
o f the l a y o u t u n t i l the f a c i l i t i e s were t e m p o r a r i l y
lished,
were now i n s e r t e d
in the space a l l o t e d .
ment o f equipment and p a r t i t i o n s needed a f t e r
was t e n t a t i v e l y
found.
the
out
estab­
Rearrange­
the
layout
c o m p l e t e d w e r e made as d i s c r e p a n c i e s
were
A g a i n , during the f i n a l stages o f the l a y o u t
(oper­
a t i o n s 13 A , B , a n d D o f A p p e n d i x C ) , c h a n g e s t o p r o v i d e a
b e t t e r arrangement were f o u n d n e c e s s a r y .
Construction
t h e b r i d g e c r a n e s y s t e m was c o n f i n e d t o M e t h o d s I I I
as t h e o t h e r methods were n o t s u i t a b l e
ing projections.
of
and I V
f o r showing overhang­
P l a n view photographs of each method are
shown on the f o l l o w i n g p a g e s .
METHOD I • Dl
Pig.
3
Fig.
k
26
Pig.
5
27
28
CHAPTER V
EVALUATION AND RESULTS
The
e v a l u a t i o n o f l a y o u t methods consisted o f a
combination o f quantitative
and q u a l i t a t i v e
studies.
Quantitative analysis.—Included in the quantitative
eval­
u a t i o n a r e t h e cost o f t h e l a y o u t i n terms o f l a b o r a n d
material,
t h e time r e q u i r e d t o perform t h e l a y o u t , a n d t h e
degree o f f l e x i b i l i t y i n c r e a t i n g t h e l a y o u t and making
changes•
The a s s i g n m e n t o f a d e f i n i t e m o n e t a r y v a l u e t o l a b o r
Is a d i f f i c u l t
t a s k a s s e c t i o n s o f t h e l a y o u t may be p e r f o r m ­
ed b y n o n - t e c h n i c a l p e r s o n n e l w i t h a $200/month s a l a r y , o r
by p r o f e s s i o n a l e n g i n e e r s w i t h $ 9 0 0 / m o n t h s a l a r y . F o r
purposes o f comparison, t h e t y p i c a l salary o f a n i n d u s t r i a l
engineering trained supervisor
was
( a b o u t |600/month o r $3.50/hour)
used f o r a l l operations i n each method.
Cited costs o f
m a t e r i a l were purchase p r i c e s a t l o c a l a r c h i t e c t s '
houses o r q u o t a t i o n s from " V i s u a l " P l a n t L a y o u t s
Oakmont, Pennsylvania.
pared i n the following
Time and m a t e r i a l
supply
Inc.,
data were p r e ­
t a b l e s , summarized from Appendix C
F l e x i b i l i t y was d e t e r m i n e d b y c o m p u t i n g t h e t i m e
and
expense i n v o l v e d i n r e a r r a n g i n g t h e l a y o u t a s shown b y
O p e r a t i o n s 6B, 7 B , 8 B , 9B, 1 0 B , 1 1 , a n d 1 3 E i n T a b l e 5.
T a b l e 3.
Method
Cost Analysis
Material
Labor
Cost a t
$3.50/Hr.
I
II
III
$69.23
51.62
24.88
None
1
S c o t c h Tape
1 s1/h2e1e t 2i-1/V
grid
R o l l o f l/V
x
S c o t c h Tape
1 L1/u 2
'
x
2'
1/V
grid
cite board
R o l l o f 1/V
15 L u c l t e c o l u m n s
12" o u t s i d e w a l l s
V inside
partitions
130 m o d e l s
Crane s y s t e m ( h a n d made)
IV
61.95
Same m a t e r i a l s
Method I I I
as i n
Material
Cost
Total
Cost
Cost
Ratio
None
169.23
1.30
#1.15
.55
0
"1.6
1.15
1
..0
0
178
1.0
20
5
72.5.000
311
0)
358.5.V
53.27
1
383.28
7.19
3581
.+0
1*203
.5
7.90
30
T a b l e 4*
Time E l e m e n t
Method
Time i n
Honrs
Time R a t i o
I
II
III
IV
19.78
14.75
7.11
17.70
2.78
2.08
1.00
2.49
By s u b s t i t u t i n g
ly different
variations
results appeared.
o f each method
significant­
F o rexample, i f ready-made
t e m p l e t s were p u r c h a s e d i n s t e a d o f made i n M e t h o d I I , t h e
cost o f time i n Table
of material
E
|79.13.
similar
increased
The time i n
3. d e c r e a s e d t o §23.63 a n d t h e c o s t
t o $55.50, p r e s e n t i n g a n e w t o t a l o f
T a b l e 4* d e c r e a s e d b y e i g h t h o u r s . A
decrease i n labor cost, increase i n material
a n d d e c r e a s e i n t i m e was e v i d e n t i n M e t h o d I V .
cost
O f course,
these variations a r e contingent on the a v a i l a b i l i t y
of
the exact templets needed.
If
t h e crane assembly i n Methods I I I a n d I V c o u l d be
purchased, t h e cost o f these methods would be decreased i n
time a n d increased I n m a t e r i a l ;
these layouts would have
a f f o r d e d a b e t t e r comparison t o Methods I and I I
cannot s a t i s f a c t o r i l y
which
i l l u s t r a t e the crane assembly.
Q u a n t i t a t i v e r e s u l t s . — T h e q u a n t i t a t i v e a n a l y s i s shows
Method I I t o be favored s i g n i f i c a n t l y
i n terms o f cost and
f l e x i b i l i t y , b u t only second best i n time.
e
Accordingly,
Quoted from " V i s u a l " Plant Layouts I n c . , Oakmont, P a .
T a b l e 5.
Flexibility
Method
Operation
II
I
IV
III
Time i n
Hours
Labor
Cost $
Time I n
Hours
Labor
Cost #
Time i n
Hours
Labor
Cost $
Time i n
Hours
Labor
Cost !
6B
2.63
9.21
0.35
1.23
0.75
2.63
0.35
1.23
7B
0.85
2.97
0.25
0.87
0.47
1.65
0.25
0.87
8B
0.78
2.73
0 20
0.70
o.J+2
1.47
0.20
0.70
9B
0.73
2.55
1.05
0.ii8
1.68
11
0.25
13E
2.88
4.31
0.87
10.08
1.47
2.38
1.05
1.23
0.42
0.68
0.20
10B
0.30
0.^8
Total
9.35
$32.72
Ratio
5.114-
o
1.68
*
0.24
0.84
0,59
1.82
$6.37
3.33
1
•JI-
•>«•
2.07
0.78
2.73
$11.67
2.36
$8.26
1.83
#Too s m a l l t o be s i g n i f i c a n t
1.30
32
Method I I
w o u l d be c h o s e n ;
sounder basis i f
it
w o u l d be s e l e c t e d on a
t h e a s s u m p t i o n c o u l d be made t h a t t i m e ,
terms o f o v e r - t i m e hours a n d / o r purchased t e m p l e t s ,
in
could
be m o r e e a s i l y p r o c u r e d i n a j o b s h o p t h a n c o u l d c a p i t a l
investment.
1:7.19
for
The 2 0 8 ; l time r a t i o would then overbalance the
o
cost r a t i o in Methods I I and
III,
Q u a l i t a t i v e a n a l y s i s , - - F o u r factors which are d i f f i c u l t
precise measurement enter into
the selection o f the
layout technique f o r the job shop, namely;
r e q u i r e d t o do t h e l a y o u t ,
best
(1) t h e e d u c a ­
t i o n a l l e v e l required to perform the l a y o u t ,
effort
of
(2) t h e m e n t a l
f3) t h e s p a c e
perception
and u t i l i z a t i o n a t t a i n e d by the l a y o u t t e c h n i c i a n , and
(li)
the decision influence on management.
level
The e d u c a t i o n a l
f a c t o r would q u e s t i o n the use o f the l a y o u t techniques
the equivalent a b i l i t y o f a technician,
or even a mechanic.
with
engineer, executive,
The second c o n s i d e r a t i o n would w e i g h
the r a t i o o f s e l f e v i d e n t procedure t o matters
deep t h o u g h t a n d c o n s t a n t s e a r c h i n g ,
requiring
Given a
specific
l e n g t h o f time to perform a l a y o u t , space p e r c e p t i o n and
utilization
would test the r e l a t i v e
technique.
The i n f l u e n c e d e c i s i o n on management q u e s t i o n s
the coraprehensibility
effectiveness of
of the respective results
each
obtained
t h r o u g h use o f techniques by the p o l i c y - m a k e r s w i t h i n the
industrial
enterprise.
I n o r d e r t o a r r i v e a t some s i g n i f i c a n t
conclusion,
f o r m o f d e c i s i o n t h e o r y was e m p l o y e d t o w e i g h t h e a b o v e
a
33
factors.(20) In essence, this theory proposes that for each
probe
lm there can be see
l cted several meh
tods of solution
(Mi) whcih will in turn result in several possible acto
i ns
(Aj). The probabilty (Pij - i meh
tods with j possible
actions) that a meh
tod will produce a certain acto
i n is one
of the consd
i erato
i ns in makn
ig the decs
io
i n whcih is the
choc
ie of the best a
l yout meh
tod. The chances of success Iin
i
any situation must be estm
i ated; however, the best decs
io
in
will not aw
l ays depend on the hg
i hest probabilty atan
i ed
i
sn
i ce the resulting acto
i ns (Aj) shoud
l be assg
i ned ranked
vau
l es in accordance with an individual's preference. By
assg
i nn
i g A^ with an evau
l ato
i n factor (Ej - a measure of
i
individual preference) the best decs
io
i n may now be deter­
mn
ied by the meh
tod whcih maxm
i zies P^jEj. If w
t o meh
tods of
solution M
( _] and M) were to be decd
ied upon, each producn
i
three results (Ai, A, and A3), selection of one by rankn
ig
ao
lne mg
i ht produce one decs
io
i n whereas co
l ser investigation
by assg
i nn
iT
gabe
vlau
le
s D(Ei
,s
En, TahnedoryE^)
to
thne results and
6.
e
c
i
o
i
E
v
a
u
l
a
t
o
i
weg
ihn
ig each Ej in each probabilty coud
l produce a
diferent d
io
in=
—6)
a moe
rAac(E
cur=
ate5)one. A
F3or (E
ex=am
l:
le
<cs
1
1)pe
l
= 10
P12= 2
13 = 3
M
21= 3
P =7
23= 8
2
2
2
A
E
2
2
M
3
p
P
2
P
22
34
i n T a b l e 6 . w h e r e S P ( M ) = 15
1
w o u l d l e a n t o w a r d Hg*
and 2 P ( M ) = 1 8 , the
1
i
However, by a s s i g n i n g E j t o each A j
and w e i g h t i n g these v a l u e s , the r e s u l t s
are:
P
2
P
i J
(
V
=
P
E
+
?
E
+
11 1
12 2
= (60) + ( 1 0 ) +
= 73
2P
l t j
choice
2
(M ) = ^21^1
P
+
2
=
P
E
+
22 2
(35)
(18) +
E
13
3
(3)
E
233
+
(8)
= 61
This is a r e v e r s a l o f the decision in f a v o r o f M^;
latter
the
case b e i n g more a c c u r a t e .
The P ^ j i s d e t e r m i n e d b y t h e i n d i v i d u a l ' s
o f how w e l l t h e A j w i l l s a t i s f y
estimate
the given s i t u a t i o n
(or
effectiveness) with comparison to other P ^ j ' s , e t c ,
a selected linear
scale.
The E j is d e t e r m i n e d by
ranking the A j in order o f r e l a t i v e
consideration of value.
importance,
On a l i n e a r
the values E
2
given
first
without
scale, values
are then t e n t a t i v e l y assigned to the A . ,
(Ej)
S t a r t i n g w i t h A]_,
, E ^ , • • • E ^ . are checked f o r t h e i r
relative
w i t h E-j_ b y q u e s t i o n i n g t h e p r e f e r e n c e o f A ^ o v e r t h e
ation A
0
+ A~ + •••A, ,
^3
k
Eg, E ^ , •••Ej
c
decision,
2
A^,o,,A^,
A
I f A_ <, = , > A
0
previous relationships
the a p p l i c a t i o n
combin­
the
k
m u s t be a l t e r e d a r i t h m e t i c a l l y
a n d so f o r t h .
rank
+ A . + A, , then
1 ^ 3
is chosen n e x t to t e s t
its
to s a t i s f y
the relationship
When n u m e r i c a l
the
of
changes are made,
s h o u l d n o t be d i s t u r b e d u n l e s s
of t h i s process the reasoning is
in
changed.
35
A p p l i c a t i o n o f t h e d e c i s i o n t h e o r y was a c c o m p l i s h e d
by asking ten graduate i n d u s t r i a l engineering students
l i t t l e layout experience and four i n d u s t r i a l
with
engineering
professors w i t h moderate but not extensive experience
rate the p r o b a b i l i t i e s of
effort,
(A-^) e d u c a t i o n a l l e v e l ,
( A ^ ) space p e r c e p t i o n , and ( A ^ ) d e c i s i o n
under the p o s s i b l e methods (M^) d r a f t i n g ,
m o d e l s , and (M^) templets and m o d e l s .
to
( A ) mental
2
influence
(M 3 t e m p l e t s ,
(M^)
They were then asked
to evaluate A-^, A ^ , A ^ , and A ^ by a s s i g n i n g values E ^ ,E
E ^ , a n d E^_ s i m i l a r t o t h e p r e v i o u s e x a m p l e .
2
F o r a more
d e t a i l e d account o f the i n f o r m a t i o n asked, a copy o f
data
e v a l u a t i o n survey is
included in Appendix D together
with
the r e s u l t s o f each
participant.
The c o m p u t a t i o n p r o c e d u r e o f t h e s o l i c i t e d
data
a p p e a r s o n d a t a e v a l u a t i o n s h e e t number one o n l y , as
other procedures are similar.
Since the i n d i v i d u a l
e v a l u a t i o n s d i f f e r e d w i d e l y i n s c a l e , r e s u l t s were
into a per cent value o f 100 f o r
raw
transformed
shown i n
A s t a t i s t i c a l a n a l y s i s o f the r e s u l t s o f
m e t h o d i s s h o w n i n T a b l e 8.
all
comparison.
A t a b u l a t i o n of the adjusted r e s u l t s is
Table 7»
each
where X is the a r i t h m e t i c
average
and s is the unbiased estimate o f the standard d e v i a t i o n
the f o u r t e e n determinations
of
f o r each method.
The f i r s t h y p o t h e s i s t e s t e d i s
the f o u r methods are homogeneous.
i n T a b l e 8.,
,
that the variances
of
I n terms o f the d a t a shown
this would imply that the results f o r
each
36
Table 7. Summation o f Data E v a l u a t i o n
Participant
Method
I
1.
2.
3.
k.
5,
6
6
7
8.
9.
10o
11.
12,
13.
Ik.
io.5
17a
8.6
12.9
12.9
i|-6
0
ik.o
k.5
2I+.3
13.1
15.2
13.7
10.3
IV
III
II
20.3
21.0
32.1
31.3
37.1
30.5
15.5
25.k
SO.k
27.9
22.0
29.7
42.0
37.0
33.0
26.6
2k.k
26.8
21.9
16.1
18.6
23.3
19.8
17.7
25.2
36.3
lf-1.7
35.7
26.1
28.2
31.6
29.7
18.5
34.2
Table 8. S t a t i s t i c a l
28.2
il-1.2
26.3
38.9
25.4
31
37.0
.k
Tabulation
Method
I
s
II
IV
III
11.5
21.2
3 L 9
35.3
6.0
3.9
5.8
6.7
m e t h o d h a d t h e same d i s p e r s i o n o r v a r i a b i l i t y .
This hypothesis
was t e s t e d s t a t i s t i c a l l y b y t h e u s e o f B a r t l e t t ' s
Test.(21)
The r e s u l t s o f t h i s t e s t i n d i c a t e d t h a t t h i s h y p o t h e s i s o f
homogeneity o f variances is reasonable, since the P value
obtained did not approach significance.
all
tests can be found i n A p p e n d i x E .
The calculations f o r
37
Since the hypothesis o f equal variances is accepted,
the method p r e f e r e n c e shown b y t h e Ts
1
ficance.
was t e s t e d f o r
signi­
T h e s e c o n d h y p o t h e s i s m a d e i s t h a t e a c h X" i s n o t
significantly
different
from t h e o t h e r s , o r no one method
was p r e f e r r e d o v e r a n y o t h e r .
closest preference ratings
Methods I I I and I V w i t h t h e
were s e l e c t e d f i r s t
using
S t u d e n t ' s t distribution(22) f o r t e s t i n g t h e d i f f e r e n c e b e ­
tween p a i r s
o f sample means.
T h e sample v a l u e f o r t was
l.lj.8, a v a l u e w h i c h i s n o t c o n s i d e r e d s t a t i s t i c a l l y
ficant.
Methods I and I I having t h e next l a r g e s t
o f X's w e r e t h e n t e s t e d .
o f X's
at less
t h a n t h e 0.25
Since the differences o f the remaining
are larger
differences
are
difference
T h e s a m p l e v a l u e f o r t w a s 5»07*
a value which is significant
level.
signi­
than t h e case j u s t c i t e d ,
per cent
combinations
all
other
significant*
Q u a l i t a t i v e r e s u l t s . — T h e conclusions reached i n the quali­
tative analysis section are that
choice,
(2) M e t h o d I I I s a b e t t e r
C3) M e t h o d s I I I a n d I V a r e b e s t .
(1) M e t h o d I i s t h e p o o r e s t
selection than Method I, and
A l t h o u g h Method I V does
have a h i g h e r T than Method I I I , t h i s d i f f e r e n c e
f o u n d t o be s t a t i s t i c a l l y s i g n i f i c a n t
o f t h e o t h e r X ' s were f o u n d t o be
was n o t
whereas t h e d i f f e r e n c e s
significant.
38
CHAPTER V I
CONCLUSIONS
The r e s u l t s
different
o f each e v a l u a t i o n a n a l y s i s
optimum methods.
specify
I f t h e two e v a l u a t i o n s had
r e s o l v e d i n t o t h e same a n s w e r , t h e r e i n f o r c e m e n t o f o n e
s o l u t i o n upon the o t h e r would have l e f t no doubt as t o
best
the
selection.
Upon i n s p e c t i o n o f the space p e r c e p t i o n and
data, it
utilization
was f o u n d t h a t t h e p r e m i s e o f e q u a l " t h i n k "
times
does n o t n e c e s s a r i l y h o l d t r u e because o f the v a r i e d a s s i g n ­
ment o f v a l u e s i n each m e t h o d .
It
is assumed t h a t
using any l a y o u t technique the f i n a l space
by
utilization
w o u l d be t h e s a m e , as d e s i g n e d i n t h e e x p e r i m e n t .
This
means t h a t space p e r c e p t i o n m u s t v a r y f r o m one m e t h o d to
the next which also infers
times f o r Method I I ,
times.
"Think"
the i n i t i a l procedure, would remain
same w h i l e M e t h o d I " t h i n k "
of
varying "think"
the
t i m e s w o u l d be i n c r e a s e d b e c a u s e
the low values assigned " C . " in the evaluation data survey
sheet.
Conversely, "think"
times f o r Methods I I I
and I V
would be d e c r e a s e d because o f the h i g h v a l u e s a s s i g n e d " C " .
The o v e r a l l t i m e e l e m e n t s w o u l d be c h a n g e d c o r r e s ­
p o n d i n g l y , decreasing the costs o f Methods I I I
increasing the time r a t i o o f Method I I I
and I V
with I I .
p o s s i b l y lead to the conclusion t h a t Methods I I I
while
This would
and I V
could
39
be p r e f e r r e d q u a n t i t a t i v e l y
s e l e c t i n g Methods I I I
as w e l l as q u a l i t a t i v e l y
a n d / o r I V as t h e b e s t
choice.
In view of the previous considerations,
s t a t e m e n t s can be p o s t u l a t e d .
III,
the model t e c h n i q u e ,
three
(1) F o r m a c h i n e s h o p
where time l i m i t a t i o n is the most i m p o r t a n t
thereby
factor,
is the best choice.
general
layouts
Method
For
(2)
m a c h i n e shop l a y o u t s where c a p i t a l i n v e s t m e n t m u s t be
minimized, Method I I ,
factory.
(3)
Method I I
or I I I ,
reinforcement
the templet t e c h n i q u e ,
is most
Where t h e r e is a q u e s t i o n o f u s i n g
Method I I I
satis­
either
s h o u l d be s e l e c t e d because o f
by the q u a l i t a t i v e
analysis.
CHAPTER
VII
RECOMMENDATIONS
Although it
was q u a l i t a t i v e l y
perception varies with the "think"
several layout techniques,
it
determined that
time r e q u i r e d in
this paper.
effect
the procedure or conclusions
An effort
the
is the o p i n i o n o f the a u t h o r
t h a t t h e s e times would n o t be s i g n i f i c a n t l y
to invalidate
space
changed so as
presented
in
s h o u l d be made t o q u a n t i f y t h e
true
o f t h i s phenomenon f o r the purpose o f a c c e p t i n g
rejecting
the previous
conclusions.
Rather than perform a duplicate
in this work, it
or
is suggested that
test of the
several different
problem
problems
be d e s i g n e d , e a c h t o b e p e r f o r m e d o n l y o n c e a n d e a c h p r o b l e m
t o be s o l v e d w i t h a d i f f e r e n t
method.
In t h i s way, any
person p e r f o r m i n g the l a y o u t would n o t use any method more
t h a n o n c e , n o r w o u l d h e w o r k t h e same p r o b l e m m o r e t h a n o n c e .
For purpose of comparison, participants
w i t h as n e a r
t h e same b a c k g r o u n d i n l a y o u t e x p e r i e n c e m u s t be
T h e y s h o u l d be t i m e d i n d e p e n d e n t l y t o s u f f i c i e n t l y
"think"
times from other time.
A complete
a n a l y s i s c o u l d be used t o e v a l u a t e t h e
selected.
distinguish
statistical
results.
APPENDIX
A
AMERICAN
PROPOSED
CODE
CONDENSED
SOCIETY
FOR
OF
A
FORM
OF
THE
MECHANICAL
STANDARDIZING
ENGINEERS
LAYOUT
NOMENCLATURE
42
A CONDENSED FORM O F T H E
AMERICAN SOCIETY OF MECHANICAL ENGINEERS
PROPOSED CODE F O R STANDARDIZING
LAYOUT NOMENCLATURE
(23)
Templets.--The standard covers two-dimensional, oneplane templets and three-dimensional equipment models.
T e m p l e t s c a l e i s 1/4 i n . e q u a l s 1 f t . , U . S . m e a s u r e .
This scale is standard w i t h a r c h i t e c t s , e n g i n e e r s , f u r n i ­
ture and equipment manufacturers, e t c , f o r planning
p u r p o s e s . E q u i p m e n t o u t l i n e s a r e those which would be
made a r o u n d t h e p e r i p h e r y o f a p i e c e o f e q u i p m e n t b y a
plumb l i n e h e l d 7 f t . above the f l o o r , and passed around
the o u t l i n e o f the m a c h i n e . P r o j e c t i o n s such as w h e e l s ,
h a n d l e s , e t c , a r e s e p a r a t e l y i n d i c a t e d as d e t a i l s n o t i n
the p e r i p h e r y .
D e t a i l s o n t h e t e m p l e t a r e t h o s e n e c e s s a r y t o make i t
d i s t i n g u i s h a b l e and to l o c a t e important p o i n t s .
Kinds and
r e l a t i v e weights of lines used a r e :
F i x e d o u t l i n e of machine t o o l or
equipment
Thick solid line
D e t a i l parts and substructures
Thin solid line
Clearances f o r moving parts of
machine t o o l or equipment
Thick dash l i n e
Overhead or underground elements,
foundation pits, service
clearances and o t h e r elements
important to the templet
•••Medium dot-anddash l i n e
Center lines
•
Thin dot-and-dash
line
Clearances f o r movable p a r t s , access and operation are
shown i n dash l i n e s .
T e m p l e t s do n o t i n c l u d e
storage, service or other space.
I n t e r f e r e n c e s a r e i n d i c a t e d by medium d o t - a n d - d a s h
lines and are included i n f i n a l drawings.
Data on the templets i n c l u d e s :
over-all length,
width, height, including travel clearance but not
operator or feed clearances.
Weight and h o r s e ­
power are g i v e n .
S p e c i f i c a t i o n s f o r i d e n t i f i c a t i o n a r e : model or
s t y l e , name, s i z e , u s e r company i d e n t i f i c a t i o n
marks or numbers.
O p e r a t o r p o s i t i o n Is shown b y a s h o r t h e a v y a r r o w .
Other data included are controls, service provisions,
power c o n n e c t i o n p o i n t s , and s i m i l a r
indicators
of necessary a u x i l i a r y o p e r a t i n g f a c i l i t i e s .
k3
Templets should be printed on 110 l b . , or more,
index b r i s t o l or similar durable stock. It i s
preferable to use colored stock:
Machine tools and other operating or production
equipment • • • •
.Salmon
Office equipment and standard factory equipmentb i n s , racks, locker room equipment, t o i l e t
and washroom f a c i l i t i e s * *
Green
Materials handling equipment
••••••Yellow
A u x i l i a r i e s - p a l l e t s , s k i d s , tote boxes,
t r a y s , pans, e t c » • • • • • • • • • • • • • • • • • • - R e d
0
Models.—Three dimensional scale representations of
equipment and f a c i l i t i e s , c a l l e d models, are made from
wood, metal or p l a s t i c by appropriate processes, in­
cluding tool and machine fashioning, die c a s t i n g , and
p l a s t i c production methods.
The scale i s the same as that for templets, 1/1+ i n .
equals 1 f t . , U. S. measure.
Details included are those s u f f i c i e n t , without d i s ­
t o r t i o n , to identify the model and show i t s important
structural and operating features for ready i d e n t i f i c a t i o n
of the equipment and indication of i t s operating require­
ments so far as plant layout i s concerned. Control
points and hazard areas are shown, with a l l controls
and operating or moving parts located in neutral p o s i t i o n ,
no moving parts being designed into the model unless I t
is impossible to show them in any other way.
Models are made in finishes and colors as near as
possible to the actual item represented-including
multiple f i n i s h e s , as in o f f i c e furniture.
Machine-tool model finishes should follow the recommend
ations of the National Machine Tool Builders A s s o c i a t i o n .
Machined surfaces can be shown by aluminum paint.
Control points should be shown by l i g h t buff paint,
conforming to the present-day p r a c t i c e s for greater
v i s i b i l i t y and s a f e t y . The p r a c t i c e of the individual
company should be followed where models are used exclu­
s i v e l y for a company.
Allowances and clearances should not be exaggerated.
Accompanying templets should show these allowances for
extreme operating and service conditions, but should not
include any operator or f a c i l i t i e s allowances, as stated
above under discussion of templets. These accompanying
templets should carrjr at l e a s t name or description and
model number, and, i f p o s s i b l e , type, s i z e , maximum
dimensions, certer l i n e s , weight, e t c . , and data on over­
head and underfloor requirements.
Models should be durable, not e a s i l y damaged, have a
l a s t i n g f i n i s h , and have s u f f i c i e n t weight to stay in
position when placed, or be equipped with holes in the
base for insertion of fastening p i n s .
kk
A l l necessary i d e n t i f i c a t i o n markings—name, number,
s i z e , d e s c r i p t i o n , e t c . s h o u l d be g i v e n i n a b b r e v i a t e d
form and in the most s u i t a b l e p l a c e .
M o d e l s s h o u l d be so d e s i g n e d a s t o be u s e d w i t h
accompanying standard templets f o r the i d e n t i c a l equip­
ment. This p r o v i s i o n f a c i l i t a t e s drawing the l a y o u t on
the f l o o r plan.
APPENDIX B
EQUIPMENT LIST - GIVEN CONDITIONS
EQUIPMENT LIST - GIVEN CONDITIONS
Production Area
12-Lathes
Universal Turret
1-Gisholt # 3 Turret
3-LeBlond Engine, 1 0 " , 1 2 " , 1 6 "
I-II4." Warner and S w a s e y E n g i n e
1 - l i j . " P r a t t and W h i t n e y E n g i n e
1 - R i v e t t P r e c i s i o n (Cabinet)
5>-#3
6 - M i l l i n g Machines
3 - B r o w n and S h a r p e # 2 V e r t i c a l
1-Milwaukee Horizontal
1-Cincinnati #3 Plain
1 - B r o w n and S h a r p e # 2 P l a i n
1 - C i n c i n n a t i 21}." S h a p e r
Ii--Drill P r e s s e s
1-Cincinnati-Bickford
1-8" Sho-speed
1-llj." D e l t a P e d e s t a l
1-Knight Boring M i l l
Radial
1 - 2 2 Ton L & J Punch P r e s s
2-Grinders
1 - B r o w n and S h a r p e # 2 S u r f a c e
1-Hammond Heavy Duty T o o l
1 - R a c i n e Hack Saw W3BX
2 - D o - A l l HP-36 Band Saws
2-Welders
1 - D i r e c t C u r r e n t A r c on t r u c k 3 ' x 6' x ij.
1-Heliarc l
1
1-Denison Arbor
1L.-Benches
6-3' x 5'
2-3' x 8'
1-2 1 / 2 ' x
1-2' x 8'
2 - 3 ' x 6'
1 - 5 ' x i|.'
1-2' x 5
1
8»
x 2 ' x 3'
Press
EQUIPMENT L I S T - GIVEN CONDITIONS
Production Area
1-Water
(CONTINUED)
(Con'd)
Fountain
26-Machine Stands 1 1 / 2 ' x 2'
l-Foreman*s
x3»
Desk
1 - 5 Ton Bridge Crane Assembly
S u p p l y a n d T o o l Room
3-3'
x 1 0 » x 6'
I-I4.8"
Bins and
Shelving
Rotabin
1 - B e n c h 2 ' x 1±»
1-Dial Platform Scale 2' x 3 1/2" x
1-12"
Delta Pedestal D r i l l
1-10"
S o u t h Bend L a t h e
1 - C i n c i n n a t i #2 P r e c i s i o n
2-Stock Racks
1 - 2 1 / 2 ' x 6 ' x 6'
1 - 2 ' x 9 l / 2 » x 6»
Men's
Lavatory
2-Toilets
2-Urinals
2 - C i r c u l a r ii
1
Wash Basins
2-Benches 1 1 / 2 ' x 1 0 '
6-Lockers 1 '
Ladies'
1-Toilet
1-Sink
x
I4.'
Lavatory
Press
Grinder
3'
EQUIPMENT L I S T - GIVEN CONDITIONS
Offices
3-Desks
1-Typist
1-60"
1-72"
3-Letter
Piles
23 P e r s o n n e l
(or
operators)
3-Office
1 - S u p p l y a n d T o o l Room
19-Production
(CONTINUED)
APPENDIX C
ROCEDURE DATA
PROCEDURE DATA
METHOD
I
Operation
1 . Review given condi­
tions of problem;
l i s t requirements
for equipment and
services.
2. Sketch and measure
tools and equip­
ment from manufac­
turers catalogs or
actual f a c i l i t i e s .
Act
20
III
II
Total
20
3130 3*30
3. Draw templets, ink
in contours and
controls, and
cut out.
il. Draw sketch of build­
ing floor plan; de­
termine general ser­
vice areas with
regard for building
design; sketch
approximate grouping
of a l l i e d equipment
within areas.
(Times in Hours and Minutes)
Think
Act
Total
Act
20
20
20
3130 3.30
IV
Total
20
3130 3:30
8.00 85OO
35
35
35
35
Act
20
Total
20
3.30 3:30
85OO 8:00
35
35
35
35
PROCEDURE DATA
I
Operation
5.
A . Draw building
outline with
e x i s t i n g doors
and columns.
B. Tape i n b u i l d ­
ing outline
with existing
doors and
columns.
C. Cut plastic
walls to length
and glue to
baseboard to
form building
o u t l i n e ; glue in
columns and doors.
Sub-Total:
Act
20
(CONTINUED)
II
Total
Think
Act
6. A . D r a w o r p l a c e
production tools
with a l l i e d equip­
ment in general
areas bearing in
mind the o v e r a l l
arrangement r e ­
quired in exist­
ing f a c i l i t i e s .
2:03
B« R e a r r a n g e t h e
following equip­
ment (with mach­
ine stands) in
the given o r d e r :
Total
Act
IV
Total
Act
Total
20
07
20
III
20
2:03
07
59
59
07
07
59
59
0l\.
0J+
11
11
07
07
59
59
1:06
0i+
1:06
0k
PROCEDURE DATA (CONTINUED)
I
Operation
Act
l)LeBlond En­
gine Lathe
with Brown
and Sharpe
#2 V e r t i c a l
mill.
2)Turret lathe
with #3
heavy duty
grinder.
3)Two #3 Uni­
v e r s a l Tur­
ret lathes
with two
Brown and
Sharpe #2
Vertical
mills.
1±) Small LeBlond
lathe with
boring m i l l
5)Brown and
Sharpe #2
Vertical mill
with turret
lathe.
6)#3 Turret
lathe with
Brown and
Sharpe #3
Plain m i l l .
7)Remove from
layout:
Boring mill
0
II
Total
Think
Act
III
Total
Act
Total
IV
Act
Total
PROCEDURE DATA
(CONTINUED)
I
Operation
Act
II
Total
Think
Act
III
Total
Act
IV
Total
Act
Total
LeBlondEngine lathe
Turret lathe
Radial D r i l l
Hack Saw
2 - D o - a l l saws
B&S #2 V e r t i ­
cal m i l l
Porman s desk
2-welders
!
8)Brown and
Sharpe Surface
grinder.
9) C i n c i n n a t i
Shaper w i t h
bench
10)Punch Press
with Slo-speed
D r i l l press
1 1 ) 3*™benches
12)5-benches
2:23
2:38
S\lfc) — T O t a l t
— — — — ——>— — — —>
2+: 2 6 k ' M
7.
A . Draw or place
S u p p l y and
T o o l Room e q u i p ­
ment in general
area.
B« R e a r r a n g e t h e
following
equipment in
the given order:
16
16
15
15
06
21
_ — — — — — ___
30
k$
__—
_____
06
— ——
21
—— — — — — — — —
10
25
hi
56
10
25
02
02
05
05
02
02
PROCEDURE DATA
I
Operation
1)Shelving and
racks
2 ) S h e l v i n g and
racks
3)Stock rack
Ij.)Rotabin
5)Draw o r p l a c e
temporary
partitions
6)10"
lathe
with bench
7)Grinder with
D r i l l Press
8)Move i n s i d e
partition
9)Stock rack
Act
1+1
(CONTINUED)
II
Total
51
Think
Act
III
Total
Act
IV
Total
Act
Total
10
05
15
18
28
05
15
10
07
17
23
33
07
17
01
01
02
02
01
01
Sub-Total:
57
8. A . D r a w o r p l a c e
men's l a v a t o r y
equipment in
general area,
17
B. R e a r r a n g e t h e
following equip­
ment i n the
given order:
l)Toilets with
urinals
2)Wash b a s i n
3)Wash b a s i n b a c k
to original place
1:07
17
PROCEDURE DATA
I
Operation
14.)Draw o r p l a c e
in temporary
partitions
5)Move p a r t i ­
tion with
toilets,
urinals and
basins.
Sub-Total:
5k
9« A . D r a w o r p l a c e o f ­
fices and ladies'
lavatory equip­
ment i n g e n e r a l
area.
B. Rearrange t h e
following equip­
ment i n t h e
given order:
1 ) A 1 1 equipment
for both
offices
2)Draw or place
in temporary
partitions
II
A c t Total
37
12
(CONTINUED)
Think
III
A c t Total
IV
A c t Total
Act
Total
k l
10
02
12
\ $
2 $
02
12
l:0i|.
10
03
13
17
27
03
13
01
01
02
02
01
01
12
3)Desk
desk
with 3 files
5) Desk
29
Sub-Total:
k)Typewriter
k l
kk
15
03
18
10
25
03
18
56
15
ok
19
12
27
0k
19
PROCEDURE DATA
I
Operation
10*
Act
A . Draw or place b a l ­
ance o f p r o d u c ­
t i o n equipment
(from 6-B-7) i n
proper area.
33
B. R e a r r a n g e t h e
following equip­
ment i n t h e
given,order:
1) S h a p e r
2) P u n c h p r e s s
3) A r b o r p r e s s
%) S l o - s p e e d D r i l l
press
5) F o u n t a i n
6) H e l i - a r c
Welder
7) D . C A r c
Welder
8) H a c k s a w w i t h
foreman s desk
9) D o - a l l B a n d
saw
10) 1+ b e n c h e s
11) F o u n t a i n w i t h
2 welders and
hack saw
5k
Sub-Total:
(CONTINUED)
II
Total
Think
33
III
IV
Act
Total
Act
Total
Act
Total
01
01
02
02
01
01
^
09
29
1
1:27
1 1 . Switch Basins,
t o i l e t s , and
urinals with
partitions
±5
1:11+
20
09
29
21
.
1+1
1:1+7
20
10
30
23
1+3
10
30
01
01
01
01
01
01
15
n
PRODUCTION DATA (CONTINUED)
I
Operation
1 2 . Draw or place oper­
ators in p o s i t i o n .
Act
01+
1 3 . A. Draw a l l l i n e s
in heavy.
1:27
B. Glue down a l l
templets and
permanent
partitions•
C Put models in
place.
D. Cut p a r t i t i o n s
and doors from
p l a s t i c and
glue in p o s i t i o n .
E. Rearrange the f o l ­
lowing equipment
(with operators
and stands) in the
given order:
1) Rotabin with
dial scale
2) Stock rack
3) 5 benches
4) Iii" D r i l l press
5) k benches
6) Small Engine
lathe
7) Do-All Band
saw with D r i l l
press
8) Boring m i l l
with Arbor press
9) Shaper with #3
Turret lathe
II
Total
Oi^
Think
Act
III
Total
01
01
10
10
Act
01
IV
Total
01
Act
Total
01
01
08
08
1:27
40
1+0
ko ko
P R O D U C T I O N DATA.
I
Operation
Act
Precision
Lathe with small
LeBlond lathe
11) P u n c h p r e s s w i t h
B&S #2 V e r t i c a l
mill
2:37
Sub-Total:
(CONTINUED)
II
Total
Think
2:£2
15
4:19
15
Act
III
Total
Act
02
17
20
12
27
IV
Total
Act
Total
10)
If.: 01+
14•
15•
1:00
Construct bridge
crane system from
balsa wood, wire,
and thumb-tacks;
paint with tem­
pera; and i n s t a l l .
P r i n t equipment
nomenclature on
drawing,
50
50
35
32
1:15
1:20
50
47
1:35
50
50
50
TOTAL TIMES:
19:47 =
14:45
=
7:07
=
17:42
=
19.78
14.75
Hours
7.11
Hours
17.70
Hours
Hours
59
APPENDIX
DATA
EVALUATION
SURVEY
D
AND
COMPUTATIONS
60
DATA E V A L U A T I O N
SURVEY
In order t o complete data needed f o r a thesis on
plant l a y o u t , i t is requested that you read the following
i n s t r u c t i o n s and comply w i t h them t o t h e b e s t o f your
a b i l i t y . Y o u r a s s i s t a n c e w i l l be g r e a t l y a p p r e c i a t e d .
P o u r methods o f p l a n t l a y o u t t e c h n i q u e s a r e t o be
evaluated:
METHOD
I.
Drafting
(Block Porm)
II.
Templets
(Contour)
III.
IV.
The
following
Models
(Prototype)
Templets and Models
(Superimposed)
c r i t e r i a w i l l be used f o r e v a l u a t i o n :
A.
Education level required to
the layout
perform
B.
Mental effort
C.
Space p e r c e p t i o n a n d u t i l i z a t i o n
attained by layout engineer
D.
Decision influence
r e q u i r e d t o do t h e l a y o u t
EVALUATION
(E)
I.
on management
I n t h e space p r o v i d e d below, rank t h e e f f e c t i v e n e s s
of " A " i n Methods I, I I , I I I , and I V by assigning the
method i t best s a t i s f i e s w i t h a value o f " 1 0 " d e c r e a s i n g
t h e v a l u e s o f t h e r e m a i n i n g m e t h o d s w i t h "0" a s t h e p o s s i b l e
lower l i m i t . Repeat t h i s procedure with B, C , and D .
Finish this section before reading I I .
Best s a t i s f a c t i o n o f A a n d B would mean l e a s t r e q u i r e d
Method
II
III
IV
EVALUATION
A
B
D
II.
As a separate procedure, rank A , B, C , and D in
o r d e r o f i m p o r t a n c e w i t h a t e n t a t i v e v a l u e o f "10" g i v e n t o
61
L A T A E V A L U A T I O N SURVEY/
(CONTINUED)
the most i m p o r t a n t , and smaller values g i v e n the r e s t , a c ­
c o r d i n g t o t h e i r r e l a t i v e i m p o r t a n c e ("0" i s t h e l o w e r
limit).
Space is p r o v i d e d below.
The most important
e v a l u a t i o n w i l l b e t e r m e d E-]_, n e x t i m p o r t a n t E , e t c .
C o m p a r e E-, w i t h E2 + E? + E L . I f En i s p r e f e r r e d o v e r t h e
sum o f t h e o t h e r s , t h e v a l u e s s h o u l d b e a d j u s t e d s o t h a t
E-,>Eo + Eo + E, . S i m i l a r l y , t h e v a l u e s w o u l d b e a d j u s t e d
i r Ei ^ E2 + E^ + E. • H o w e v e r , i f E n < E + Eo + E. t h e n
E-j_ s h o u l d b e f u r t h e r c o m p a r e d t o E2 * E3 o n l y f o l l o w i n g t h i s
e x a c t p r o c e d u r e t o r e f i n e i t s v a l u e < , = , o r > t h e sum o f E +
Eo#
This step is repeated u n t i l a value - E is determined.
T n e same p r o c e d u r e i s f o l l o w e d c o m p a r i n g E2 w i t h E~ + E> •
R e a d j u s t m e n t s i n v a l u e s s h o u l d be f o l l o w e d a c c o r d i n g l y . * ^
2
2
2
2
For example, the ranking might follow this action:
A , most p r e f e r r e d , B, n e x t i n importance, C , n e x t , and D
l a s t . A m i g h t b e v a l u e d 10; B , 7; C , j?; a n d D , 2; t e n t a t i v e l y .
Upon comparison, A is not equal to or p r e f e r r e d over B + C + D ,
t h e r e f o r e , n o t o n l y does t h e combined w e i g h t o f B , C , a n d D
e x c e e d A , b u t A m u s t b e c o m p a r e d t o B + C . H e r e we d e c i d e
A = B + C . I f A = 10, t h e n B + C = 10. T h e r e f o r e , t h e v a l u e s
f o r B a n d C a r e a d j u s t e d f r o m 7 a n d 5 t o 6 a n d ii r e s p e c t i v e l y .
B I s e v a l u a t e d n e x t b y c o m p a r i n g w i t h C + D . I f B (6) i s
d e c i d e d t o b e m o r e i m p o r t a n t t h a n C (ii) + D (2), t h e n t h e
v a l u e o f D I s c h a n g e d t o 1. T h i s m a k e s B (6) g r e a t e r t h a n
C + D (5) a n d d o e s n o t d i s t u r b t h e p r e v i o u s r e l a t i o n s h i p
o f A (10) = B (6) + C (k) a n d A (10) < B (16) + C (1+) + D (1).
EVALUATION
fl
CRITERIA
(A,B,C,
OR D )
TENTATIVE VALUE
ASSIGNED
FINAL VALUE
ASSIGNED
62
DATA SURVEY SHEET
I.
M e t h o d CM)
Evaluation (E)
I
(P
II.
II
)
x j
( P
III
IV
7
10
8
2
)
J
A
5
B
i
1*
8
10
C
2
5
8
10
D
k
6
9
10
Evaluation
E
l
h
2
E
Criteria
Preference
3
=
Z P J J C M J J )
2
p
i j
(
M
i n
)
E
il l
P
P
=
(2) (10)
1
1
E
+
=
=
Similarly,
P
20
1
+
Pinal Value
Assigned
C
D
10
B
3
A
2
7
E
+
i2 2
P
1
2
E
+
2
'
+
ft)(7)
+ 2 8
=
61
=
10.5%
=
118
=
20.3%
=
187
=
32.1%
=
216
=
37.1%
E
in n
r
13 3
lij. 4
• ^ P ,
E
+
P
E
+ (D(3)
+ (5)(2)
+
+
3
10
63
DATA SURVEY SHEET
2.
I.
E v a l u a t i o n (E)
M e t h o d (M)
I
{p
II.
lj>
II
(p
CP
2J>
III
IV
33>
< V
A
7
8
10
9
B
7
9
10
8
C
k
5
10
10
D
5
6
9
10
Evaluation
E
4
A
Criteria
Preference
Pinal Value
Assigned
C
D
B
10
8
6
A
3
= lir-3 = 1 7 . 1 $
= 176
= 21.C >*
= 262
=
3 1 . : \%
= 255 = 30.5 '4
DATA SURVEY SHEET
3.
I.
EVALUATION
(E)
METHOD
II
I
tt-
II.
IJ
CM)
.)
FP
2 J
III
IV
)
A
2
5
7
10
B
it
5
8
10
C
2
k
8
10
D
7
8
9
10
EVALUATION
PINAL VALUE
ASSIGNED
CRITERIA
PREFERENCE
10
5
2
1
c
A
D
B
E^
SP
L J
FM )
I
2P. . CM
)
=
kQ
=
86 =
2P. , C M _ ) = LI+1
T T
2P
FM
)
=
8.6$
15.5$
=
= 280 = 50.
W
65
DATA SURVEY
SHEET
I*.
I.
Evaluation
(E)
Method
I
(
IIo
(M)
II
III
CP )
(P
2j
V
3J
IV
)
A
10
10
10
10
B
10
10
10
10
C
2
7
5
10
D
2
7
5
10
Evaluation
E
l
E
2
Criteria
Preference
Pinal , Value
As s i g n e d
D
C
B
A
.0
3
2
1
=
56 = 12.c
= 121 = 27.<
2
p
2
P i j
(
i j V
CM )
i v
=
95 = 22.0%
= 160
= 37.C
66
DATA SURVEY
SHEET
5.
I.
M e t h o d CM)
Evaluation (E)
I
II
III
IV
5
7
9
10
B
6
9
10
C
8
9
10
7
9
10
V
A
D
II.
3
Evaluation
E
Criteria
Preference
Pinal Value
Assigned
C
1.0
6
2
2
i
E
D
A
B
2
\
2P i W
2P
2P
=
is*!*
78 = 12.9$
= 11+8 = 21+.
1
W
)
= 180 = 29.7$
2 P . .CM )
ij
IV
= 200 = 3 3 . 0 $
t
J
f t
n
i
67
DATA SURVEY; S H E E T
6.
I*
M e t h o d (M)
Evaluation (E)
I
II
CP )
2 j
II.
III
(p
IV
(p
3j>
4j>
A
1
10
8
4
B
1
5
10
8
C
1
3
10
7
D
1
3
10
7
Evaluation
E
i
E
3
Criteria
Preference
Pinal Value
Assigned
A
D
C
B
10
8
6
1
K
2P
l j
=
(M )
I
25 = 4.6%
= 147 = 26.8%
S P
ijCM
sp
CM
ij
)
= 230 = 42.0%
)
= 146 = 2 6 . 6 %
I I T
iv
68
DATA SURVEY
SHEET
7.
Io
Evaluation
(E)
Method
I
(M)
I I
III
IV
io
5
10
10
8
10
8
io
(p )
2j
II.
A.
0
B
0
C
0
D
0
5
5
Evaluation
E
E
Criteria
Preference
10
8
2
1
D
C
A
B
l
2
E3
E
Pinal Value
Assigned
k
S P . . (M_)
ij
I
2P (M )
l j
I I
0 =
= 105
0%
= 21.9 $
= 174 = 36.3
= 200
= 1+1.7$
69
DATA SURVEY
SHEET
8.
I.
Evaluation
Method
(E)
i
II
V
II.
(M)
III
IV
CP..)
A
5
7
10
9
B
2
6
10
8
C
3
3
10
6
D
k
10
8
Evaluation
E
i
E
2
P i n a l Val ue
Assigned
Criteria
Preference
Eo
4
2P.
ij
2p
ij
J !
(M
)
III
T T T
CM i v)'
c
10
D
B
A
2
1
7
=
67
=
=
77
=
1 6 . 1 %
= 200
= 41.7%
=
= 2802%
135
DATA SURVEY
I.
SHEET
Evaluation (E)
Method
I
II
CP
II.
(M)
III
IV
)
A
0
6
8
10
B
0
5
7
9
C
2
9
10
D
1
9
10
Evaluation
E
i
E
2
E
3
E
k
Criteria
Preference
Pinal Value
Assigned
c
10
D
B
A
2 p . . (
2
sp
M
l
)
W
l y
Cm
)
in'
2P..(M
ij
)
IV
8
5
3
=
28
=
4.5$
=
1 1 5
=
18.6$
= 221
=
3 5 . 7 $
=
= 111
255
.2$
71
DATA SURVEY
SHEET
10.
I.
Ev ,luation ( E )
Method (M)
8
II
I
fp
II.
1 3
)
IV
III
CP )
CP3j)
2 j
A
10
8
6
B
8
6
10
C
4
5
7
10
D
7
8
9
10
Evaluation
Criteria
Preference i
%
E
Pinal Value
A s s ig n e d
C
A
D
B
2
<
s
2P
Z
2
M
V
i
j
}
i
(M )
n
M
*iJ< III>
P
i J
C
V
10
8
5
3
1 7 9 =24.3%
=
=
172
=
4
4
= 23.3%
1 9 3 ==
26.1%
= 194 =2 6 . 3 %
72
D A T A SURVEY"
SHEET
11.
I.
M e t h o d (M)
Evaluation (E)
i
CP,.)
II.
A
2
B
3
C
3
D
3
Evaluation
E
III
I I
(p
3
6
(
M
5
10
6
10
8
10
8
10
c
10
6
4
2
Eo
U
4j>
Pinal Value
Assigned
D
B
A
P
(P
3j>
Criteria
Preference
i
2
IV
I I >
=
64 = 13.1%
=
97 = 19.8%
= 138 = 28.2%
= 1 9 0 = 38o 9%
73
DATA SURVEY SHEET
12.
I.
Evaluation
Method
(E)
(M)
II
III
CP )
< 3J>
I
P
2 j
A
3
B
3
C
D
II.
E
E
E
5
8
k
5
8
5
10
10
10
10
5
Evaluation
Pinal Value
Assigned
Criteria
Preference
10
10
5
5
c
D
B
A
l
2
3
i
SP^CM.)
ij
II
IV
= 120
= 15.2$
= ll+O = 1 7 . 7 $
= 250
= 31.6$
= 280
=
25.4$
74
DATA SURVEY
SHEET
13.
Io
Method
Evaluation (E)
I
(M)
II
III
(P )
( 3j>
10
k
3
5
8
10
6
9
10
2 j
A
8
B
2
C
D
II•
E
l
E
2
E
3
E
k
p
8
Evaluation
=
^ i j ^ I I I
2 p
ijt iv>
M
10
9
k
k
= 106 =
)
5
194
242
13*7%
= 25.2%
= 229 =
=
10
Pinal Value
Assigned
D
C
B
A
I
p
( 4j
10
Criteria
Preference
2P^(M
ij
IV
29.7$
= 31.k%
}
75
DATA SURVEY
SHEET
Ik.
I.
Evaluation (E)
Method
I
A
B
II
f
V
V
III
II•
E
10
9
5
7
10
8
8
10
9
10
l
4
Criteria
Preference
D
C
B
A
i
2
E3
\
=
2 p
1
J
C M
i
n
i^ iv)
M
7
3
2
59 = 1 0 . 3 %
)
= 1 9 6 = 34.2%
= 2 1 2 = 37.0%
}
Pinal Value
Assigned
10
= 1 0 6 = 18.5%
2P..CM,,)
^
^
5
Evaluation
E
fp
'V
C
D
IV
Lo
f
(M)
APPENDIX
.MPLE
E
CALCULATIONS
77
SAMPLE
BARTLETT'S
S a m p l e
S i z e
=
ru
=
CALCULATIONS
TEST
OF
s
1[|_
FOR
EQUAL
=
i
VARIANCES
u n b i a s e d
e s t i m a t e
s t a n d a r d
Zn
±
Number
o f
B a r t l e t t
!
=
N
t h e
= 5 6
s a m p l e s
s
o f
d e v i a t i o n
T e s t
=
i s
K
=
4
s h o w n
I I
S
I I I
5 8
5 . 7 8
S
I V
5 8
6 . 6 6
«
3 . 8 7
b y :
f
F
S
2
M
=
f - ^ b - M )
M
w h e r e
s^
2
=
=
t h e
CN-K)
I n
v a r i a n c e
s
o f
2
p
t h e
-
2
=
* P
2
•)->->
U
i
1
1
I n
s a m p l e ;
s^J
the
p o o l e d
v a r i a n c e
z
2(n -l)s
±
[ f n j - 1 )
±
=
N - K
=
1 3 ( 3 5 . 8 8
+
1 4 . 9 8
+
3 3 . 4 1
+
¥ + . 3 5 )
5 6 - 4
=
I n
3 2 . 1 5
=
3 2 , 1 5
3 . 4 4
I n
3 5 . 8 8
=
3 . 5 8
I n
1 4 . 9 8
=
2 . 7 1
I n
3 3 . 4 1
-
3 . 5 1
I n
4 4 . 3 5
=
3 . 7 9
=
1 3 o 5 9
2 1 n
M
=
=
5 2 ( 3 . 4 4 )
2 . 1 7
-
1 3 ( 1 3 . 5 9 )
2
S
i
78
A =3(K1-1) ' i-1/ \ N1-K
1 ~ 4 1 = 0.0321
(3)(3) 13 52
_ = k-1 = 3
K+
_5 = ij.868,5
(0.032)2
n
f
1
1
b
=
f2
1 - A +i
4868.5
= 5027.9
1 - 0.0321 4+8168.5
fM
= (4868.5)(2.17)
(3)(5027.9 - 2.17)
t
±
2(b-M)
= 0.701
At 5% level of significance, I? ,
= 2.60
(3, 4.060.3)
0/0
X
s
SAMPLE CALCULATO
INS FOR
STUDENTS' t DS
I TRB
I UTO
IN
Meh
tod
II
III
H.55
31.86
21.21
5.99
5.78
3.87
2 =•
8P
IV
35.34
6.66
N-K
Students' t = 1+1
l 2
= 14; N = 28; K = 2;
Degrees of rfeedom (d.f.) = n^_ + n^ - 2 = 26
For meh
tods III and IV:
13 [(5.78) + (6.66)]
24
t = 35.34 - 31.86
1.48
(1
1
Ilk
n
n
n
±
2
6.24
2
+
Ik
At d.f. = 26, t ^ = 1,71
For meh
tods I and II, 13fc5o99) + C3.87)J
26
= 5.11
s
2
2
80
t
=
21.21 5.ii
At d f . = 26,
e
= 1.71
11.55
1
1
+
Ik
lk
= 5.07
BIBLIOGRAPHY
82
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