Factors for One Sided Tolerance Limits and Variables Sampling Plans

8/11/2019 Factors for One Sided Tolerance Limits and Variables Sampling Plans

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2/25


3/25

TABLES

FOR

ONE-SIZED

STATISTICAL

TOLERUCE

LIMITS

Z:::J.BY

Z~GERALD

J.

LIEBRM

TECHNICAL

REPORT

NO.

34

NOVEKBER

I,

1957

PMEARE

UNDER

CONTIRACT

N6onr

-25126

GERALD

J, LIKEKAN,

PROJRT

DIRECT'OR

FOR

OFFCR

OF

NAVAL

R

ACH

REPOUTION

IN WHOLE OR IN PART

IS

KI1TKD

FOR

ANY

rURPOSE

OF

THE

UNITED

STATE

APPLIED

MATHD(ATICS

AND STATISTICS

LABORATORY

STANFORD

UNIVERSITY

STANFORD,

CALIFORNIA


4/25

.-

1,

-

.-

\

.

"

.

,. ,.q

TABLES FOR ONE-SIDED STATISTICAL TOLERANCE

LIXITS

by

Gerald

J.

Lieberman

'A

1.

INTROUCTION.

The

quality

of

manufactured

product is often

specified

by

setting

a range,

the bounds

of

which are

called

tolerance

i ts.

These

limits

have

the

property

that a

certain

percentage,

00(]-a)

% , of

the

product

may

be

expected

to fall

within

these limits.

If

the

quality

of the items

is

normally

distributed

with known mean,

14

and

known

standard

deviation,

a , two-sided tolerance

limits

are

formed by

adding

to and subtracting

from

p

he quantity

K

a' , where

K2

is the normal

deviate

corresponding

U 22

to

a/2

.

An

upper

one-sided tolerance

limit Is

given

by p + K or

and

a

lover

one-sided tolerance

limit is

given

by

p- K

a

. Unfortunately,

In

a

practice,

the values

p

and

a, are

rarely

known

and

estimates

of these

A

values,

- and a

,

respectively,

are used.

However,

where before it

could

be

stated

that 95

of a manufactured

product

lies

below

1 + .64 a

the

upper one-sided

tolerance

limit,

this

statement

cannot

be

extended to

the limit

i + 1.645

a

. The quantities

i and

s

arp

random

variables,

and hence the

limit

depends

upon

the

particular

outcome

of

the sample.

Different

samples

will lead to

different

limits. How

close thebe

11mit

are to

u +

1.645 a

depends

upon how

good

the

estimates

are.

It

is evidnt

then

that the fraction

of

the ;tems

lnc'u,&ed

bet.--,r

A,,

A~

-


5/25

-

~;

-2

",a. t -K., ,

i

+

K

a.,s

for two-sided tolerance

limits,

b. - o, +

K

]

for an upper

one-sided

tolerance

limit,

c. Ix- Kas , co]

for a lower

one-sided

tolerance limit

will not

always contain a specified

proportion I- of

the

manufactured

items. However, it is

possible to determine constants K such

that in a

large series of samples from

a normal distribution, a

fixed

proportion

7

of

the

int(

rvals

a. [-Ks, +

Ks

]

for two-sided tolerance

limits,

b.

[- ;0,+ Ks] for an upper one-sided tolerance limit,

and

-c. -

Ks,

co]

for a lower one-sided tolerance

limit

will

include

100(1-a)%

or

more of the distribution.

The

finite

limits

of

these intevals are known as statistical tolerance limits. Thus, an

upper

one-sided

statistical

tolerance limt is given by

x +

Ks and has

the property that the

probability is

equal

to a

preassigned value

7

that

the

interval

[-

co,

i

+

Ks]

includes

at least a

specified proportion

1

-

a

of

the distribution.

Note

that

in

most practical situations

y

is

usually

a

large number close to 1 . Statistical tolerance intervals

should not be confused

with confidence intervals for a

parameter of

th e

distribution. Confidence limits

for the mean of a normal distribution

are

such

that in a given fraction, say

.95

,

of

the samples

from which they

are computed, the interval bounded by

the

limits

will include

the

true mean

of

the

distribution. For confidence interval

estimation,

.95

is a lso

called the confidence coefficient.


6/25

Many

extensive

tables

of

factol-i

K

for

two-sided

o~lera~n:e limits

have

been

computed.

A. R.

Bovker

presents

such a table

in

[1)

and

very

recently A.

Lieberman issued

a set of tables [2)

which

are

an extension

of Bowker's tables in

that they can be used when s

is computed from saple

si~es

other

than n . Resnikoff

33 and

JMitra (14)

computed values of

K when a

Is

estimated by

the average

range

of

subgroups. Tables

of

factors

K for

one-sioe.

tolerance

limits

have

never

been conputed anid

It

is

the

purpose

of

this

paper

to

present

such

tables.

2.*

TABfL OF

ONE-SIDED T01 ACE

LIM.

Factors

K such

that

i+ Ku

and

-Ks

are

an

upper

one-sided

tolerance

limit

and

a

lower

one-sided

tolerance

limit,

respectively, for

a

normal universe

are given

in Table

1

for

n

a3,2d,...,2530,354,245,50;

for

Y

a 0.75,

0.90, 0.95,

0.99; and

for

Q

a 0.25, 0.1000.05,0.01..0.001

iis

the

sample

mean

a

(x

1

+ x',

x.. /n )

and a

is the

sample

st~zdard

deviation

a __( )2

+ (x2- ) + .+(Xn

)

2

/(n-l).

For

n greater

than 50

the values

of K can

be obtained

using the

asymptotic

normality

property of x+

Ks .

With tLhis approximation,

K

is

given

by

K

a

a

where

K'~

a 1

K

2

.... .-.

..

. .

. . .

. .1

- b


7/25

. . . 3CM .

1-.. 4.

-4--

and K and

K (which

equals -K,

that

2

)

are th e

a

-7 7

normal deviates

corresponding

to a and 7

respectively,

i.e.

o-1

2

00

1

2

fe

nds dz -,

7

3.

.XAMPLZ.

A

mnufacturer of light

bulbs would like to specify a single

lower

limit above which he can be assured, with probability

0.95 , that

at

least

99 of his

production

will

lie. A

sample

of

30 bulbs

is taken

and the sample mean and sample standard

devir.tion

are

found to be

987.2

and 5

963

respectively. A value

of

K a

3.064 corresponding

to

a

- 30

7 a 0.95 and

a

a 0.01 is

obtained from Table

1 . The required lower

tolerance

limit

is given by

- Ks -

987.2

- (3.064)(5.963)

-

968.9

4

C0TRT

ION

OF

TRE

TAM.U

For

the

case of a normal distribution

with wkziown parameters

P

and w

,

exact

one-sided tolerance limits

my be

computed by the follow-

ing

procedure.

Let ta -

1

,

IS %

be a

non-central

t statistic with

n-i

degrees

of freedom and non-etrality parameter

n K .

K is

aa

defined

by

2

S e-

Z

dz -a

Determine

t

0

such that P tn

K > t

1

- '

Let

K

- to/ /'-. Then

if i and s

are the

sample

mean

and

the sample

standard

deviation, respectively,

bae. on

a sample

x ,x ,.

.V

n

.e


8/25

-2

%

X

2

_ _i

x=

-

and

s

n

n

n-i

i

+

Ks

and x

-

Ks are

upper

one-sided

tolerance

limit

and a

lower

one-sided

tolera-ice

limit,

respectively

Thus,

the

probability

is

y that

.

at

least a

proport on

l-a

of the

distribution

will be

less

than

x

+

Ks

(or greater

than

x

.. Ks

)

The value

t

o

may be

obtained

from tables

of

the

distribution

of the

non-central

t

sta'clstic.

Such tables

are

those of

Johnson

&

Welch [5]

and

Resnikoff

and

Lieberman

[6]. The

latter

tables

are perhaps

more

convenient

for

thiv application,

and

were

used

in the computation

of Table

1.

2

:i

I

-p.

.1

---------.--

p~ .

.


9/25

TABLE

1.

Tolerance

Factors

for

Normal

Distributions

Factors

K

such

that

the

probability

is

7

that

at

least

a

proportion

-a

of

the

distribution

will

be

less

than

x +

Ks

(or

greater

than

x

-

Ks),

where

i

and

s

are

estimates

of

the

mean

and

the standard

deviation

com-

puted

from

a sample

of

size

n

7

-

0.75

I

7

- 0.90

['-Cr-0.25

0.10 0.05 0.01 0.001

0.25

0.10 0.05 0.01

0.001

3

1.464

2.501

3.152

4.396

5.805

2.602

4.258

5.310

7.340

9.651

4

1.256

2.134

2.680

3.726

4.910

1.972

3.187

3.957

5.437

7.128

5

1.152

1.961

2.463

3.421

4.507

1.698

2.742

3.400

4.666

6.112

6

1.087

1.860

2.336

3.243

4.273

1.540

2.494

3.O91

4.242

5.556

7

1.043

1.791

2.250

3.126

4.118

1.435

2.333

2.894

3.972

5.201

8 1.010

1 740

2,190

3.042

4.OO8

. 1.360

2.219

2.755

3.783

4.955

9

0.984

1.702

2,141

2

977

3.924

1.302

2.133

2.649

3.641

4.772

1o

0.964

1.671

2.103

2,927

3.858

1.257

2.065

2.568

3.532

4.629

11

0.947 1.646

2.073

2.885

3.8c4

1

219

2.012

2.503

3.444 4.515

12

0.933

1.624

2.048

2.851

3.760

1.188

1.966

2.448

3.371

4.420

13

0.919

1.606

2.026

2.822

3.722

1..162

1.928

2.403

3.310

4.341

14

0.909

1.591 2.007

2.796

3.690

1.139

1.895

2.363

3.257

4.274

15

0.899

1.577

1.991

2.776

3.661

1.119

1.866

2.329

3.212

4.215

16

0.891

1.566

1.977

2.756

3.637

1.101

1.842

2.299

3.172

4.164

17

0.883

1.554

1.964

2.739

3.6 r-

1.085

1.820

2.272

3.136

4.118

18 0.876

1,544 1.951 2.723

3.595 1.071

1.800

2.249

3.106

4.078

:19

0.870

1.536

1.942

2.710

3.577

1.058

1.781

2.228

3.078

4.O41

i20

0865

1.526

1.933

2.697

3.561

I.o46

1.765

2.208

3.052

4.009

21

0.859

1.520

1.923

2.686

3.545

1.035

1.750

2.190

3.028

3-979

022

851,

1.514

1.916

2.675

3.532

1.025

1.736

2.174

3.007

3.952

23 0.849

1.508

1.907 2.665

3.520

1.016

1.724

2.159

2.987

3.927

24

0.845

1.502

1.901

2.656

3.509

1.007

1.712

2.145

2.969

3.904

25

0.842

1.496

1.895

2.647

3.497

0.999

1.702

2.132

2.952

3.882

S3

0.825 1.475

1.869

2.613

3.441

0.966

1.657

2.c80 2.884 3.794

35

0.812

1.458

1.849

2.588

3.421

0.942

1.623

2.041

2.833

3.730

40

0.803

1.445

1.834

2.568

3.395

0.923

1.598

2.010

2.793

3.679

45

0.795

1.435

1.821

2.552

3.375

0.908

1.577

1.986

2.762

3.638

. 0 788

1.426 1.811 2,538

3.358 ,894 .56G

1.965 2 73c 3.604

iT-4


10/25

t

--7.

TkA=L

1.

Tolerance

Factors

for

Normal

Distributions

(continued).

7 -

0.95

7

-

0.99

\i

0.25

0.10

0.05

0.01

0.001

0.25

0.10

0.05

0.01

0.001

3

3.8C14

-.

.

7.655

10.552

13.857

4

2.619

4.163

5.145

7.o42

9.215

5

2.149

3.4o7

4.202

5.741

7.501

6

1.895

3.006

3.707

5.062

6.612

2.849

4.4o8

5.409

7.334

9.540

7

1.732

2.755

3.399

4.641

6.o61

2.490

3.856

4.730

6.411

8.348

8

1.617

2.582

3.188

4.353

5.686

;Z

52

3.496

4.287

5.811

7.566

1.532

2.454

3.031

4.143

5.414

2.085

3.242

3.971

5.389

7.0]4

10

1.465

2.355

2.911

3.981

5.203

.954

3.048

3.739

5.075

6.603

11

1.411

2.275

2.815

3.852

5.036

1.854

2.897

3.557

4.828

6.284

2

1.366

2.210

2.736

3.747

4.900

1.771

2.773

3.41o

4.633

6.032

13

1.329

2.155

2.670

3.659

4.787

1.702

2.677

3.290

4.472

5.82b

14

1.296

2.108

2.t,14

3.585

4.690

1.645

2.592

3.189

4.336

5.651

15

1.268

2.068

2.566

3.520

4.607

1.596

2.521

3.102

4.224

5.507

6

1.242

2.032

2.523

3.463

4..534

1.553

2.458

3.028

4.124

5.374

17

1.220

2.001

2.486

3.415

4.471

1.514

2.405

2.962

4.038

5.268

13

1.200

1.974

2.453

3.370

4.415

1.1481

2.357

2.906

3.961

5.167

19

1.183

1.9149

2.423

3.331

4.364

1.450

2.315

2.855

3.893

5.078

1.167

1.926

2.396

3.295

4.319

1.424

2.275

2.807

3.832

5.003

21

1.152

1.905

2.371

3.262

4.276

1.397

2.241

2.768

3.776

4.932

122

1.138

1.887

2.350

3.233

4.238

1.376

2.208

2.729

3.727

4.866

23

1.126

1.869

2.329

3.206

4.204

1.355

2.179

2.693

3.680

4.806

24 1.114 1.853

2.309

3.181

4.171

1.336

2.154

2.663

3.638

4.755

25

1.103

1.838

2.292

3.158

4.143

1.319

2.129

2.632

3.6ol

4.706

3C

1.059

1.778

2.220

3.064

4.022

1.249

2.029

2.516

3.446

4.508

35

1.025

1.732

2.166

2.99'.

3.934

1.195

1.957

2.431

3.334

4.36,.

40

0.999

1.697

2.126

2.941

3.866

1.154

1.902

2.365

3.2'0

-..

2

5

45

0.978

1.669

2.092

2.897 3.811

1.122

1.857 2.313

3.181

4.168

50

0.961

1.646

2.065

2.863

3.766

1.096

1.821

2.296

3.124

,.0

9

6


11/25

~-8-

BIBLIOGRAPHY

[i

Bowker,

Albert

H.,

"Tolerance

Limits

for

Normal

Distributions,"

Techniques

of

Statistical

A

edited

by

Eisenhart,

Hastay

.

and

Wallis,

McGraw-Hill,

New

York,

1947,

Chapter

2.

12)

Lieberman,

Alfred,

"Table

for

the

Determination

of

Two-sided

Tolerance

Limits

for

the

Normal

Distribution,

Report

No.

373-17(55), Bureau

of

Ships,

Navy

Department,

Washington

25,

D.C.,

20

August

1957.

(33

Resnikoff,

George

J.,

"Two-sided

Tolerance

Limits

for

Normal

-

Distributions

Using

the

Range,

Technical

Report

No.33,

Applied

-

Mathematics

and

Statistics

Laboratory,

Stanford

University,

California,

April

25,

1957.

41

Mitra,

S.

K.,

"Tables

for

Tolerance

Limits

for a

Normal

Pcpulation

*

-Based

on

Sample

Mean and

Range

or

Mean Range,"

Journal

of

th e

American

Statistical

Association

March

1957.

(5]

Johnson,

N.

L.,

and

Welch,

B.

L.,

"Applications

of

the

on-central

t-

Distribution,"

Biometri

Vol.

31,

(1940),

Pp. 362-389.

L61

Resnikoff,

George

J.,

and

Lieberman,

Gerald

J.,

'"ables

of

the

Son-central

t-

Distribution,

Stanford

University

Press,

Stanford,

California,

(1957),

pp

736.

0.


12/25

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Air Force Base

Ohic


13/25

SChief

chief

L-''Detroit

Air

P)

:-r

fnt

Distriet

Rochesret-

Air

Procurement

District

4obile

Air

Materi,

Area

Middle

o

A

r

Materiel

Area

Attn:

quality

Control

Division

Attn:

Qwlity

Contr-J.

Division

W,

1

rren

Ave.

&

TOnyo

Blvd.

20

S

ylingtov

. ace,

P.

0.

Box

1669

Detroit

32.

Michitan

Rocheeter

3,

New

Yor;L

Chief

Indianapolis

Air

- ocurentt

District

Di ti

Mobile

Air

Materlel

Area

Oklahoma

City

Aii,

Materiel

Area

Attn:

quality

Cotrol

Division

54

Monument

Cire:e

.~td~o

,, 10.ia~.

U14

Mar, Street

St.

Lovf

,

Missouri1

Chief

Chief

LAs

Angeles

Air

Orocureaent

District

SAi

e&c

Ir

Procuremat

District.

San

Ben~r-no

.r

Matertel

Ar

.a

San

..

.

Air

teriel

Area

*.At:Quality

Control

D-,vision

Att~r:

-A

,tY

Cnt-.o1

Divisionendix

Building

P.

0.

IOx

1I' .

1206

8

Mple

Street

'.,id

8m.

Diego

;3.t.

-in

-

',-

..,

;

Angeles,

California

3

i

.

.4325

Pac-ific

.

,;hwiy

San

Diego

10,

(clifornia

m.

kee

Air

Procurtmnt

Dijtrict

Chief

Oklahoma

City

A'

Materiel

Ara

San

Francisco

Air

PrOeuremont

District

ttn:

Quality

Control

Division

Sacra.wnto

Aiv

'

iLerlel

a-ftr

70

D.

Plankinton

Aventv

Attn: Quality Control Division

2-.Milw~aukee,

Wisconsin

151.5

Clay

S re

Chief

Okkland

12p

California

c .

iNewark

Air

Procurement

Distrl

Chief,

Bureau

of

Aeronautics

Middletown

Air

Materiel

Area

Department

of

t~.e

Navy

Att.:

Quality

Control

D,-visich

Wshington

25,

D.

C.

'(3;

;

Mi

r*';et Street

Wsigo

5

.C

- '.' '.

Attn:

Q4Ality

Control

Division

Newark,

New

Jersey

C

Chief..

Bureau

or

Ordnance

hief

quality

Control

Division,

QCC

New

York

Air

Procurement

Distrint

Department

of

the

Navy

iddletown.

ir

W*'eriel

Are,

Washington

25,

D.

C.

Attn:

QuAlity

Liz:

Divibion

Wsigo

5

.C

last

16th

Stetn

Attn:

Dr.

W.

B.

Pabst

l

East

16th

Street

Mr.

if.

34.

Rosenblatt

3

New

York 3,

New York

r

Chief,

Bureau

of

Ship8

hief

Research

and

Dev.

Division,

Philadelphia

Air

Procurement

District

Code

373

Middletown

Air

Materiel

Area

Department

of

the

Navy

Attn:

Quality

Contr,.

Division

Washington

25,

D.

C.

6

I1

'Walnut

Street

Philadalphia

2,

Pennsylvania


14/25

Chief of

Naval Materiel

Cora,,der

Code M533,

Room 2236

14

dletown

Air

Materiel Area

Main Navy Bldg.

Olmsted

Air

Force

Base

Washington 25, D.C. 1 Middletown, Pa.

Attn.

MAPQc

Chief of

Naval

Operations

Operations

Evaluation Group Commander

he (OP-3g)

U.S.

Naval

Ordnance

Test

Station

The Pentagon

China Lake, Calif.

Washington 25,

D.C.

1

Attn: Technical Library

Chief of Ordnance Commander

U. S. Army

U.S.

N.O.T.S.

Research

and

Developmert Division Pasadena Annex

Washington

25, D.C. 3202 E.

Foothill Blvd.

Attn: Brig. General L.E. Simon 1 Pasadena 8, California

Mr. Charlea Bicking 1

Commander

Chief, Procuremen t-Maintenance

U.S.

Naval Proving Ground

Engineering Division

Dahlgren,

Virginia

Fort Monmouth,

New Jersey

Attn: Technical Library

Attn.

Procurement Data Branch

SIGEL-PP-l 1

Commander

Middletown

Air

Materiel Area

Chief,

Quality Control Branch Attn:

Quality

Control Office

Artillery Ainunltion Dept. Olmsted Air Force Base

Inspection Engineering Division Middletown, Pennsylvania

1

Frankford

Arsenal

Philadelphia

37, Pa. 1 Commander

Middletown Air Materiel Area

Chief,

Statistical Engleering Lab.

Attn:

Quality

Control

Dlvi-

National Bureau of

Standards

sion-Directorate

of

Washington

25,

D.C.

1

Procurement

&

Production

Cleveland Air

Procurement District Olmsted Air

Force

Base

1279

West Third

Street

Middletown, Pennsylvania

Cleveland

13,

Ohio

Attn: Quality Analysis Section

1

Commander

?-iddletown Air

Materiel

Area

Chief, Bureau of Yards and Docks Attn: Assistant for Quality

Materiel Division

Directorate

of

Maintenance

Dept. of the Navy Engineering

Washington 25, D.C. Olmsted

Air

Force Base

Attn: Mr. W. Wolman 2 Middletown, Pennsylvania

1

Commander Commander

Air

Technical Intel igence

Center Middletown Air Materiel

Area

Attn: Myron

A. tengoff

(AnOIN-4cI) Atta.

Materiel

Quality

Division

Wright-Patterson

Ala

Force Base

Directorate

of Supply

Ohio

1 and

Services

Olmsted

Air Force

Base

Midlletown,

P-nn6ylvir. ti


15/25

-iv-

Commnder

el.-,zander

Mobile Air

Materiel

Area

Oklahom&

city Air Materiel

Area

Attn: Quality Control Office Attn:

Materiel

Quality Division

Brookley Air Force Base

Directorate

of

Supply and

Alabama Services

Tinker

Air

Force

Base

Commander

Oklahoma

City,

Oklahoma

AMobile

ir Materiel

Area

:.,.,.Attn:

quality

Control Division

Commader

-. :Directorate of Procurem|ent

Ogden

Air Materiel Area

S&Production

Attn:

quality Control

Office

Frookley

Air

Force

Base

Hill Air Force

Base

,

Alabam

Utah

Commander

Commander

Mobile

Air Materiel

Area

Ogden

Air

MaTczC.el

Area

Attn: Assistant

for Quality


Division

Directorate

of

Maintenance

Directorate

of

Procurement

Engineering

& Production

Brookley Air Force

Base

Bill

Air Force Base

Alabama

Utah

Coinsnder

Commander

Mobile

Air Materiel Area

Ogden Air Materiel Area

Attn: Materiel Quality Division Attn:

Assistant

for Quality

Directorate of

Supply

and

Directorate of

Maintenance

Services

Engineering

Brookley Air Force

Base Hill

Air

Force Base, Utah

1

Alabama 1

Comander

Cozander

Ogden Air

Materiel

Area

Oklahoma City

Air

Materiel Area

Attn: Materiel Quality Division

Attn: Quality

Control

Office

Directorate

of Supply and

Tinker Air

Force Base

Services

Oslahoma

City,

Oklahom 1 Hill

Air Force Base,

Utah

Conmander

ComwAnder

Oklahoma City Air

Materiel Area San

Antonio

Air Materiel

Area

-ttn:

Quality

Control

Division

Attn:

Quality

Control Office

Directorate of

Procurement

Kelly

Air Force

Base,

Texas

&

Production

Tinker Air Force Base

Commander

Oklahoma City, Oklahoma 1

San

Antonio

Air Materiel

Area

Attn:

Quality

Control Division

Commander

Directorate

of

Procurement

Oklahoma City

Air

Materiel

Area

& Production

Attn:

Assistant

for

Quality

Kelly

Air

Force

Pase,

Texas i

Directorate

of

Maintenanre

bigineering

Comnder

Tinker Air Force

Base

San Antonio

Air Materiel Area

Oklahoma

City,

Oklahoma 1 Attn:

Assistant for Quality

Direitorate

of

Maintenance

Engineering

Kelly

Air Force Base, Texas


16/25

L

'

X

.

Com.ander

Commander

San

Antonio Air Materiel

Area Sa-ramento

Air

Materiel

Area

Attn:

Materiel quality Division Attn: Assistant for

Quality

Directorate

of Supply

ani

Directorate

of Maintenance

Services

Engineering

Kelly

Air Force

Base, Texas 1

McClellan

Sr

Force

Base

California

Commnder

San Bernardino

Air Materiel

Area

Comader

Attn: Quality Contrul

Office

Sacramento kir

Materiel

Area

Norton Air

Force Base

Attn:

Materiel

Quality

Division

California 1

Directorate of Supply an d

L

Services

Comder

McC'ellan Air Fc,

eie

San

Bernardino Air kateriel

Area (alifor'

i

Att" Quality

Control Division

Directorate

of

Procurement

Coumandee

& Production

Warner Robin

Air Materiel Area

Norton Air Force

Base

Attn:

Quality

Control Office

California

Robins Air

Force

Base

ComziderGeorgia

Commander

San

Bernardino

Air

Materiel

Area

Conmander

Attn:

Assistant for Quality

Warner

Robins Air

Materiel Area

Directorate

of

Maintenance

Attn: Quality

Control Division

Engineering

Directorate of Procurement

Norton

Air

Force

Base &

Production

"

California

Robins Air Force

Base

Georgia

Comnmder

San

Bernardino Air

Materiel

Area

Commander

Attn:

Materiel

Quality Division

Warner Robins

Air Materiel

Area

Directorate

of Supply and

Attn: Assistant

for Quality

Services

Directorate of Maintenance

Norton Air

Force

Base

Engineering

California

Robins Air Force

Base

Georgia

Comander

Sacramento

Air Materiel

Area

Comander

Attn:

Quality

Control

Office

Warner

Robins Air Materiel Area

McClellan Air Force Base

Attni

Materiel Quality Division

California

1

Directorate

of

Supply and

Services

Commnder

Robins Air Force Base

Sacramento Air Materiel

Area

Georgia

Attn:

Quality Control

Division

Directorate

of

Procurement

& Production

McClellan

Air

Force Base

California


17/25

,.


18/25

-vii.

Commander

-umader

Maywood

Air

Force Depot

4

,ain

Air Materiel

Area

Chell Air Force Station Attn: uality Control Office

Attn: Directorate of Supply & APO 28i

Services

New

York, New York

P. 0. Box 310

Maywood,

L. A.

County

Comander

Cal ifornia 1

Air

Materiel Command

Attn:

Quality

Control

Office,

MCQ

Comander

Wright-Patterson Air Force

Base

Air

Materiel

Force,

European Area

Ohio 10

Attn: Quality Control Office

APO

633, New York, New

York

1 Comaunder

San Antonio

Air

Materiel

Area

Commander

Attn: Quality

Control

Division

Northern

Air Materiel

Area,

Europe

Directorate Special Weapons

At-tn:

Quality

Control

Office

Kelly

Air Force Base,

Texas

APO

12h,

New York, New York 1

Chief, Bureau of Ordnance

Commander Attn: A.

Rothstein,

Code REVg

Central

Air

Materiel Area,

Europe

Department of Navy

Attn: Quality

Control Office

Washington 25, D.

C.

APO 10,

New York, New York 1

Commanding General

Comander

Chemical Corps

Materiel Comnd

Southern

Air

Materiel Area,

Europe 200 West Baltimore Street

Attn:

Quality

Control Office

Baltimore

1, Md.

APO

30,

New

York,

New

York

I

Attn:

Quality Assurance

Division

1

Commander

Air Materiel Force, Pacific Area Commanding General

Attn:

Quality

Control Office Chemical

Corps

Materiel Command

FEANCOM

Air

Base

200

West

Baltimore Street

APO

323

Baltimore 1, Maryland

San Francisco, California 1

Attnw

Quality

Evaluation

Branch

SCommander

Northern Air

M tere l Area, Pacific Commanding General


Office Ordnance, Amunition

Center

FEANCOM Air

Base Joliet,

Illinois

APO 323

Attn: ORDLY

AR.V

4

San

Francisco, California 1

Comanding

Officer

Comander Office

of Naval

Research

Southern Air

Materiel Area,

Pacific

Branch

Office

Attn: Quality Control Office

346

Broadway

Clark Air Force Base New

York 13,

New York

APO

74 Attn: Dr. J. Laderman

San

Francisco,

California

I


19/25

Commanding

Officer

Commanding

Officer

Office

of

Naval

Research

S. C.

Supply

Agency

Branch Office

225

South

18th

Street

1000

Geary Street

Philadelphia

3,

Ph.

San Prancisco

9, California

1

Attn: Chief,

SIGSU-H6d

2

Commanding Officer

Commanding Officer

Diamond

Ordrance

Fuze Laboratories

U. S.

Naval

Underwater

Ordnance

Washington

25,

D. C.

Station

Attn:

Library, Room

211,

Newport,

Rhode

Island

Bldg.

92 1 Attrb:

Technical

Library

Office,

Chief

of

Engineers

Computation

Division

Attn: Procurement

Division,

Directorate

of

Managemnt

Military

Supply

Analysis

Dept. of

Army

I/Comptroller,

Hq. U.S. Air Force

Washington

25,

D. C.

2

Washington

25, D.

.

3

Commanding Officer

Detroit

Air

Pro-'tremenz D

strict

Diamond Ordnance

Fuze

aboratories

W.

Warren

Aven . Linyc Bl,,d.

Attn: Mr.

N.

S.

Leibmn

bttroit 32, Michigpn

Room

100,

Bldg.

52

Attn:

14OHDQPQ

Connecticut

Ave.

and Van

Ness St.

Washingten

25, D. C.

1

Director, Development

Division

Field

Comnd

Commanding

Officer

'med

Forces Special

Weapons

Naval

Awmnition and

Net Depot

Project

Seal

Beach,

California

Albuquerque, New

,.exico

Attn:

QE

Laboratory

(Technical

Library)

1

Engineering

Statir'Acs Group

Research

Division

Coanding

Officer

New York

University

Office

of Naval Resedrch

New York

53,

N. Y.

Branch Office

Navy No. 100

Field Inspectton

Section

Fleet Post Office

DES Division

New

York,

N.

Y.

2

Armed Services

Medical

Procurement

Agency

Comm ding

Officer

84

Sands Street

New York

Chemical Procurement

Brooklyn

1,

New York

I

District

180

Varick

Street

Head, Statistics

Branch

New

York

14,

F. Y.

Office

of

Naval Research

Attn:

Qu~lity

Surety Division

I

Washington

25, D.

C.

2

Quality

Assurance Section 1

Sperry

Gyroscope C:.

Commanding Officer

Great Neck,

New York

Rock Island

Arsenal

Attn:

Mr.

Herbert Jaffe, CP-25

L

Rock Island,

Illinois

Attn:

R D Division


20/25

-ix-

Eq.

Mobile

Air

Materiel

Area

office

of

Operations

AnalySis

Materiel

Quality

Division

(MOSQA)

DCS/Operationgs

Brookley

A.Lr

Force

Base

Hq.

Air

Proving

Ground

CoUmYnd

Alabama

Eglin

Air

Force

Base

Florida

Inspection

and

Quality

Control

Divisic.n

Office

of

Technical

Services

Office,

Assietant

Secretary

of

Department

of

Commerce

Defense

(S L,

Washington

25,

D.

C.

Washington

25,

D.

C.

Attn:

Mr. Irving

B.

Altman

1

Ordnance

Corps

Industrial Engineering Division

Inspection

an

Quality

Control

Disamond

Ordnance

Fuze

Leboratory

A

Division

Washington

25,

D.

C.

Office,

Assestant

Secretary

of

Defense

(S&L)

Qulity

Evaluation

Laboratory

-Washington

5,

D. C.

U.

S.

Naval Magazine

Attn:

Mr.

John

J.

Riordan

1

Port

Chicago,

California

Librarian

The

RAND

Corporation

Numerical

Analysis

Research

1700

Main

Street

University

of

California

Santa

14onica,

California

Los

Angeles

24,

California

Attn-

Library

Logibtics

Research

Project

Scranton

Ordnance

Plant

George

Washington

University

156

,.-dar

Avenue

707

22nd

Street,

N.

W.

Scranton,

Pa.

Washington

7,

D.

C.

IAttn:

Mr.

Carl

D. Larson

Wahno

7Chief

Inspector

52HN.A.

3

N .

t;tiattcal

Laboratory

\

-. 1512

S.

N -

.W.

Wes&"

-

n

25,

D.

C.

Univerity

of

California

Atthr:

Div.

of

Rezc?1-ch

Berkeley

4,

Calif'Olnia

Infowwt,-.

.

Tecnnical

Information

Officer

Naval

Inspector

of Ordnance

Naval

Research

Laboratory

Na .va Iecer

St rt

Washington

25, C. C.

6

/,'...',

00

S.

Bieger

Street

Mishawaka,

Indiana

SAttn:

N.

L.

Lindemmnn1

TchcaLiry

AOffice,

Assistant

Secretary

of

Naval

Inspector

of

Ordnance

Defense

(Research

& Dev.

50

West

Main

Street

Room

3 E

1065,

The

ps.ntagon

Rochester

4,

N.

Y.

1

Washington

25,

D

C.

Office

of

Naval

Research,

Code

200

Technical

Operation,

Tnc.

A

w

and

C.O..O.

Washington

25,

D.

C.

-..-..

Attn:

Mr.

John

D.

Wilkes

Hq.

Contnetal

1\rny

C'

.vIt-

.

F.-

Monrre,

Vlrg

in

i

a

.

-


21/25

Dr. Adam

Abruzzi

Mr.

Carlton

M. Beyer

Dept. of

Economics

of Engineering

Office

of

Ou-.ded Missiles

Stevens

Inst.

of Technology

Office, Asst.

Secretary

of

Hoboken,

New Jersey

1

Defense

(R & E)

Washington

25, D.C.

Prof.

Stephen

0. Allen

24

4

Laurel Street

Mr.

P.M. Blunk

San

Francisco,

California

I

Box

53 2

Fair

Oaks, California

Prof.

T. W.

Anderson

Center

for Advanced

Study

of

Mr.

Milton N.

Bradley

Behavioral Sciences

2481

Davidsozi

Avenue

Stanford,

California

1

New

York, N.Y.

Prof. Fred

C. Andrews

Prof.

Russell

Bradt

Mathematics

Dept.

Dept.

of Mathematics

University

of Nebraska

University

of

Kansas

Lincoln

8,

Nebraska

1 Lawrence,

Kansas

Prof.

Max

Astrachan

Prof.

Irving

W.

Burr

Institute

of

Technology,

USAF

Dept.

of Mathematics

Air

University

Purdue

University

Wright-Patterson

Air Force Base

Lafayette,

Indiana

Ohio

1

Prof.

A.

Charnies

Prof. Robert echhofer Statistical Laboratory

Dent. of

Mechanical

Engineering

Purdue

University

Cornell University

Lafayette,

Itiuiana

Ithaca,

N.Y.

Mr. Allen

Chop

Mr.

J. R.

Beck

162

-

8th

Street

Kodak

Processing

Laboratory

Oakland

7,

alifornia

925

Page Mill

Road

Palo Alto,

California

1

Prof.

Paul Clifford

New Jersey

State

Teachers

College

Professor

R. E. Beckwith

Montclaire,

New

Jersey

Statistical

Laboratory

Purdue

University

Prof.

Edward

P.

Coleman

Lafayette,

Indiana

1

Engineering

Department

University

of California

Prof. Maurice

H. Belz

Los

Angeles

24, California

University

of

Melbourne

Carlton

N.

3

Mr.

A.

F. Cone, Manager

Victoria, Australia

I

Quality

Assurance,

Dept. 551

Sandia Corporation

Prof. J. N.

Berrettoni

Albuquerque,

New

Mexi'o

Western

Reserve

University

Cleveland,

Ohio

I

Dr

Louts COuurt

Division

.'

N-t.nnal u.reau

o:

Stnl.ar

Wasnington

2 ., D.c'

..

?


22/25

.-

Mrs.

J.

Henley Crosland

Mr.

Donald

Flischel

Director

of

Libraries

Attn:

MCRR

Georgia

Inst. of Technology

WA-ight-Patterson

Air

Force

Base,

Atlanta,

Ga.

Ohio

Dr.

Joseph Daly

Mr.

F.

Frishman

Bureau

of the Census

Research

and

Development

Dept.

Washington

25,

D.C.

1

U.

S.

Naval

Powder

Factory

Indianhead,

Maryland

Prof.

Georges Darmois

Director,

Institute

de Statistique

Mr.

Ora E. Gaines

11 Rue Pierre Curie

Hayes

Aircraft Corp.

Paris

5,

France P.O. Box 2287

c/o

Office of

Naval

Research Birmingham,

Alabama

London

Branch

Navy

No. 100,

Fleet Post

Office Mr.

S. Gaspar

New York,

N.Y.

I U.S.

N.O.T.S.

Pasadena

Annex

Prof.

Cyrus Derman

3202

E.

Foothill

Blvd.

Dept. of Industrial

Engineering

Pasadena

8, California

Col

umbia

University

New

York 27,

N.Y.

1

Mr.

Leoi Gilford,

ADSS

~ 5j~yikuan 1-2U.

S. Census Bureau

Mr. Sidney Dickman,

9-2

Wuahington 25,

D.C.

Sperry

Gyroscope Co.

Great Neck,

New

York

1

Mr. Bernard

P. Goldamith

.Qality ontrol Engineer

Mr. H.

F.

Dodge

Raytheon

Mfg. Co.

Bell

Telephone Labs.,

Inc.

55

Chapel

Street

463

West

Street

Newton 58,

Mass.

New

York, N.Y.

1

Prof.

Leo

A.

Goodan

Mr. B.F. Doetsch

Statistical

Research

Center

1519

Z. Fox Street

University

of

Chicago

South Bend

1s,

Indiana

1 1126

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Street

Chicago

37, Illinois

Dr.

Francis

Dresch

Stanford Research

Institute

Prof. Eugene

L.

Grant

1915 University

Avenue

Civil

Engineering

Dept.

Palo

Alto,

California

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Stanford

University

Stanford,

California

Prof.

Acheson J. Duncan

Dept.

of

Industrial

Engineering

Mr.

Geoffrey

Gregory

The

Johns Hopkins

University

4, Osboine

Grove

Baltimore 18,

Maryland

1

Gatley,

Cheadle

Cheshire,

England

Prof.

Meyer Dvass

c/o

Office

of Naval Research

Dept. of Mathematics

London Branch

Northwestern University

Navy No. 100,

Fleet Po3st 0:'f

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Evanston,

Illinois

1

New Yorm,

N.Y.


23/25

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Prof.

P ank

M.

Oryna,

Jr.

Mr.

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Lindren

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Control

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Joy

Man,I'etu,

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Company

Signal

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Monmouth,

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Jersey

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C:remont,

New

ashire

Mr.

Douglass

Hawks,

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dminist*rative

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Prof-

Sebastian

Littauer

ept.

of

Industrial

Engineering

American

Bosch

Arm

Corp.

Columbia

University

5555

So.

Archer

Avenue

New

York,

N.Y.

Chicago

38,

Illinois

Dr.

Leon

H.

rerbach

Dr.

Eugene

Lukacs

epartment

of

Mathematics

Dept.

of

Utnimts

Catholic

U.liversity

ew

York

University

Washington

17,

D.C.

ew

York

53,

N.Y.

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1

Dr.

Clifford

J.

Maloney

Mr.

Walter

V.

Box"

Chief, Statistics Branch

ought

Aircraft,

Inc.

Allied

Sciences

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ull

as,

Texas

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Camp

Detrick

Dr.

James

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Frederick,

Maryland

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Maclrath

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Dept.

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University

of

California

net

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nesota

University

of

Minnesota

Los

Angeles

24,

California

i

Minneapolis

14,

Minn.

Mr

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C.

J&cb,

Jr.

Dr.

Paul

Meyer

Chief

ndustrial

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Department

of

Mathematics

hrysler

Division-Chrysler

Corp.

Washington

State

College

2200

E.

Jefferson

Avenue

Detroit

14,

Michigan

Pulman,

Washington

Dean

Paul

z.

Mohn

r.

J.

P.

Kearney

School

of

Rngineering

uality

Control

Division

University

of

Buffalo

General

Services

Adm.

Buffalo,

N.

Y.

Room

6316

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3

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Washington

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Mr.

Leo

9.

Morris

Prof.

oslo

K

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Evaluation

Laboratory

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N.A.D.

Bangor

Faculty

of

Science

Bremerton,

Washington

Kyusyu

University

Dr.

R.

B.

Murphy

ukuoka,

Japan

c/o

Bell

Telephone

Labs.,

Inc.

Mr.

Howard

Laitin

463

West

St.

2134

Homecrest

Ave.

New

York

14,

N.Y.

Brooklyn

29,

N.Y.

Mr.

Monroe

Norden

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Statistical

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0-50

Thirtieth

Street

College

of

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Long

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City,

New

York

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New

York

University

401

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205th

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r.

George

J.

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New

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34,

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Bell

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Marray

Hill,

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Dept. of Mathemwtics

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Carnegie

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Technology Unersity

of Pennsylvania

Pittsburgh,

Pa.

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Philadelphia

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Mr.

Cyril

Peckham

Mr.

Walter

Shewart

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Bell

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University

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Dayton

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Hill,

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Jersey

Dayton,

Ohio

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Pu

.Mr.

J.

Gordon

Siddons

SDr.

Paul

R.

Rider

aality

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Boeing

Airplane

Company

Aeronautical

Research

Laborary

Seattle

i,

Washington

Wright

Air

Development

Center

Wright-Patterson Air Force Base

Dr. Rosedith

Sitgreaves

Ohio

1 Teachers College

Columbia

University

Dr. Harry G.

Romig New

York 27, N.Y.

351

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Real

Drive

Pacific Palisades,

California

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Sobel

Bell

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Alan J. Rowe

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Production

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Herbert Solomon

New York 22, N.Y.

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College

Columbia University

Prof. Herman Rubin

New

York

27,

N.Y.

Dept. of

Mthematics

University

of Oregon

Dr. M. D. Springer

Eugene,

Oregon

Head,

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Analysis Branch

PU.S.

Naval Ordnance Plant

Prof.

Norman

Rudy

Indianapolis,

Indiana,1

Statistics

Department

Sacramento

State College

Mr.

Selig Starr

Sacramento,

California

1 Research

& Development

Dept.

Pro-

U.S.

Naval

Powder Factory

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h-

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Indianhead,

Md.

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Arthur

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Berkeley

4,

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Robert

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Buffalo,

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Graduate

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Harvard

University

Mr.

M.P. Straubel

Boston

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Grand

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Michigan

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Cleveland 7, hio

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