Front Matter

Front MatterSource: Operations Research, Vol. 13, No. 2 (Mar. - Apr., 1965), pp. i-xiiPublished by: INFORMSStable URL: http://www.jstor.org/stable/168070 .

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OPERATIONS

The Journal of the Operations Research Society of America

March-April 1965 VOLUME 13 NUMBER 2

AI9S2 Pages 169-342

PUBLISHED BIMONTHLY BY THE

OPERATIONS RESEARCH SOCIETY OF AMERICA



OPERATIONS RESEARCH

The Journal of the Operations Research Society of America

EDITOR THOMAS E. CAYWOOD

Peat, Marwick, Caywood, Schiller & Co.

203 N. Wabash Ave., Chicago, Ill. 60601

ASSOCIATE EDITORS WILLIAM W. COOPER, Carnegie Institute of Technology, Pittsburgh, Pennsylvania GEORGE B. DANTZIG, University of California, Richmond, California WALTER L. DEEMER, Operations Analysis Office, Hq., U.S.A.F., Washington, D. C. ROBERT DORFMAN, Harvard University, Cambridge, Massachusetts JOSEPH H. ENGEL, Operations Evaluation Group, Washington, D. C. CHARLES GOODEVE, British Iron & Steel Assn., London W1, England JOSEPH 0. HARRISON, JR., Research Analysis Corporation, Bethesda, Maryland G. RONALD HERD, Kaman Aircraft Corporation, Bethesda, Maryland ROBERT HERMAN, General Motors Research Laboratories, Warren, Michigan WILLIAM J. HORVATH, University of Michigan, Ann Arbor, Michigan RONALD HOWARD, Massachusetts Institute of Technology, Cambridge Massachusetts HUGH J. MISER, The MITRE Corporation, Box 208, Bedford, Massachusetts GEORGE E. NICHOLSON, University of North Carolina, Chapel Hill, North Carolina THORNTON PAGE, Wesleyan University, Middletown, Connecticut E. W. PAXSON, The Rand Corporation, Santa Monica, California PAUL RANDOLPH, Purdue University, Lafayette, Indiana ANDREW SCHULTZ, JR., Cornell University, Ithaca, New York GEORGE SHORTLEY, Booz * Allen Applied Research Inc., Bethesda, Maryland RYSZARD SYSKi, University of Maryland, College Park, Maryland LAJOS TAKXCS, Columbia University, New York, New York R. M. THRALL, Editor, Management Science, Univ. of Mich., Ann Arbor, Mich. ROBERT S. WEINBERG, International Business Machines Corp., New York, N. Y. PETER B. WILSON, Canadian National Railways, Montreal, Quebec

MANUSCRIPTS of papers and Letters to the Editor should be submitted to the Editor or to one of the Associate Editors. Submission of a manuscript is considered to be a representation that it has been neither copyrighted nor published, that it is not being submitted for publication elsewhere, and that, if the work results from a military contract, it has been released for open publication. Material for the Analyst's Bookshelf should be submitted to HUGH J. MISER, Analyst's Bookshelf Editor, The MITRE Corporation, Box 208, Bedford, Massachusetts. Announcements should be sent to the Editor.

MANAGING EDITOR AND ADVERTISING MANAGER

CHARLES P. CHADSEY Research Analysis Corporation

McLean, Virginia 22101

Copyright ? 1965 by the Operations Research Society of America. Published bimonthly by the Operations Research Society of America at Mount

Royal and Guilford Avenues, Baltimore, Maryland, 21202. Second-class postage paid at the Post Office at Baltimore, Maryland. Subscriptions and orders for back issues should be addressed to the Business Manager,

NORVELL E. MILLER, III, Mount Royal and Guilford Aves., Baltimore, Md. 21202. Subscription Rate: $10.00 per volume (outside U. S. and Canada, $7.50 per volume).

Back volumes through 1959, $9.00. Single copies of back issues through 1959, $1.50; 1960, $2.00 per issue.

Reprints of individual articles are not available from the SOCIETY.



Scientifically trained individuals with, grounding in operations research are being sought by the Weapons Systems Evaluation Division of the Institute for Defense Analyses. Working near1the Pentagon with military.,members of the Defense Department's Weapons Systems Evaluation Group, staff members of this private research organization apply techniques of military operations research and related sciences to problems of highest importance to national defense. The goal of their effort is to provide complete evaluations for use by the Joint Chiefs of Staff and the Director of Defense Research and Engineering, as well as by other elements of the Office of the Secretary of Defense. In service to the Nation, in intellectual challenge, and in personal growth potential, a position in this body offers unique opportunities. Individual inquiries are invited and should be addressed to Mr. Thomas J. Shirhall.

B. O. KOOPMAN, Director WeaponsSystems Evaluation Division

I IDA

INSTITUTE FOR DEFENSE ANALYSES 400 Army-Navy Drive, Arlington, Virginia 22202

An equal opportunity employer sponsored by twelve of the nation's leading universities.



ENGINEERS * PHYSICISTS * MATHEMATICIANS

AREER APPOINTMENTS IN OPERA TIONS ANAL YSIS

The Applied Physics Laboratory of The Johns Hopkins Univer- sity now offers highly attractive career appointments to the professional stag of its Military Operations Analysis Group. The atmosphere within the Group is one of imagination, origi- nality of thought, informality and independence . . . there is a minimum of formal organization. Staff members will enjoy a freedom to define and redefine problems and methods of solution, working individually for the most part, in an essentially academic atmosphere.

The Group receives its assignments from other divisions at APL, the APL management and the Navy, although a considerable number of projects are self-generated by Group members. Cur- rent problem areas include anti-air warfare, Marine Corps tactical operations, tactical data systems, strategic weapons systems, weapon control, radar systems analysis, and operational readiness.

Respondents must have a degree in one of the physical sciences and three or more years experience in a scientific or technical field. Creativeness should be balanced by a practical-minded atti- tude, and the ability to function effectively with scant supervision.

APL's modern facilities are located in Silver Spring, Md., a residential suburb of Washington, D. C., affording a choice of city, suburban or country living. The area is known for its high living standards, excellent public schools and extensive opportunities for graduate study.

Direct your inquiry to: Professional Staff Appointments

The Applied Physics Laboratory* The Johns Hopkins University 8681 Georgia Avenue, Silver Spring, Maryland (Suburb of Washington, D. C.)

ALL QUALIFIED APPLICANTS WILL RECEIVE CONSIDERATION FOR EMPLOYMEN WITHOUT REGARD TO RACE, CREED, COLOR, OR NATIONAL ORIGIN.

ii



Exceptional Opportunities for

EXPERIENCED

OPERATIONS RESEARCHERS

As a result of our Firm's continuing expansion of its OPERATIONS RESEARCH capability, we have need for thoroughly seasoned practitioners in all phases of OPERATIONS RESEARCH consulting-from initial client contact through the implementation phase.

We are so sure of the merits of what we have to offer that we invite you to get in touch with us to explore how your talents and our needs can be combined to great mutual advantage.

For our part, we offer opportunity to use to the full your skill and versatility, in many industrial and business contexts. This means the challenge to meet high standards of professional performance, with commensurate rewards -in job satisfaction-in association with other highly- qualified professionals from our own and other disciplines- and in other and more usual ways.

We'd prefer to hear from you now-but are always on the lookout for the right men. Write to the personal attention of:

Dr. E. Leonard Arnoff Principal and

Director of Operations Research

Ernst & Ernst Cleveland, Ohio 44114

iii



_ .... Anneuxnoe Apjntmonte For

gLTHiNKITE OPERATIONS I1 FRANKLIN

INSTITUTE ANALYSTS LABORATORIES

The Operations Research Division of The Franklin Institute is expanding its professional staff in the area of military operations analysis and cost effectiveness studies. The design of systems involving the in- teraction of men and machines are of particular interest. Positions are open for Operations Research Scientists, Economists & Systems Design- ers, with experience in the analysis, simulation, and synthesis of problems associated with the control of military operations.

Current projects include the analysis of military command, control and communication systems, the assessment of air traffic control systems, and the development of mathematical models for psychomotor performance in control tasks and decision making.

Staff members of the laboratories work as members of interdisciplinary teams in close collaboration with Psychologists, Mathematicians, and military and civilian government personnel.

The Franklin Institute is a non-profit scientific institution located in center city Philadelphia. Good housing, cultural institutions, universities, and recreational facilities are all conveniently located. These Appointments Offer MR. EZRA S. KRENDEL, Technical Director Exceptional Opportunities. OPERATIONS RESEARCH DIVISION For Information- WRITE TO: THE FRANKLIN INSTITUTE

Philadelphia, Pa. 19108 An Equal Opportunity Employer

I I I I I I 1

It,

OPERATIONS RESEARCH

SCIENTISTS

All degree levels are sought to fill the needs of the many employers in every conceivable field who have adopted this technique for the solution of the varied problems that beset the many facets of all in- dustry. Professional men well qualified in mathematics, statistics, economics and in the physical, engineering and biological sciences are highly de- sirable. Submit your resume and outline your career objectives and let us help you reach your goal.

BARNEY CORRIGAN, Director Theoretical Sciences Division

CADILLAC ASSOCIATES, INC. 29 E. Madison Bldg. FI 6-9400 Chicago 2, Illinois

"Where More Executives Find Their Positions Than Anywhere Else in the World."

iv



There's a beautiful problem out tonight

You might like our way of looking at the moon. It's a different way, because our assignment is to do systems

engineering for the National Aeronautics and Space Adminis- tration's manned space flight effort.

Getting to the moon and back is a series of problems which not only have to be solved-first of all, they have to be identified, defined, understood.

Bellcomm has rewarding openings right now for advanced thinkers in such fields as physics, mathematics, engineering, chemistry, propulsion, flight mechanics, computing and programming, guidance and trajectory analysis.

If you are highly qualified and experienced, your resume will be welcomed by Mr. N. W. Smusyn, Personnel Director, Bellcomm, Inc., Room 1302-H, 1100 17th St., N. W., Washington, D. C. 20036. We are an equal opportunity employer.

(ai) Bellcomm, Inc. A Bell System Company



Dear Mr. Halbrecht:

RESEARlCH For a good part of the last seven years < TTERIAJNGLE

that you have been specializing in EDP and

T \ )OR recruitment and placement, I have been S[NS r/ rE reading your exceptional listings of employ-

ment opportunities in the fields of:

OPERATIONS RESEARCH * MANAGEMENT SCIENCES 0

ELECTRONIC DATA PROCESS-

RESEARCH TRIANGLE PARK ING * MATHEMATICS/STA-

NORTH CAROLINA TRATI ON o ECONOM ICS/ECON- NORTH CAROLINA ~~OMETRICS * etc., etc., etc.

excellent opportunities At this time, I LOVE MY JOB, MY BOSS IS

immediately available GREAT, THE COMPANY I WORK FOR IS TER-

RIFIC, THE OPPORTUNITIES THEY PROVIDE

FOR FINANCIAL AND PROFESSIONAL GROWTH OPERATIONSJ ANAL YSTS ARE TREMENDOUS, AND MY GEOGRAPHIC

LOCATION IS PROBABLY BEYOND COMPARISON

IMAGINATION and resourcefulness are WITH ANY OTHER SPOT ON THE FACE OF THE

needed at all levels for expanding programs EARTH. ALSO, GOOD AS I AM, I AM PROBABLY

in civil and military defense, information- , management systems, transportation, tex- OVERPAID.

tile and other types of industrial operations However, just for the heck of it, please research. Unusual opportunities are of- send me your latest list of employment op- fered experienced operations analysts and . . exceptionally well-qualified recent gradu-portunities as well as your position ap- ates in mathematics, statistics, engineering, praisal form which would help me to objec- the physical sciences, and economics. Abil- tively evaluate my job in comparison with ity to write fluently is essential. others.

STIMULATING environment for profes- P.S. Also, just for the heck of it, of sional and cultural development is provided enclosed is my resume. by close association with the Triangle universities: Duke, University of North Caro- lina, and North Carolina State. Nearby mountains and beaches enhance pleasant To: Mr. Herbert Halbrecht living conditions. 4641 Montgomery Avenue

APPLY- but only if prepared to meet the Bethesda, Maryland 20014 continuing challenges of interdisciplinary name, projects and deadlines! home telephone

address

For further information, city state

please write: company

Dr. Edgar A. Parsons, Director current position

Operations Research Division current salary salary desired- (Be realistic, now)

Tote A DftlI T ~l A 1n1 position sought

RESEARCHn TRIArlNlULE geographic area I will not consider

INSTITUTE All inquiries are considered strictly confidential and receive prompt attention. All fees are assumed by our

^ ... ~~client companies.

Box 490, Durham, North Carolina client-compan-e-----

An independent non-profit research organi- HALBRECHT ASSOCIATES, INC. nation located on its own campus in North 4641 Montgomery Ave. * Bethesda, Md. Carolina's Research Triangle Park. (Suburb, Washington, D.C.) Phone: (301)

"An equal opportunity employer" 656-9170

vi



If you thrive on challenge..

The sea has always challenged man. Throughout history, bold and creative imagination has met the challenge by finding new ways to control the use of the sea for maritime advantage. Today, the age-old challenge remains. New concepts of ships and weapons design, of tactics and strategy are still needed to assure national security now and in the future. Discovery and evaluation of these new concepts are among the tasks of the Center for Naval Analyses of The Franklin Institute. CNA is a private scientific organization engaged in operations research and broad-based studies for the United States Navy. A few CNA staff appointments are available to operations analysts, mathematicians, physical scientists, and research engineers of superior competence. For more information, write:

Director CENTER FOR NAVAL ANALYSES Dept. RSJ 1401 Wilson Blvd., Arlington 9, Va.

^N XJA CENTER FOR NAVAL ANALYSES OF THE FRANKLIN INSTITUTE

OEG * Operations Evaluation Group INS * Institute of Naval Studies An equal opportunity employer NAVWAG * Naval Warfare Analysis Group Aneuloprniymlyr



MANAGEMENT CONSULTANT

O.R. - MANAGEMENT CONTROLS

Leading general management consulting firm seeks a young man, age 27-32, with an operations research background, to work on varied and challenging client assignments. We prefer some industrial experience, for example, production and/or inventory control exposure. Our primary requirement, however, is training and experience in O.R. and statistical techniques such as linear programming, simulation models, exponential smoothing, queueing, gaming theory, etc. Background requirements other than the preceding are flexible, and could include experience in systems and procedures, E.D.P., production/inventory control, or other, with some preference for industrial manufacturing and distribution applications. Degree required, likely in math., statistics, or eng'g/ind'l mgt., probably supplemented with additional studies in the field of O.R. Commensurate salary, bonus, and profit-sharing. Home all weekends whenever travel is required. Chicago base. We invite your interest by full reply, in complete confidence to:

Box 6511 OPERATIONS RESEARCH Mount Royal and Guilford Avenues Baltimore, Maryland 21202

II i1,m I...EE..E I .1 1E11.

;ii - IM IE E E EIIIEII Al .WEAPONS iii i |immi im...i iii |SYSTEMS

_nn uuuinuuu ANALYSTS lii MIM I... . Ilo1EE1 a I I1 1

STANFORD RESEARCH INSTITUTE S

has several openings for Senior Weapons Systems Analysts. Activities involve engineering analyses and evaluations of advanced design alternatives on a variety of existing and newly proposed weapons systems, with special emphasis on Air and Ballistic Missile De- fense Systems. Opportunities exist to participate both individually and as team members on highly challenging research programs.

In addition to a broad advanced systems background, experience in one or more of the following areas is of immediate interest: Nuclear Weapons Effect, Re-entry

| Physics and Decoy Discrimination, Radar Systems, Radar Signal and Data Proc- essing, Missile Guidance & Electronics, Computer Simulation and Missile Systems Cost Evaluation.

* Engineers, Physicists and Mathematicians, preferably with advanced degrees and with broad systems backgrounds, or specialists in the areas mentioned who desire to apply their experience to systems problems, are invited to submit resumes. Industrial level salaries and benefits are provided.

For further information, I STANFORD RESEARCH 333 Ravenswood -an equal please contact: R. B. Cantu INSTITUTE Menlo Park, i opportunity

viii



* o0

0 X) 0

0 Would you like to 0

COUPLE YOUR SKILLS in

* Computer-based Disciplines * Operations Research o Management Sciences * Behavioral Sciences

Management Systems * With a desire to shape in an innovative way * How managers organize their efforts to accomplish 0 ? business objectives? 0

O YES, 0

these efforts are broad, yet specific. They begin with clarification of business objectives and include providing creative management systems to achieve those objectives, optimizing performance, design

O automation, and near and real time control of complex production Ad processes-all brought together into an integrated whole. These * efforts are truly multidisciplinary.

0 0 0 At Tl, 0

the coupling of fundamental skills in one or more disciplines with * "how" to run the business is recognized as significant to the con- 0 tinued growth of TI and to the growth of individuals having those

skills. Several

* important new positions are being created for those with PhD level 0 * skills in Math, Computer Science, Electrical Engineering, Physics, or 0 O Behavioral Sciences (or educational equivalent, however acquired) 0 O with three or more years' experience accumulating the required skills. * Successful candidates for these positions must be able to direct efforts * of highly competent groups with similar skills. They must also have * the ability to apply their capabilities to such areas as adaptive systems e development and implementation, hybrid computer usage, real time e process control, information retrieval, communications theory, and * new program language development. The ability to communicate with * operating managers in the full implementation of their efforts is also * essential.

Please send confidential resume to C. J. Thomsen, Senior Vice Presi- * dent, Management Systems, Department C-131. * * 0

TEXAS INSTRUMENTS * I N C OR P OR A T E D

P. 0. Box 5474 Dallas, Texas 75222 An Equal Opportunity Employer

0~~~~~~~~~~~~~~~~~

ix



Journal of the

AMERICAN STATISTICAL ASSOCIATION

Volume 60 March 1965 Number 309

Quality and Quantity in Higher Education (Presidential Address) ........ A. H. Bowker An Estimation Procedure for Range Composition Problems ..... ...... Dennis J. Aigner Bayesian Analysis of the Independent Multinormal Process-Neither Mean nor Precision

Known . . . Albert Ando and G. M. Kaufman Prediction of an Autoregressive Variable Subject Both to Disturbances and to Errors of

Observation. ................................................. M martin J. Bailey A Nomograph for Chi-Square ..................................... William C. Boyd Errors of Classification in a Binomial Population ................... Marion R. Bryson Systematic Statistics Used for Data Compression in Space Telemetry

Isidore Eisenberger and Edward C. Posner The Reliability of Consumer Surveys of Financial Holdings: Time Deposits

Robert Ferber Optimum Allocation of Sampling Units to Strata When There Are R Responses of

Interest .John Leroy Folks and Charles E. Antle Design For Optimal Prediction In Simple Linear Regression

D. W. Gaylor and H. C. Sweeny On the F-Test in the Intrablock Analysis of a Class of Two Associate PBIB Designs

N. Giri Some Graphs Useful for Statistical Inference. . William C. Guenther and P. 0. Thomas A Two-Parameter Model for the Survival Curve of Treated Cancer Patients

J. L. Haybittle Applications of Probability Theory in Criminalistics ................... C. R. Kingston Ratios of Normal Variables and Ratios of Sums of Uniform Variables . . George Marsaglia Principal Components Regression in Exploratory Statistical Research. . William F. Massy A Bayesian Approach to the Analysis of Data from Clinical Trials

Melvin R. Novick and James E. Grizzle The Power of Student's t-Test .............. D. B. Owen On a Method of Using Multiauxiliary Information in Sample Surveys and Variance

Estimation in Randomized Systematic Sampling with Probability Proportionate to Size ............................................................... Des Raj

Probabilistic Prediction .......................................... Harry V. Roberts Some Nonparametric Tests for m-Dependent Time Series ...... ............. P. K. Sen A History of Distribution Sampling Prior to the Era of the Computer and its Relevance

to Simulation .............................................. Daniel Teichroew Randomized Response: A Survey Technique for Eliminating Evasive Answer Bias

Stanley L. Warner Minimal Sufficient Statistics for the Two-Way Classification Mixed Model Design

Robert A. Hultquist and Franklin A. Graybill Confidence Intervals Based on the Mean Absolute Deviation of a Normal Sample

Erna M. J. Herrey Comparison of Some Ratio Estimators ................................... Myint Tin Book Reviews

For further information, please contact:

American Statistical Association 810 18th Street, N. W.

Washington, D. C. 20006



MAN AND HUMAN PROGRESS ... ONE IN A SERIES

Peace is not achieved merely by desiring it." May 27, 1959. For official Washington and In the national interest, the much of the free world, it was a day of mourn- Research Analysis Corpo- ing . . . the day of John Foster Dulles' funeral. ration applies scientific

Ironically, it was also the deadline, set forth thought to major military, in an ultimatum six months earlier by Nikita technical, economic and ianultimatum Wsi mo gea

by Nikita political problems. Non-

Khrushchev, for the West to get out of Berlin. profit and multidisciplinary, But because Dulles had stood firm-as he had RAC invites scientists and in so many earlier showdowns between West- engineers with advanced ern determination and Communist expansion- degrees and superior capa- ism-May 27, 1959 was a carefree spring day bilities to investigate its in Berlin, nothing more, nothing less. career opportunities; please

Dulles, often stressing that peace is not to send your resume to Mr. be had simply for the wanting, fought all his John G. Burke, Professional be had simply for the wanting, fought all his Staffing, Research Analysis life for a just and moral peace, a peace founded Corporation, McLean, Vir- on interdependence of nations and the dignity ginia 22101 (suburb of of man. We have not yet achieved his objec- Washington, D. C.). An tives. But time has both vindicated his judg- equal opportu- ment and affirmed the remarkable breadth of nity employer. his accomplishment. RESEARCH ANALYSIS CORPORATION



Operations Research Society of America

1 9 6 4 - 1 9 6 5

OFFICERS OF THE SOCIETY

GEORGE E. KIMBALL, President GEORGE SHORTLEY, Vice-President Arthur D. Little, Inc. Booz, Allen Applied Research, Inc. 35 Acorn Park 4815 Rugby Avenue Cambridge, Massachusetts 02140 Bethesda, Maryland 20014

JOSEPH H. ENGEL, Secretary JOHN E. WALSH, Treasurer Operations Evaluation Group System Development Corporation Center for Naval Analyses 2500 Colorado Avenue 1401 Wilson Boulevard Santa Monica, California 90406 Arlington, Virginia 22209

COUNCIL OF THE SOCIETY

1963-65 Past President, HUGH J. MISER, The MITRE Corporation, Box 208, Bed- ford, Massachusetts

1964-66 Past President, ALEXANDER M. MOOD, Office of Education, Washington, D.C. 20202

1962-65 ROGER R. CRANE ANDREW W. MARSHALL Touche, Ross, Bailey & Smart The RAND Corporation 80 Pine Street 1700 Main Street New York, N. Y. 10005 Santa Monica, Calif. 90401

1963-66 WALTER E. CUSHEN LESLIE C. EDIE Institute for Applied Port of New York Authority

Technology 111 Eighth Avenue National Bureau of Standards New York, N. Y. 10011 Washington, D. C. 20234

1964-67 MURRAY GEISLER DAVID B. HERTZ The RAND Corporation McKinsey & Co., Inc. 1700 Main Street 270 Park Avenue Santa Monica, Calif. 90401 New York, N. Y. 10017

CHAIRMEN OF STANDING COMMITTEES

Membership Committee Education Committee NEWTON A. ABLAHAT HARVEY M. WAGNER

General Electric Company Dept. of Industrial Engineering 777 14th Street, N. W. Stanford University Washington, D. C. 20005 Stanford, California

Publications Committee Nominating Committee ROBERT E. MACHOL GEORGES BRIGHAM

Dept. of System Engineering Arthur Andersen & Co. College of Engineering 501 Norton Building University of Illinois Seattle, Washington 98104 Chicago, Illinois

CHAIRMEN OF OTHER COMMITTEES

Lanchester Prize Committee Representative to IFORS ALEXANDER M. MOOD HUGH J. MISER

Sections Committee Representative to the NRC ROBERT MIRSKY ROBERT F. RINEHART

Meetings Committee Representatives to the AAAS PAUL STILLSON RALPH W. GERARD

21 Marinero Circle ELLIS A. JOHNSON Tiburon, California



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