SIMULATION METHODOLOGY FOR STATISTICIANS, OPERATIONS ANALYSTS, AND ENGINEERS

434 Pages·2017·21.02 MB·English

by  LEWIS

The Wadsworth & Brooks/Cole Statistics/Probability Series
Series Editors
O. E. BarndorfT-Nielsen, Aarhus University
Peter J. Bickel, University of California, Berkeley
William S. Cleveland, AT&T Bell Laboratories
Richard M. Dudley, Massachusetts Institute of Technology
R. Becker, J. Chambers, A. Wilks, The New S Language: A Programming Environment for
Data Analysis and Graphics
P. Bickel, K. Doksum, J. Hodges, Jr., A Festschrift for Erich L. Lehmann
G. Box, The Collected Works of George E. P. Box, Volumes I and II, G. Tiao, editor-in-
chief
L. Breiman, J. Friedman, R. Olshen, C. Stone, Classification and Regression Trees
J. Chambers, W. S. Cleveland, B. Kleiner, P. Tukey, Graphical Methods for Data Analysis
W. S. Cleveland, M. McGill, Dynamic Graphics for Statistics
K. Dehnad, Quality Control, Robust Design, and the Taguchi Method
R. Durrett, Lecture Notes on Particle Systems and Percolation
F. Graybill, Matrices with Applications in Statistics, Second Edition
L. Le Cam, R. Olshen, Proceedings of the Berkeley Conference in Honor of Jerzy Neyman
and Jack Kiefer, Volumes I and II
P. Lewis, E. Orav, Simulation Methodology for Statisticians, Operations Analysts, and
Engineers
H. J. Newton, TIMESLAB
J. Rawlings, Applied Regression Analysis: A Research Tool
J. Rice, Mathematical Statistics and Data Analysis
J. Romano, A. Siegel, Counterexamples in Probability and Statistics
J. Tanur, F. Mosteller, W. Kruskal, E. Lehmann, R. Link, R. Pieters, G. Rising, Statistics:
A Guide to the Unknown, Third Edition
J. Tukey, The Collected Works of J. W. Tukey, W. S. Cleveland, editor-in-chief
Volume I: Time Series: 1949-1964, edited by D. Brillinger
Volume II: Time Series: 1965-1984, edited by D. Brillinger
Volume III: Philosophy and Principles of Data Analysis: 1949-1964, edited by L. Jones
Volume IV: Philosophy and Principles of Data Analysis: 1965-1986, edited by L. Jones
Volume V: Graphics: 1965-1985, edited by W. S. Cleveland
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First published 1989 by Wadsworth & Brooks/Cole Advanced Books & Software
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Reissued 2018 by CRC Press
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Preface
Simulation is essentially a controlled statistical sampling technique that, with a
model, is used to obtain approximate answers for questions about complex, multi(cid:71)
factor probabilistic problems. It is most useful when analytical and numerical
techniques are unable to supply exact answers. In attempting to provide these
approximate answers by repeated sampling on a digital computer, a host of tech(cid:71)
niques and disciplines are called into play:
• Probability concepts in the modeling of systems
• Human experience and intuition in the laying out of the assumptions and
specifications of the model
• Number theory in the generation of uniform pseudo-random numbers
• Probability theory in the generation of nonuniform pseudo-random numbers
• Stochastic process theory for estimation techniques based on sample paths
(ergodic theory)
• Computing science in the implementation of random number generators and
for the organization and graphical display of data sets
• Statistical theory for the all-important design of the simulation and the analysis
of the data obtained as output
It is this interaction of experience, applied mathematics, statistics, and computing
science that makes simulation such a stimulating subject, but at the same time a
subject that is difficult to teach and write about. The sophisticated practice of
simulation requires a broad background on the part of the user and healthy
interdisciplinary interaction.
In fact, we have only to examine the contents of introductory courses on
simulation to see the complexity and diversity of the subject. Some courses deal
primarily with random number generation, some concentrate on modeling, and
some teach only simulation programming languages. Seldom do we find a course
with a basic emphasis on the statistical and modeling techniques, which is where
we feel the emphasis should be. In writing this simulation text, we have attempted
to provide in one place many of the prerequisite statistical and graphical techniques
that are unavailable or unknown to engineers, scientists, and computing specialists.
iii
IV PREFACE
We have also tried to stress the strong interaction of applied mathematics, statistics,
and computing in simulation. Finally, we emphasize, mostly by example, the prob(cid:71)
abilistic and human sides of modeling operational systems. Thus, our goal is to train
a practitioner who can detect the shortcomings of reported simulation results and
who can personally carry out a valid simulation.
The work has been divided into two volumes, more for the sake of manage(cid:71)
ability and readability than because of any deep logical division between the
contents of the two volumes. In fact, the main division of the complete work is
between crude simulation techniques, which are given in Part I of Volume I, and
sophisticated simulation techniques, which take up the rest of Volume I and all of
Volume IL This first volume is a prerequisite for the second volume and for the
running of any simulation, in that these five chapters contain the basic ideas for
modeling and random number generation, while the remaining six chapters discuss
more advanced but fundamental topics such as variance reduction and comparison
of simulations. Moreover, if the simulation produces replicates of independent
output, either univariate or bivariate, then the statistical and graphical output
analysis techniques described in this first volume should be applied. Such inde(cid:71)
pendent output is almost always the result of statistical simulations and, when
performed crudely, of systems simulations as well. Volume II goes on to consider
more sophisticated methods for analyzing the dependent output that can often
result from systems simulations. It also covers the sophisticated generation of
random variables and the generation of random stochastic sequences as input to
simulations. These are very advanced topics not essential to most beginning and
intermediate simulation practitioners.
Three features of the book make it unique.
First, we deal with simulation methodology for problems in both mathematical
statistics and systems simulation. The problems in these two areas vary somewhat
but also have a large common stratum, which is laid out in Volume I.
Second, we have included statistical methods based on graphical techniques
and exploratory data analysis, thereby emphasizing the importance of the analysis
of simulation output data.
Third, the book is organized to present the simplest ideas of simulation (crude
simulation) before proceeding to ideas of sophisticated simulation. Thus, the first
five chapters of Volume I should serve as an introduction to simulation for engineers,
operations analysts, scientists, statisticians, and computing specialists, who may
have only a minimal background in statistics and probability theory. These five
chapters are also written at a lower level of sophistication in probability and
statistics than the remainder of the book.
This complete first volume is most appropriate for an introductory simulation
course of one or more semesters in the second half of a master’s level program in
operations research, industrial engineering, civil engineering, electrical engineering,
computer science, or statistics. Preferred prerequisites are one quarter of probability
theory, one quarter of stochastic processes, one quarter of statistical theory (infer-
PREFACE V
enee) at a master’s level, and one quarter’s introduction to computing and program(cid:71)
ming. Although not necessary, it is helpful to have (again at a graduate level) a one
quarter course in regression analysis and analysis of variance, a one quarter course
in probabilistic models, and an introductory course in computer science dealing
with machine organization and languages. The book, however, does develop the
material that is particularly germane to simulation and that normally would be
covered in the latter courses. Also, references are given to fill in many of the details
presumed already known.
The second volume serves as the basis for an advanced course in simulation
with an emphasis on discrete-event and systems simulation. Prerequisites would
include a course based on the first volume, as well as additional background in
stochastic processes and applied probability.
We believe that the purpose of simulation is, generally, to facilitate choice
among several different and competing schemes for a practical operational or
statistical situation, such as which of several queue disciplines or which of several
inventory policies is better. Therefore, it is with reluctance that we have limited
much of the book to techniques for analyzing one sample in detail and for comparing
two samples. Extensive graphical methods, however, are given for comparing multi(cid:71)
ple samples, as well as an introduction in Chapter 8 to the literature available on
experimental design and multifactor experiment analysis. We have done this pri(cid:71)
marily because the comparison of two samples is fairly straightforward, whereas
the comparison or ranking of more than two samples creates a quantum jump in
the amount and sophistication of statistical methodology needed.
Finally, we point out that one reason many practical operational problems
seem intractable is that they overtax available or foreseeable analytical techniques
(exact and approximate); moreover, the problems often are too complex to be solved
with sufficient precision by simulation on presently available digital computers. The
limitations imposed on simulation by the size and speed of computers are likely to
become less important because of new developments in computer hardware and
software. The remaining problem will then be the available statistical methodology
that is applicable in these simulations.
We hope that by presenting the available and newly developed statistical and
modeling methodology, we will stimulate the development of new ideas to extend
the use of digital simulation techniques.
Acknowledgments
Many people have contributed to this book, mostly by reading it, correcting it, and
commenting on it. Special thanks are due to Professor Arie Hordijk, University of
Leiden, whose invitation to lecture on simulation to students at the Free University
in Amsterdam, Amsterdam University, and the Mathematics Center in Amsterdam
provoked the first draft of this book. We also thank Professor Bruce Schmeiser,
whose initial reading of the chapter on variance reduction made us rethink the whole
topic.
VI PREFACE
The following people have read and commented on parts of the book: David
Burns, Paul Fishbeck, Tony Lawrence, Thomas Lewis, Eddie McKenzie, Steve
Pilnich, Richard Ressler, Edward Rockower, Lee Schruben, and Al Washburn.
Many students in simulation classes at the Naval Postgraduate School helped
to correct the manuscript and to test its suitability as a textbook. Typing was
performed principally by Susie “Turbo” Pickens; her good cheer and incredible
competence were a great source of inspiration. We also thank Barbara Potkay, Ellen
Saunders, and Sabrina O’Jack for typing and editorial assistance.
Luis Uribe provided valuable insights into computing problems and is the
coauthor, with us, of the software supplement to the book. Many figures in the
book, particularly the figures from the SMTBPC program, were created with this
package. This software supplement has gone through three editions, all published
by Wadsworth & Brooks/Cole under the titles Introductory Simulation and Statistics
Package (1985), Advanced Simulation and Statistics Package (1986), and the current
version, Enhanced Simulation and Statistics Package (1989).
Reviewers of this book, William Biles, Louisiana State University; Larry
George, Lawrence Livermore National Laboratory; Donald Haber, University of
Idaho; and Lee Schruben, Cornell University, also provided valuable comments.
Some of the figures in this book were created with the APL-based graphics
program GRAFSTAT from IBM Research. We are indebted to Dr. Peter D. Welch
for making this program available on a test-bed basis at the Naval Postgraduate
School. Other members of the IBM research staff who helped with our use of
GRAFSTAT are P. Heidelberger, D. Stein, T. Lane, A. Blum, and G. Berkland.
Other figures were created using the STATGRAPHICS program distributed by
STSC, Inc.
Finally, the research of P. A. W. Lewis was supported, for much of the time
during which this book was being written, by the Office of Naval Research under
various grants. We are grateful for their continued support.
P. A. W. Lewis
E. J. Orav
Brief Contents of Volume I
Introduction 1
Part I Modeling and Crude Simulation 7
Chapter 1 Definition of Simulation 9
Chapter 2 Golden Rules and Principles of Simulation 15
Chapter 3 Modeling: Illustrative Examples and Problems 17
Chapter 4 Crude (or Straightforward) Simulation and Monte Carlo 32
Chapter 5 Uniform Pseudo-Random Variable Generation 65
Part II Sophisticated Simulation 101
Chapter 6 Descriptions and Quantifications of Univariate Samples:
Numerical Summaries 103
Chapter 7 Descriptions and Quantifications of Univariate Samples:
Graphical Summaries 158
Chapter 8 Comparisons in Multifactor Simulations: Graphical and Formal
Methods 202
Chapter 9 Assessing Variability in Univariate Samples: Sectioning,
Jackknifing, and Bootstrapping 251
Chapter 10 Bivariate Random Variables: Definitions, Generation, and
Graphical Analysis 291
Chapter 11 Variance Reduction 334
Author Index 409
Subject Index 411
VÜ
Contents of Volume I
Introduction 1
References and Literature 2
Use of This Book in Teaching 4
References 5
Part I Modeling and Crude Simulation 7
Chapter 1 Definition of Simulation 9
Exercises 13
References 14
Chapter 2 Golden Rules and Principles of Simulation 15
Chapter 3 Modeling: Illustrative Examples and Problems 17
3.1 The Modeling Aspect of Simulation 17
3.2 Single-Server, Single-Input, First-In/First-Out (FIFO)
Queue 18
3.3 Multiple-Server, Single-Input Queue 21
3.4 An Example from Statistics: The Trimmed t Statistic 21
3.5 An Example from Engineering: Reliability of Series
Systems 23
3.6 A Military Problem: Proportional Navigation 25
3.7 Comments on the Examples 28
3.7.1 The Role of a “Time” Evolution Parameter 28
3.7.2 Stability and Convergence Considerations 29
3.7.3 Assumptions and the Use of Simulation in
Experimentation 29
viii