Production Systems Engineering

673 Pages·2009·18.09 MB·English

by  Jingshan Li, Semyon M. Meerkov (auth.)

Production Systems Engineering
Production Systems Engineering

Jingshan Li
Electrical and Computer Engineering, University of Kentucky
Lexington, Kentucky

Semyon M. Meerkov
Electrical and Computer Science, University of Michigan
Ann Arbor, Michigan
Jingshan Li
University of Kentucky
Electrical and Computer Engineering
Lexington, Kentucky 40506

Semyon M. Meerkov
University of Michigan
Electrical and Computer Science
Ann Arbor, Michigan 48109

ISBN 978-0-387-75578-6 eISBN 978-0-387-75579-3

Library of Congress Control Number: 2008937464

© 2009 Springer Science+Business Media, LLC

All rights reserved. This work may not be translated or copied in whole or in part without the
written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring
Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or
scholarly analysis. Use in connection with any form of information storage and retrieval,
electronic adaptation, computer software, or by similar or dissimilar methodology now known
or hereafter developed is forbidden. The use in this publication of trade names, trademarks,
service marks and similar terms, even if they are not identified as such, is not to be taken as an
expression of opinion as to whether or not they are subject to proprietary rights.

Cover illustration: In 1932, the famous Mexican artist, Diego Rivera, was commissioned by
Edsel Ford, President of Ford Motor Company, to create two murals for the Detroit Institute of
Arts. The murals, completed in 1933, are currently located on the Northern and Southern walls
of the Detroit Institute of Art’s Rivera Court. The cover image of this book is a fragment of the
Northern Wall’s mural. It depicts operations involved in the production of the engine and trans-
mission for the 1932 Ford V8. Although the manufacturing technology has changed dramatically
since then, the fundamental principles of production systems did not. This textbook is devoted
to these principles.

Photograph ©2001 The Detroit Institute of Arts

Printed on acid-free paper.

9 8 7 6 5 4 3 2 1

springer.com
To the memory of SMM’s parents,
To JL’s parents, and
To our families, whose love and support made this
book possible
JL and SMM
v
“... of making many books,
there is no end; and much study is a weariness of the flesh.”
Ecclesiastes, 12:12
Preface
Production systems are a major part of modern technology. However, there
hasnotbeenasingleuniversity-leveltextbookdevotedexclusivelytothistopic.
This volume is intended to fill this void. It presents the area of production
systems basedon the first principles and at the same level of rigor as other
engineering disciplines. Therefore, we use the title Production Systems
Engineering (PSE).
Alongwithrigor, thisbookemphasizespracticalapplications. Infact, every
problem considered here originated on the factory floor and, after conceptu-
alizations and analyses, was implemented in practice, leading to productivity
improvements and savings. The case studies included in this text are based on
these applications. Thus, a rigorous, first-principle-based presentation of PSE
problems of practical significance is the main emphasis of this textbook.
Preliminaryversionsofthistexthavebeenusedbyundergraduateandgrad-
uate students in courses offered in the US (the University of Michigan and the
University of Kentucky), China (Tsinghua University) and Israel (Technion),
and found overwhelming approval of students and instructors alike. We hope
that the publication of this volume will contribute to engineering education of
all students interested in production and, as a result, to an increased efficiency
in manufacturing.
Jingshan Li
Lexington, Kentucky
Semyon M. Meerkov
Ann Arbor, MI
August 15, 2008
vii
Contents Synopsis
I. BACKGROUNDMATERIALANDMATHEMAT-
ICAL MODELING 1
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Mathematical Tools: Elements of Probability Theory . . . . . . 13
3. Mathematical Modeling of Production Systems . . . . . . . . . . 61
II. SERIAL PRODUCTION LINES WITH BER-
NOULLI MODEL OF MACHINE RELIABILITY 121
4. Analysis of Bernoulli Lines . . . . . . . . . . . . . . . . . . . . . 123
5. Continuous Improvement of Bernoulli Lines . . . . . . . . . . . . 167
6. Design of Lean Bernoulli Lines . . . . . . . . . . . . . . . . . . . 201
7. Closed Bernoulli Lines. . . . . . . . . . . . . . . . . . . . . . . . 221
8. Product Quality in Bernoulli Lines. . . . . . . . . . . . . . . . . 247
9. Customer Demand Satisfaction in Bernoulli Lines . . . . . . . . 293
10. Transient Behavior of Bernoulli Lines . . . . . . . . . . . . . . . 315
III. SERIAL PRODUCTION LINES WITH CONTIN-
UOUS TIME MODELS OF MACHINE RELIABILITY341
11. Analysis of Exponential Lines . . . . . . . . . . . . . . . . . . . 343
12. Analysis of Non-exponential Lines . . . . . . . . . . . . . . . . . 391
13. Improvement of Continuous Lines . . . . . . . . . . . . . . . . . 411
14. Design of Lean Continuous Lines . . . . . . . . . . . . . . . . . . 441
15. Customer Demand Satisfaction in Continuous Lines . . . . . . . 471
IV. ASSEMBLY SYSTEMS 493
16. Assembly Systems with Bernoulli Model of Machine Reliability . 495
17. AssemblySystemswithContinuousTimeModelsofMachineRe-
liability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
V. SUMMARY, PSE TOOLBOX, AND PROOFS 545
18. Summary of Main Facts of Production Systems Engineering . . 547
19. PSE Toolbox . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555
20. Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587
Epilogue 653
Abbreviations and Notations 655
Index 661
ix
Contents
Dedication v
Preface vii
Contents Synopsis ix
Foreword xxiii
I BACKGROUNDMATERIALANDMATHEMAT-
ICAL MODELING 1
1 Introduction 3
1.1 Main Areas of Manufacturing . . . . . . . . . . . . . . . . . . . . 3
1.2 Main Problems of Production Systems Engineering . . . . . . . . 4
1.2.1 Complicating phenomena . . . . . . . . . . . . . . . . . . 4
1.2.2 Analysis, continuous improvement, and design problems . 6
1.2.3 Fundamental laws of Production Systems Engineering . . 7
1.2.4 Techniques used in this textbook . . . . . . . . . . . . . . 8
1.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Annotated Bibliography . . . . . . . . . . . . . . . . . . . . . . . 10
2 Mathematical Tools: Elements of Probability Theory 13
2.1 Random Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.2 Axioms of probability and their corollaries . . . . . . . . . 14
2.1.3 Conditional probability . . . . . . . . . . . . . . . . . . . 16
2.1.4 Independence . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1.5 Total probability formula . . . . . . . . . . . . . . . . . . 19
2.1.6 Bayes’s formula . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.2 Discrete random variables . . . . . . . . . . . . . . . . . . 22
2.2.3 Continuous random variables . . . . . . . . . . . . . . . . 26
xi
xii CONTENTS
2.2.4 Expected value, variance, and coefficient of variation . . . 36
2.2.5 Vector random variables . . . . . . . . . . . . . . . . . . . 38
2.2.6 Asymptotic properties of sums of random variables . . . . 40
2.3 Random Processes . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3.2 Continuous time, continuous space random processes . . . 44
2.3.3 Markov processes . . . . . . . . . . . . . . . . . . . . . . . 46
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.6 Annotated Bibliography . . . . . . . . . . . . . . . . . . . . . . . 59
3 Mathematical Modeling of Production Systems 61
3.1 Types of Production Systems . . . . . . . . . . . . . . . . . . . . 62
3.1.1 Serial production lines . . . . . . . . . . . . . . . . . . . . 62
3.1.2 Assembly systems . . . . . . . . . . . . . . . . . . . . . . 64
3.2 Structural Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.3 Mathematical Models of Machines . . . . . . . . . . . . . . . . . 68
3.3.1 Timing issues . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.3.2 Machine reliability models . . . . . . . . . . . . . . . . . . 70
3.3.3 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.3.4 Machine model identification . . . . . . . . . . . . . . . . 75
3.3.5 Calculating parameters of aggregated machines . . . . . . 77
3.3.6 Machine quality models . . . . . . . . . . . . . . . . . . . 82
3.4 Mathematical Models of Buffers . . . . . . . . . . . . . . . . . . . 83
3.4.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.4.2 Buffer parameters identification . . . . . . . . . . . . . . . 83
3.5 Modeling Interactions between Machines and Buffers . . . . . . . 84
3.5.1 Slotted time case . . . . . . . . . . . . . . . . . . . . . . . 85
3.5.2 Continuous time case . . . . . . . . . . . . . . . . . . . . 85
3.6 Performance Measures . . . . . . . . . . . . . . . . . . . . . . . . 86
3.6.1 Production rate and throughput . . . . . . . . . . . . . . 86
3.6.2 Work-in-process and finished goods inventory . . . . . . . 87
3.6.3 Probabilities of blockages and starvations . . . . . . . . . 88
3.6.4 Residence time . . . . . . . . . . . . . . . . . . . . . . . . 89
3.6.5 Due-time performance . . . . . . . . . . . . . . . . . . . . 90
3.6.6 Transient characteristics . . . . . . . . . . . . . . . . . . . 90
3.6.7 Evaluating performance measures on the factory
floor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.7 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.8 Steps of Modeling, Analysis, Design, and Improvement . . . . . . 92
3.8.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.8.2 Analysis, continuous improvement, and design . . . . . . 92
3.9 Simplification: Transforming Exponential
Models into Bernoulli Models . . . . . . . . . . . . . . . . . . . . 93
3.9.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.9.2 Exponential and Bernoulli lines considered . . . . . . . . 93
CONTENTS xiii
3.9.3 The exp-B transformation . . . . . . . . . . . . . . . . . . 94
3.9.4 The B-exp transformation . . . . . . . . . . . . . . . . . . 100
3.9.5 Exp-B and B-exp transformations for assembly systems . 101
3.10 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.10.1 Automotive ignition coil processing system . . . . . . . . 102
3.10.2 Automotive paint shop production system . . . . . . . . . 106
3.10.3 Automotive ignition module assembly system . . . . . . . 110
3.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.12 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.13 Annotated Bibliography . . . . . . . . . . . . . . . . . . . . . . . 117
II SERIALPRODUCTIONLINESWITHBERNOULLI
MODEL OF MACHINE RELIABILITY 121
4 Analysis of Bernoulli Lines 123
4.1 Two-machine Lines . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.1.1 Mathematical description . . . . . . . . . . . . . . . . . . 124
4.1.2 Steady state probabilities . . . . . . . . . . . . . . . . . . 126
4.1.3 Formulas for the performance measures . . . . . . . . . . 131
4.1.4 Asymptotic properties . . . . . . . . . . . . . . . . . . . . 133
4.2 M >2-machine Lines . . . . . . . . . . . . . . . . . . . . . . . . 133
4.2.1 Mathematical description and approach . . . . . . . . . . 133
4.2.2 Aggregation procedure and its properties . . . . . . . . . 137
4.2.3 Formulas for the performance measures . . . . . . . . . . 141
4.2.4 Asymptotic properties of M >2-machine lines . . . . . . 143
4.2.5 Accuracy of the estimates . . . . . . . . . . . . . . . . . . 143
4.3 System-Theoretic Properties . . . . . . . . . . . . . . . . . . . . . 154
4.3.1 Static laws of production systems . . . . . . . . . . . . . . 154
4.3.2 Reversibility . . . . . . . . . . . . . . . . . . . . . . . . . 154
4.3.3 Monotonicity . . . . . . . . . . . . . . . . . . . . . . . . . 156
4.4 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
4.4.1 Automotive ignition coil processing system . . . . . . . . 156
4.4.2 Automotive paint shop production system . . . . . . . . . 159
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
4.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
4.7 Annotated Bibliography . . . . . . . . . . . . . . . . . . . . . . . 165
5 Continuous Improvement of Bernoulli Lines 167
5.1 Constrained Improvability . . . . . . . . . . . . . . . . . . . . . . 168
5.1.1 Resource constraints and definitions . . . . . . . . . . . . 168
5.1.2 Improvability with respect to WF . . . . . . . . . . . . . 169
5.1.3 Improvability with respect to WF and BC simultaneously 172
5.1.4 Improvability with respect to BC . . . . . . . . . . . . . . 174
5.2 Unconstrained Improvability. . . . . . . . . . . . . . . . . . . . . 176
5.2.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . 176
xiv CONTENTS
5.2.2 Identification of bottlenecks in two-machine lines . . . . . 179
5.2.3 Identification of bottlenecks in M >2-machine lines . . . 179
5.2.4 Potency of buffering . . . . . . . . . . . . . . . . . . . . . 189
5.2.5 Designing continuous improvement projects . . . . . . . . 190
5.3 Measurement-based Management of Production Systems . . . . . 190
5.4 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
5.4.1 Automotive ignition coil processing system . . . . . . . . 194
5.4.2 Automotive paint shop production system . . . . . . . . . 195
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
5.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
5.7 Annotated Bibliography . . . . . . . . . . . . . . . . . . . . . . . 199
6 Design of Lean Bernoulli Lines 201
6.1 Parametrization and Problem Formulation . . . . . . . . . . . . . 201
6.2 Lean Buffering in Bernoulli Lines with Identical Machines . . . . 202
6.2.1 Two-machine lines . . . . . . . . . . . . . . . . . . . . . . 202
6.2.2 Three-machine lines . . . . . . . . . . . . . . . . . . . . . 204
6.2.3 M >3-machine lines . . . . . . . . . . . . . . . . . . . . . 204
6.3 Lean Buffering in Serial Lines with Non-identical Bernoulli Ma-
chines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
6.3.1 Two-machine lines . . . . . . . . . . . . . . . . . . . . . . 207
6.3.2 M >2-machine lines . . . . . . . . . . . . . . . . . . . . . 208
6.4 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
6.4.1 Automotive ignition coil processing system . . . . . . . . 216
6.4.2 Automotive paint shop production system . . . . . . . . . 217
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
6.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
6.7 Annotated Bibliography . . . . . . . . . . . . . . . . . . . . . . . 219
7 Closed Bernoulli Lines 221
7.1 System Model and Problem Formulation . . . . . . . . . . . . . . 223
7.1.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
7.1.2 Problems addressed . . . . . . . . . . . . . . . . . . . . . 223
7.2 Performance Analysis, Monotonicity,
Reversibility, and Unimpeding Closed Lines . . . . . . . . . . . . 225
7.2.1 Two-machine lines . . . . . . . . . . . . . . . . . . . . . . 225
7.2.2 M >2-machine lines . . . . . . . . . . . . . . . . . . . . . 228
7.3 Improvability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
7.3.1 Two-machine lines . . . . . . . . . . . . . . . . . . . . . . 230
7.3.2 M >2-machine lines . . . . . . . . . . . . . . . . . . . . . 231
7.3.3 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . 235
7.4 Bottleneck Identification . . . . . . . . . . . . . . . . . . . . . . . 236
7.4.1 Two-machine lines . . . . . . . . . . . . . . . . . . . . . . 236
7.4.2 M >2-machine lines . . . . . . . . . . . . . . . . . . . . . 237
7.5 Leanness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
7.6 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241