Reliability Engineering Handbook
Kececioglu
Notes on:
Reliability Engineering HandbookKececioglu |
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Reliability Engineering Handbook, Dimitri Kececioglu; Prentice Hall, Englewood Cliffs NJ, 1991. (two volume set; 1229 pages+). ISBN 0-13-772294-X (vol. 1), 0-13-772302-4 (vol. 2).
This book is a comprehensive look at reliability theory, and especially the mathematical aspects of reliability. It is in many respects much more comprehensive than other books (for example, its definition of reliability has six key points rather than the usual single sentence). The author has a background in mechanical engineering as applied to aerospace systems. As a result, the book is focused primarily on failures due to mechanical wearout and breakage
Topic coverage: (*** = emphasized; ** = discussed with some detail; * = mention)
| *** | Dependability | * | Electronic Hardware | Requirements | |||||
| Safety | Software | ** | Design | ||||||
| Security | ** | Electro-Mechanical Hardware | * | Manufacturing | |||||
| Scalability | Control Algorithms | Deployment | |||||||
| Latency | Humans | Logistics | |||||||
| Affordability | Society/Institutions | Retirement |
Other topics: heavy emphasis on mathematics and reliability modelling.
The author writes:
"Now in its fourth printing, this handbook covers early, chance and wearout reliability as experienced in the three life periods of components, equipment and systems. It provides five unique models for quantifying the reliability bathtub curve which enables engineers to determine a variety of factors characteristic of components, equipment and systems including: their full-life behavior; burnin, breaking in and debugging period; spare parts provisioning; and more."
"In Volume II, Kececioglu focuses on the predictions of equipment and system reliability for the series, parallel, standby, and conditional function configuration cases. Drenick's theorem of complex systems times-to-failure distributions is presented as well as system reliability prediction and reliability goal determination, failure modes, effects and critically analysis methods to identify design improvement areas. Six reliability apportionment techniques are also covered."
Volume 1 "dust jacket" comments:
The demand for reliable products, components, and systems has never been greater, especially among organizations seeking greater competitiveness in world markets. To help you keep pace, Dimitri Kececioglu's comprehensive examination of reliability engineering was written to help you design and build a product that meets the requirements of performance specifications with a minimum of failures.
- Chapter 1 provides the important objectives of reliability engineering.
- Chapter 2 covers the history of reliability engineering.
- Chapter 3 defines reliability engineering in detail.
- Chapter 4 quantifies the concepts of times-to-failure distributions, reliability, conditional reliability, failure rate and mean life, and provides the necessary background in statistics.
- Chapters 5-11 examine the most frequently used distributions in reliability engineering: exponential, Weibull, normal, lognormal, extreme value, Rayleigh, and uniform.
- Chapter 12 covers early, chance, and wearout reliability, as experienced in the three life periods of components, equipment, and systems.
- Chapter 13 combines the three types of life characteristics into a unified approach of quantifying the full-life behavior of components, equipment, and systems.
- Chapter 14 provides five unique models for quantifying the reliability bathtub curve which enables the determination of the full-life behavior of components, equipment, and systems; their burn-in, breaking in, and debugging period; their spare parts provisioning; their provisioning; their preventive maintenance schedules; and more.
Volume 2 "dust jacket" comments:
The demand for reliable products, components, and systems has never been greater, especially among organizations seeking greater competitiveness in world markets. Dimitri Kececioglu's comprehensive examination of reliability engineering was written to help you design and build a product that meets the requirements of performance specifications with a minimum of failure. Expanding on the coverage provided in Volume 1, Volume 2 does the following:
- Covers the prediction of equipment and system reliability for the series, parallel, standby, and conditional function configuration cases (Chs. 1-4).
- Discusses the prediction of the reliability of complex components, equipment, and systems (Ch. 5) with multimode function and logic (Ch. 6), multistress level of function (Ch. 7), load sharing function mode (Ch. 8), static switches (Ch. 9), cyclic switches (Ch. 10), and fault tree analysis (Ch. 11).
- Includes five practical and comprehensive case histories of predicting equipment and system reliabilities and comparing them with their reliability goals (Ch. 12).
- Presents Drenick's theorem of complex systems times-to-failure distributions (Ch. 13).
- Explores the reliability of components with a policy of replacing those that fail by a prescribed operating time (Ch. 14).
- Talks about methods of allocation, or apportionment, of equipment's or system's reliability goal to its subsystems (Ch. 15).
- Examines reliability growth and test-analyze-and-fix models to quantify when the mean-time-between-failures (MTBF) and reliability goals of products under development will be attained.
- Contains failure modes, effects, and criticality analysis (FAMECA) methods to identify design improvement areas (Ch. 17).
CHAPTER 1 -RELIABILITY ENGINEERING: ITS APPLICATIONS
AND BENEFITS 1
1.1 - OBJECTIVES 1
1.2 - WHY RELIABILITY ENGINEERING? 2
1.3 - APPLICATIONS AND BENEFITS 6
1.4 - COMPLEXITY OF PRODUCTS 10
1.5 - WORLD INDUSTRIAL COMPETITION AND RELIABILITY
ENGINEERING 12
1.6 - RELIABILITY ADVERTISED 13
1.7 - OPTIMIZATION OF RELIABILITY 15
1.7.1 - OPTIMIZATION THROUGH INTEGRATED RELIABILITY
ENGINEERING PROGRAMS IN INDUSTRY 20
1.8 - CASE HISTORIES OF COST REDUCTION THROUGH
RELIABILITY 21
1.9 - RELIABILITY AND QUALITY CONTROL COMPARED 35
1.10- DIFFERENCES BETWEEN RELIABILITY AND QUALITY
CONTROL 36
1.11- HOW TO REDUCE THE LIFE-CYCLE COST OF EQUIPMENT
WHILE INCREASING ITS RELIABILITY,
MAINTAINABILITY, AND AVAILABILITY 37
PROBLEMS 41
REFERENCES 41
CHAPTER 2 - HISTORY, DEVELOPMENT, AND ACCOMPLISHMENTS 43
2.1 - RELIABILITY ENGINEERING IN ACTION 43
2.2 - A LOOK AHEAD 52
PROBLEMS 57
REFERENCES 58
CHAPTER 3 - RELIABILITY DEFINED 61
3.1 - OBJECTIVES 61
3.2 - COMPREHENSIVE DEFINITION OF RELIABILITY 61
3.3 - CONDITIONAL PROBABILITY IN RELIABILITY AND
SYSTEM EFFECTIVENESS 62
EXAMPLE 3 - 1 65
SOLUTIONS TO EXAMPLE 3 - 1 66
EXAMPLE 3 - 2 66
SOLUTIONS TO EXAMPLE 3 - 2 66
EXAMPLE 3 - 3 67
SOLUTIONS TO EXAMPLE 3 - 3 68
3.4 - CONFIDENCE LEVEL 69
3.5 - NO-FAILURE PERFORMANCE 72
3.6 - FAILURE CAUSES AND TYPES 72
3.6.1 - FAILURE CAUSES 72
3.6.2 - FAILURE TYPES 78
3.6.3 - FAILURES AS THEY RELATE TO THE RELIABILITY
BATHTUB CURVE 81
3.7 - EFFECTS OF AGE 82
3.8 - EFFECTS OF MISSION TIME 83
3.9 - EFFECTS OF STRESS 85
EXAMPLE 3 - 4 90
SOLUTION TO EXAMPLE 3 - 4 90
EXAMPLE 3 - 5 94
SOLUTIONS TO EXAMPLE 3 - 5 94
3.10- SYSTEM RELIABILITY AND AVAILABILITY
CONSIDERATIONS, THE MISSION PROFILE, AND
CASE HISTORIES ... 95
3.10.1 - MISSION PROFILE AND REQUIREMENTS 95
3.10.2 - CASE HISTORIES 96
3.10.2.1 - COMPUTERS - THE AUTOMATIC TELLER
MACHINE 96
3.10.2.2 - COMMUNICATIONS - THE TELEPHONE 96
3.10.2.3 - INDUSTRIAL CONTROL - CHEMICAL
PROCESS CONTROL 99
3.10.2.4 - POWER ENERGY - THE ELECTRIC
POWER SYSTEM 99
3.10.2.5 - CUSTOMER ELECTRONICS - THE
TELEVISION SET 99
3.10.2.6 - TRANSPORTATION - ELECTRONIC
ENGINE CONTROL 100
3.10.2.7 - AEROSPACE - THE AIR TRAFFIC
CONTROL SYSTEM 100
3.10.2.8 - MILITARY - THE BALLISTIC MISSILE 101
3.10.2.9 - BIOMEDICAL - THE IMPLANTABLE
PACEMAKER 101
3.10.2.10- SOFTWARE - THE COMPUTER OPERATING
SYSTEM 101
PROBLEMS 102
REFERENCES 106
CHAPTER 4 -BASIC ANALYTICAL AND STATISTICAL FUNCTIONS
IN RELIABILITY ENGINEERING 107
4.1 - OBJECTIVES 107
4.2 - THE FIVE IMPORTANT ANALYTICAL FUNCTIONS IN
RELIABILITY ENGINEERING 108
4.3 - THE DISTRIBUTION FUNCTION 108
4.3.1 - DATA 108
4.3.2 - DATA REDUCTION TO FREQUENCY HISTOGRAMS
AND POLYGONS 109
EXAMPLE 4 - 1 120
SOLUTIONS TO EXAMPLE 4 - 1 121
4.3.3 - FREQUENCY DISTRIBUTION AND PROBABILITY
DENSITY FUNCTION 123
4.3.4 - OTHER DISTRIBUTION FUNCTIONS 126
4.3.5 - THE FAILURE PROBABILITY DENSITY FUNCTION
AND ITS ESTIMATE 127
4.3.6 - CUMULATIVE FREQUENCY AND CUMULATIVE
DISTRIBUTION 134
4.3.7 - DATA AND DISTRIBUTION DESCRIPTIVE
VALUES AND PARAMETERS 139
4.3.7.1 - MEAN 140
4.3.7.2 - MEDIAN 145
4.3.7.3 - MODE 148
4.3.7.4 - DISTRIBUTION MOMENTS 150
4.3.7.5 - VARIANCE AND STANDARD DEVIATION 153
4.3.7.6 - COEFFICIENT OF VARIATION 155
4.3.7.7 - SKEWNESS 155
4.3.7.8 - KURTOSIS 156
4.3.7.9 - THE MOMENT GENERATING FUNCTION 159
4.3.7.10 - FRACTILES, PERCENTILES, AND QUANTILES 164
4.3.7.11 - DISTRIBUTION PARAMETERS 164
4.3.7.11.1 - LOCATION PARAMETER 166
4.3.7.11.2 - SHAPE PARAMETER 168
4.3.7.11.3 - SCALE PARAMETER 168
4.4 - FAILURE RATE FUNCTION 168
4.4.1 - AVERAGE FAILURE RATE ESTIMATE 171
4.4.2 - INSTANTANEOUS FAILURE RATE, OR HAZARD
RATE, OR FORCE OF MORTALITY FUNCTION 174
4.4.3 - CONSTRUCTION OF RELIABILITY BATHTUB
CURVES (RBTC'S) AND THEIR USES 179
4.5 - RELIABILITY FUNCTION 194
4.5.1 - RELIABILITY ESTIMATE 194
4.5.2 - RELATIONSHIP TO RELATIVE CUMULATIVE
FREQUENCY 195
4.5.3 - RELATIONSHIP TO PROBABILITY DENSITY AND
CUMULATIVE DISTRIBUTION FUNCTIONS 196
4.5.4 - RELATIONSHIP TO FAILURE RATE 198
4.6 - CONDITIONAL RELIABILITY FUNCTION 200
EXAMPLE 4 - 2 204
SOLUTIONS TO EXAMPLE 4 - 2 204
4.7 - MEAN LIFE FUNCTION 205
PROBLEMS 208
REFERENCES 213
CHAPTER 5 - THE EXPONENTIAL DISTRIBUTION 215
5.1 - EXPONENTIAL DISTRIBUTION CHARACTERISTICS 215
5.1.1 - THE SINGLE-PARAMETER EXPONENTIAL
DISTRIBUTION 215
EXAMPLE 5 - 1 218
SOLUTION TO EXAMPLE 5 - 1 218
5.1.2 - THE TWO-PARAMETER EXPONENTIAL DISTRIBUTION 218
EXAMPLE 5 - 2 220
SOLUTIONS TO EXAMPLE 5 - 2 221
5.2 - EXPONENTIAL RELIABILITY CHARACTERISTICS 230
5.2.1 - THE ONE-PARAMETER EXPONENTIAL RELIABILITY 230
EXAMPLE 5 - 3 231
SOLUTION TO EXAMPLE 5 - 3 231
5.2.2 - THE TWO-PARAMETER EXPONENTIAL RELIABILITY 232
5.3 - EXPONENTIAL FAILURE RATE AND MEAN-TIME-BETWEEN-
FAILURES CHARACTERISTICS 234
EXAMPLE 5 - 4 234
SOLUTION TO EXAMPLE 5 - 4 234
EXAMPLE 5 - 5 234
SOLUTIONS TO EXAMPLE 5 - 5 236
5.4 - DETERMINATION OF THE EXPONENTIAL FAILURE RATE
AND MTBF FROM INDIVIDUAL TIME-TO-FAILURE DATA 238
5.4.1 - WHEN THE TEST SAMPLE SIZE IS KEPT CONSTANT
BY REPLACING THE FAILED UNITS 238
5.4.1.1 - FAILURE TERMINATED TEST CASE 238
EXAMPLE 5 - 6 239
SOLUTION TO EXAMPLE 5 - 6 239
5.4.1.2 - TIME TERMINATED TEST CASE 240
EXAMPLE 5 - 7 241
SOLUTION TO EXAMPLE 5 - 7 241
5.4.2 - DETERMINATION OF m WHEN THE FAILED UNITS
ARE NOT REPLACED 242
5.4.2.1 - FAILURE TERMINATED TEST CASE 242
EXAMPLE 5 - 8 242
SOLUTION TO EXAMPLE 5 - 8 242
5.4.2.2 - TIME TERMINATED TEST CASE 243
EXAMPLE 5 - 9 243
SOLUTION TO EXAMPLE 5 - 9 243
5.4.3 - DETERMINATION OF m WHEN A MIXED REPLACEMENT
AND NONREPLACEMENT TEST
IS CONDUCTED 244
5.4.3.1 - FAILURE TERMINATED TEST CASE 244
EXAMPLE 5 - 10 245
SOLUTION TO EXAMPLE 5 - 10 245
5.4.3.2 - TIME TERMINATED TEST CASE 247
EXAMPLE 5 - 11 247
SOLUTION TO EXAMPLE 5 - 11 247
5.4.4 - DETERMINATION OF m WITH GROUPED FAILURE
TIMES IN A NONREPLACEMENT TIME
TERMINATED TEST 248
EXAMPLE 5 - 12 248
SOLUTION TO EXAMPLE 5 - 12 248
5.5 - DETERMINATION OF THE EXPONENTIAL FAILURE RATE
AND MTBF BY PROBABILITY PLOTTING 249
5.6 - A BETTER ESTIMATE OF RELIABILITY 254
EXAMPLE 5 - 13 254
SOLUTIONS TO EXAMPLE 5 - 13 255
EXAMPLE 5 - 14 257
SOLUTIONS TO EXAMPLE 5 - 14 258
5.7 - APPLICATIONS OF THE EXPONENTIAL DISTRIBUTION 261
5.8 - PHENOMENOLOGICAL CONSIDERATIONS FOR USING THE
EXPONENTIAL DISTRIBUTION 261
PROBLEMS 263
REFERENCES 268
CHAPTER 6 - THE WEIBULL DISTRIBUTION 271
6.1 - WEIBULL DISTRIBUTION CHARACTERISTICS 271
6.2 - WEIBULL RELIABILITY CHARACTERISTICS 279
6.3 - WEIBULL FAILURE RATE CHARACTERISTICS 280
6.4 - ESTIMATION OF THE PARAMETERS OF THE WEIBULL
DISTRIBUTION BY PROBABILITY PLOTTING 282
6.4.1 - WHEN THE DATA FALL ON A STRAIGHT LINE 282
EXAMPLE 6 - I 284
SOLUTION TO EXAMPLE 6 - 1 284
EXAMPLE 6 - 2 289
SOLUTION TO EXAMPLE 6 - 2 289
EXAMPLE 6 - 3 289
SOLUTION TO EXAMPLE 6 - 3 289
EXAMPLE 6 - 4 289
SOLUTION TO EXAMPLE 6 - 4 289
EXAMPLE 6 - 5 291
SOLUTION TO EXAMPLE 6 - 5 291
6.4.2 - WHEN THE DATA DO NOT FALL ON A STRAIGHT
LINE 291
6.4.2.1 - METHOD 1 291
EXAMPLE 6 - 6 297
SOLUTION TO EXAMPLE 6 - 6 297
EXAMPLE 6 - 7 297
SOLUTION TO EXAMPLE 6 - 7 297
EXAMPLE 6 - 8 298
SOLUTION TO EXAMPLE 6 - 8 298
EXAMPLE 6 - 9 298
SOLUTION TO EXAMPLE 6 - 9 298
6.4.2.2 - METHOD 2 299
EXAMPLE 6 - 10 299
SOLUTION TO EXAMPLE 6 - 10 299
6.4.2.3 - METHOD 3 299
EXAMPLE 6 - 11 302
SOLUTION TO EXAMPLE 6 - 11 302
6.4.3 - THE DETERMINATION OF A NEGATIVE Y 303
EXAMPLE 6 - 12 303
SOLUTION TO EXAMPLE 6 - 12 303
6.4.4 - GROUPED DATA WEIBULL ANALYSIS 306
EXAMPLE 6 - 13 306
SOLUTION TO EXAMPLE 6 - 13 306
6.4.5 - WHEN IS THE WEIBULL NOT AN APPROPRIATE
DISTRIBUTION FOR THE TIME-TO-FAILURE DATA 310
6.5 - CONSTRUCTION OF THE WEIBULL PROBABILITY PAPER 310
EXAMPLE 6 - 14 311
SOLUTION TO EXAMPLE 6 - 14 311
6.6 - PROBABILITY OF PASSING A RELIABILITY TEST 312
EXAMPLE 6 - 15 312
SOLUTION TO EXAMPLE 6 - 15 312
6.7 - APPLICATIONS OF THE WEIBULL DISTRIBUTION 313
6.8 - PHENOMENOLOGICAL CONSIDERATIONS FOR
USING THE WEIBULL DISTRIBUTION 313
6.9 - ANALYSIS OF PROBABILITY PLOTS 315
6.10- CHOOSING THE RIGHT PROBABILITY PAPER 323
PROBLEMS 324
REFERENCES 329
CHAPTER 7 - THE NORMAL DISTRIBUTION 333
7.1 - NORMAL DISTRIBUTION CHARACTERISTICS 333
7.2 - COMPUTATIONAL METHODS FOR THE DETERMINATION
OF THE PARAMETERS OF THE NORMAL DISTRIBUTION 338
7.2.1 - WITH INDIVIDUAL DATA VALUES OR MEASUREMENTS 338
EXAMPLE 7-1 339
SOLUTIONS TO EXAMPLE 7 - 1 339
7.2.2 - WITH GROUPED DATA 340
EXAMPLE 7 - 2 341
SOLUTIONS TO EXAMPLE 7 - 2 342
7.3 - DETERMINATION OF THE PARAMETERS OF THE NORMAL
DISTRIBUTION BY PROBABILITY PLOTTING 345
EXAMPLE 7 - 3 347
SOLUTIONS TO EXAMPLE 7 - 3 347
7.3.1 - USES OF AND POINTERS ON NORMAL
PROBABILITY PLOTS 351
7.4 - NORMAL RELIABILITY CHARACTERISTICS 355
EXAMPLE 7 - 4 357
SOLUTIONS TO EXAMPLE 7 - 4 360
7.5 - NORMAL FAILURE RATE CHARACTERISTICS 361
EXAMPLE 7 - 5 363
SOLUTIONS TO EXAMPLE 7 - 5 363
7.6 - THE TRUNCATED NORMAL DISTRIBUTION 363
7.6.1 - INTRODUCTION 363
7.6.2 - MLE OF u AND o2 OF A NORMAL POPULATION
FROM A SAMPLE DRAWN FROM A ONE-SIDED
TRUNCATED POPULATION 365
EXAMPLE 7 - 6 369
SOLUTION TO EXAMPLE 7 - 6 369
7.7 - ESTIMATION OF THE PARAMETERS FROM A
TRUNCATED SAMPLE 375
7.7.1 - MLE OF u AND o2 FROM A TIME
TERMINATED SAMPLE 375
EXAMPLE 7 - 7 378
SOLUTION TO EXAMPLE 7 - 7 378
7.7.2 - MLE OF u AND o2 OF A NORMAL POPULATION
FROM A FAILURE TERMINATED SAMPLE 383
EXAMPLE 7 - 8 384
SOLUTION TO EXAMPLE 7 - 8 384
7.7.3 - LINEAR ESTIMATES OF u AND o2 IN SMALL
SAMPLES 385
EXAMPLE 7 - 9 385
SOLUTION TO EXAMPLE 7 - 9 390
7.8 - APPLICATIONS OF THE NORMAL DISTRIBUTION 390
7.9 - PHENOMENOLOGICAL CONSIDERATIONS FOR
USING THE NORMAL DISTRIBUTION 391
PROBLEMS 392
REFERENCES 397
CHAPTER 8 - THE LOGNORMAL DISTRIBUTION 399
8.1 - LOGNORMAL DISTRIBUTION CHARACTERISTICS 399
EXAMPLE 8 - 1 406
SOLUTIONS TO EXAMPLE 8 - 1 407
8.2 - PROBABILITY PLOTTING OF THE LOGNORMAL
DISTRIBUTION 412
EXAMPLE 8 - 2 412
SOLUTIONS TO EXAMPLE 8 - 2 413
8.3 - LOGNORMAL RELIABILITY CHARACTERISTICS 416
EXAMPLE 8 - 3 418
SOLUTIONS TO EXAMPLE 8 - 3 418
EXAMPLE 8 - 4 420
SOLUTIONS TO EXAMPLE 8 - 4 420
8.4 - LOGNORMAL FAILURE RATE CHARACTERISTICS 421
EXAMPLE 8 - 5 424
SOLUTIONS TO EXAMPLE 8 - 5 424
8.5 - APPLICATIONS OF THE LOGNORMAL
DISTRIBUTION 425
8.6 - PHENOMENOLOGICAL CONSIDERATIONS FOR
USING THE LOGNORMAL DISTRIBUTION 425
PROBLEMS 426
REFERENCES 433
APPENDIX 8A - DERIVATION OF THE RELATIONSHIPS
AMONG THE PARAMETERS OF THE
LOGNORMAL DISTRIBUTION 434
APPENDIX 8B - FORMULAS TO CALCULATE THE MEAN,
STANDARD DEVIATION, MEDIAN, MODE,
AND THE kTH MOMENT ABOUT THE ORIGIN
OF THE LOGNORMAL DISTRIBUTION WHEN
THE LOGARITHMIC BASE IS 10 439
CHAPTER 9 - THE EXTREME VALUE DISTRIBUTION 443
9.1 - EXTREME VALUE DISTRIBUTION CHARACTERISTICS 443
9.2 - EXTREME VALUE PDF'S RELIABILITY CHARACTERISTICS 446
9.3 - EXTREME VALUE PDF'S FAILURE RATE CHARACTERISTICS 448
9.4 - ESTIMATION OF THE PARAMETERS OF THE
EVD BY MATCHING MOMENTS 448
EXAMPLE 9 - I 450
SOLUTIONS TO EXAMPLE 9 - 1 450
EXAMPLE 9 - 2 451
SOLUTIONS TO EXAMPLE 9 - 2 453
9.5 - ESTIMATION OF THE PARAMETERS OF THE
EVD BY PROBABILITY PLOTTING 454
EXAMPLE 9 - 3 459
SOLUTIONS TO EXAMPLE 9 - 3 459
EXAMPLE 9 - 4 459
SOLUTIONS TO EXAMPLE 9 - 4 461
9.6 - APPLICATIONS OF THE EVD 462
9.7 - PHENOMENOLOGICAL CONSIDERATIONS
FOR USING THE EVD 464
PROBLEMS 464
REFERENCES 466
CHAPTER 10 - THE RAYLEIGH DISTRIBUTION 469
10.1 - RAYLEIGH DISTRIBUTION CHARACTERISTICS 469
10.2 - RAYLEIGH RELIABILITY AND FAILURE RATE
CHARACTERISTICS 472
EXAMPLE 10 - 1 474
SOLUTIONS TO EXAMPLE 10 - 1 474
10.3 - ESTIMATION OF THE RAYLEIGH PDF'S PARAMETER 475
10.3.1 - MAXIMUM LIKELIHOOD ESTIMATE
OF THE RAYLEIGH PDF'S PARAMETER 475
10.3.2 - PROBABILITY PLOTTING METHOD 476
EXAMPLE 10 - 2 477
SOLUTIONS TO EXAMPLE 10 - 2 477
10.4 - APPLICATIONS OF THE RAYLEIGH
DISTRIBUTION 478
EXAMPLE 10 - 3 481
SOLUTION TO EXAMPLE 10 - 3 481
PROBLEMS 484
REFERENCES 486
CHAPTER 11 - THE UNIFORM DISTRIBUTION 487
11.1 - UNIFORM DISTRIBUTION CHARACTERISTICS 487
11.2 - UNIFORM RELIABILITY AND FAILURE RATE
CHARACTERISTICS 489
11.3 - ESTIMATION OF THE UNIFORM PDF'S PARAMETERS 490
11.3.1 - USING THE METHOD OF MATCHING
MOMENTS 490
11.3.2 - THE GRAPHICAL METHOD 492
EXAMPLE 11 - 1 492
SOLUTIONS TO EXAMPLE 11 - I 492
11.4 - APPLICATIONS OF THE UNIFORM DISTRIBUTION 496
11.4.1 - APPLICATION TO MONTE CARLO SIMULATION. 496
11.4.2 - BAYESIAN ESTIMATION 497
EXAMPLE 11 - 2 499
SOLUTIONS TO EXAMPLE 11 - 2 500
PROBLEMS 502
REFERENCES 504
CHAPTER 12 - EARLY, CHANCE, AND WEAR-OUT
RELIABILITY 505
12.1 - INTRODUCTION 505
12.2 - EARLY FAILURES AND THEIR RELIABILITY 506
EXAMPLE 12 - 1 508
SOLUTIONS TO EXAMPLE 12 - 1 509
12.3 - CHANCE FAILURES AND THEIR RELIABILITY 511
EXAMPLE 12 - 2 512
SOLUTIONS TO EXAMPLE 12 - 2 512
12.4 - WEAR-OUT FAILURES AND THEIR RELIABILITY 515
EXAMPLE 12 - 3 515
SOLUTIONS TO EXAMPLE 12 - 3 516
12.5 - RELIABILITY OF SUCCESSIVE MISSIONS IN
EARLY LIFE 516
12.6 - RELIABILITY OF SUCCESSIVE MISSIONS IN
USEFUL LIFE 523
12.7 - RELIABILITY OF SUCCESSIVE MISSIONS IN
WEAR-OUT LIFE 523
12.8 - IMPORTANCE OF UNIT CHECKOUT PRIOR TO
STARTING A MISSION 527
PROBLEMS 527
CHAPTER 13 - RELIABILITY OF UNITS WITH MULTIPLE
FAILURE MODES 531
13.1 - MIXED POPULATION MODEL 531
13.1.1 - OBJECTIVES 531
13.1.2 - MIXED POPULATION ANALYSIS 532
13.1.3 - PROBABILITY PAPER PLOTTING METHOD OF
SUBPOPULATION IDENTIFICATION 536
13.1.4 - APPLICATION OF THE METHODOLOGY 541
13.1.4.1 - GRAPHICAL ANALYSIS OF DATA USING
THREE SUBPOPULATIONS 541
13.1.4.2 - GRAPHICAL ANALYSIS OF DATA USING
TWO SUBPOPULATIONS 549
13.1.4.3 - DISCUSSION OF RESULTS 552
13.1.4.4 - APPLICATIONS OF PREVIOUS RESULTS 556
EXAMPLE 13 - 1 556
SOLUTIONS TO EXAMPLE 13 - 1 557
EXAMPLE 13 - 2 557
SOLUTIONS TO EXAMPLE 13 - 2 557
13.1.5 - DETERMINATION OF THE BURN-IN PERIOD 559
EXAMPLE 13 - 3 560
SOLUTIONS TO EXAMPLE 13 - 3 561
13.1.6 - CONCLUSIONS 565
13.2 - COMPETING FAILURE MODES MODEL 567
13.2.1 - COMPETING FAILURE MODES ANALYSIS 567
13.2.1.1 - FUNCTIONAL RELATIONSHIPS
BETWEEN NET AND CRUDE
PROBABILITIES 570
13.2.2 - ESTIMATION OF THE PARAMETERS OF THE
COMPETING FAILURE MODE MODEL 571
13.2.2.1 - MAXIMUM LIKELIHOOD ESTIMATES
USING TIME-TO-FAILURE DATA 571
13.2.2.2 - MAXIMUM LIKELIHOOD ESTIMATES
USING FAILURE FREQUENCIES 573
EXAMPLE 13 - 4 577
SOLUTIONS TO EXAMPLE 13 - 4 577
13.2.3 - COMPARISON WITH THE MIXED POPULATION
MODEL 579
PROBLEMS 579
REFERENCES 587
APPENDIX 13A - SOME RESULTS ABOUT THE FAILURE
RATE OF A MIXED POPULATION 588
CHAPTER 14 - RELIABILITY BATHTUB CURVE MODELS
AND THEIR QUANTIFICATION 597
14.1 - INTRODUCTION 597
14.2 - MODEL 1 597
EXAMPLE 14 - 1 598
SOLUTION TO EXAMPLE 14 - 1 601
14.3 - MODEL 2 603
EXAMPLE 14 - 2 610
SOLUTION TO EXAMPLE 14 - 2 610
14.4 - MODEL 3 610
EXAMPLE 14 - 3 616
SOLUTIONS TO EXAMPLE 14 - 3 616
14.5 - MODEL 4 621
EXAMPLE 14 - 4 627
SOLUTION TO EXAMPLE 14 - 4 627
14.6 - MODEL 5 628
EXAMPLE 14 - 5 634
SOLUTION TO EXAMPLE 14 - 5 634
PROBLEMS 639
REFERENCES 648
APPENDICES 651
APPENDIX A - RANK TABLES 654
APPENDIX B - STANDARDIZED NORMAL
DISTRIBUTION'S AREA TABLES 667
APPENDIX C - STANDARDIZED NORMAL
DISTRIBUTION'S ORDINATE VALUES
OR PROBABILITY DENSITIES 675
APPENDIX D - PERCENTAGE POINTS,
F DISTRIBUTION FOR F(F)=O.50 676
APPENDIX E - CRITICAL VALUES FOR
THE KOLMOGROV-SMIRNOV
GOODNESS-OF-FIT TEST 678
INDEX 679
ABOUT THE AUTHOR 687
CHAPTER I - RELIABILITY OF SERIES SYSTEMS 1
1.1 - N UNIT RELIABILITYWISE SERIES SYSTEM 1
1.2 - EXPONENTIAL UNITS 2
1.3 - WEIBULLIAN UNITS 3
EXAMPLE 1-1 4
SOLUTIONS TO EXAMPLE 1-1 8
EXAMPLE 1-2 9
SOLUTIONS TO EXAMPLE 1-2 10
PROBLEMS 11
APPENDIX 1A - DERIVATION OF THE EQUATIONS FOR
CASES 2, 4, 6 AND 7 OF TABLE 1.1 13
CHAPTER 2 - RELIABILITY OF PARALLEL SYSTEMS 19
2.1 - N UNIT RELIABILITYWISE PARALLEL SYSTEM 19
2.2 - EXPONENTIAL PARALLEL UNITS 20
2.3 - WEIBULLIAN UNITS 22
EXAMPLE 2-1 26
SOLUTIONS TO EXAMPLE 2-1 26
EXAMPLE 2-2 27
SOLUTIONS TO EXAMPLE 2-2 27
EXAMPLE 2-3 28
SOLUTION TO EXAMPLE 2-3 31
PROBLEMS 31
APPENDIX 2A - DERIVATION OF THE EQUATIONS IN
TABLE 2.1 FOR CASES 2 AND 4 36
CHAPTER 3 - RELIABILITY OF STANDBY SYSTEMS 41
3.1 - WHAT IS A STANDBY SYSTEM? 41
3.2 - RELIABILITY OF A TWO-UNIT STANDBY SYSTEM 41
EXAMPLE 3-1 47
SOLUTION TO EXAMPLE 3-1 48
EXAMPLE 3-2 48
SOLUTIONS TO EXAMPLE 3-2 50
3.3 - COMPLEX STANDBY SYSTEMS 51
EXAMPLE 3-3 52
SOLUTIONS TO EXAMPLE 3-3 54
EXAMPLE 3-4 56
SOLUTIONS TO EXAMPLE 3-4 59
EXAMPLE 3-5 68
SOLUTION TO EXAMPLE 3-5 68
PROBLEMS 72
CHAPTER 4 - APPLICATIONS OF THE BINOMIAL AND POISSON
DISTRIBUTIONS TO SYSTEM RELIABILITY
PREDICTION 83
4.1 - THE BINOMIAL DISTRIBUTION 83
4.1.1 - IDENTICAL UNITS 83
4.1.2 - DIFFERENT UNITS 84
EXAMPLE 4-1 85
SOLUTION TO EXAMPLE 4-1 85
EXAMPLE 4-2 86
SOLUTION TO EXAMPLE 4-2 86
4.2 - THE POISSON DISTRIBUTION 87
EXAMPLE 4-3 88
SOLUTIONS TO EXAMPLE 4-3 89
EXAMPLE 4-4 90
SOLUTION TO EXAMPLE 4-4 90
EXAMPLE 4-5 91
SOLUTIONS TO EXAMPLE 4-5 91
PROBLEMS 93
CHAPTER 5 - METHODS OF RELIABILITY PREDICTION
FOR COMPLEX SYSTEMS 95
5.1 - BAYES' THEOREM METHOD 95
EXAMPLE 5-1 96
SOLUTIONS TO EXAMPLE 5-1 96
EXAMPLE 5-2 98
SOLUTIONS TO EXAMPLE 5-2 99
EXAMPLE 5-3 100
SOLUTIONS TO EXAMPLE 5-3 100
5.2 - BOOLEAN TRUTH TABLE METHOD 103
5.3 - PROBABILITY MAPS METHOD 104
5.4 - LOGIC DIAGRAMS METHOD 107
EXAMPLE 5-4 109
SOLUTIONS TO EXAMPLE 5-4 110
PROBLEMS 119
REFERENCES 122
CHAPTER 6 - RELIABILITY OF SYSTEMS WITH MULTIMODE
FUNCTION AND LOGIC 123
6.1 - RELIABILITY PREDICTION METHODOLOGY 123
EXAMPLE 6-1 125
SOLUTION TO EXAMPLE 6-1 125
EXAMPLE 6-2 127
SOLUTION TO EXAMPLE 6-2 128
EXAMPLE 6-3 130
SOLUTION TO EXAMPLE 6-3 131
PROBLEMS 133
CHAPTER 7 - RELIABILITY OF SYSTEMS OPERATING AT
VARIOUS LEVELS OF STRESS DURING A MISSION 135
7.1 - FOR THE EXPONENTIAL CASE 135
7.2 - FOR THE WEIBULL CASE 136
7.3 - RELIABILITY OF CYCLICAL OPERATIONS 139
PROBLEMS 140
CHAPTER 8 - LOAD-SHARING RELIABILITY 143
8.1 - RELIABILITY OF TWO PARALLEL
LOADSHARING SWITCHES 143
8.2 - RELIABILITY OF THREE LOAD-SHARING CYCLIC
SWITCHES ARRANGED PHYSICALLY IN PARALLEL 148
8.2.1 - THREE UNEQUAL CYCLIC SWITCHES 148
8.2.2 - THREE EQUAL CYCLIC SWITCHES 156
8.3 - RELIABILITY OF TWO LOAD-SHARING WEIBULLIAN
UNITS ARRANGED RELIABILITYWISE IN PARALLEL 156
EXAMPLE 8-1 164
SOLUTIONS TO EXAMPLE 8-1 164
PROBLEMS 168
REFERENCE 171
APPENDIX 8A - THE DERIVATION OF MINER'S RULE 173
CHAPTER 9 - RELIABILITY OF STATIC SWITCHES 175
9.1 - OBJECTIVES 175
9.2 - SINGLE-SWITCH RELIABILITY 175
9.2.1 - NORMALLY OPEN SWITCH WHOSE FUNCTION
IS TO CLOSE ON COMMAND 175
9.2.2 - SPECIAL CASES 178
9.2.3 - NORMALLY CLOSED SWITCH WHOSE FUNCTION
IS TO OPEN ON COMMAND 178
9.2.4 - SPECIAL CASES 180
9.3 - STATIC SWITCHES RELIABILITYWISE IN PARALLEL 181
9.3.1 - NORMALLY OPEN SWITCHES 181
9.3.2 - NORMALLY CLOSED SWITCHES 182
PROBLEMS 183
CHAPTER 10 - RELIABILITY OF CYCLIC SWITCHES 185
10.1 - OBJECTIVES 185
10.2 - SINGLE CYCLIC SWITCH RELIABILITY 185
10.3 - UNRELIABILITY OF CYCLIC SWITCHES IN FAILING
OPEN OR FAILING CLOSED MODE 188
10.4 - CYCLIC SWITCHES PHYSICALLY IN PARALLEL 190
10.4.1 - SPECIAL CASES 191
10.5 - CYCLIC SWITCHES PHYSICALLY IN SERIES 192
10.5.1 - SPECIAL CASES 193
10.6 - COMPLEX SYSTEMS WITH CYCLICALLY
FUNCTIONING UNITS 194
EXAMPLE 10-1 194
SOLUTIONS TO EXAMPLE 10-1 198
EXAMPLE 10-2 200
SOLUTIONS TO EXAMPLE 10-2 200
PROBLEMS 203
CHAPTER 11 - FAULT TREE ANALYSIS 207
11.1 - INTRODUCTION 207
11.2 - CONSTRUCTION OF THE FAULT TREE 208
11.2.1 - THE ELEMENTS OF THE FAULT TREE 208
11.2.1.1 - GATE SYMBOLS 208
11.2.1.2 - EVENT SYMBOLS 214
11.2.2 - FAULT TREE CONSTRUCTION 214
11.2.2.1 - SYSTEM AND TOP EVENT DEFINITIONS 214
11.2.2.2 - CONSTRUCTION OF THE FAULT TREE 217
EXAMPLE 11-1 217
SOLUTION TO EXAMPLE 11-1 218
EXAMPLE 11-2 218
SOLUTION TO EXAMPLE 11-2 218
11.3 - QUALITATIVE EVALUATION OF THE FAULT TREE 222
11.3.1 - MINIMAL CUT SETS AND MINIMAL PATH SETS 222
11.3.2 - MINIMAL CUT SET ALGORITHMS 222
11.3.2.1 - ALGORITHM 1: MOCUS 222
EXAMPLE 11-3 224
SOLUTION TO EXAMPLE 11-3 224
EXAMPLE 11-4 226
SOLUTION TO EXAMPLE 11-4 226
11.3.2.2 - ALGORITHM 2 230
EXAMPLE 11-5 230
SOLUTION TO EXAMPLE 11-5 230
11.3.3 - DUAL TREES AND THE MINIMAL PATH SETS 231
EXAMPLE 11-6 231
SOLUTION TO EXAMPLE 11-6 232
11.4 - QUANTITATIVE EVALUATION OF THE FAULT TREE 234
11.4.1 - PROBABILITY EVALUATION BY THE
INCLUSION-EXCLUSION PRINCIPLE 234
11.4.1.1 - EVALUATION FROM THE MINIMAL
CUT SETS 234
EXAMPLE 11-7 236
SOLUTION TO EXAMPLE 11-7 236
11.4.1.2 - EVALUATION FROM THE MINIMAL
PATH SETS 237
EXAMPLE 11-8 238
SOLUTION TO EXAMPLE 11-8 239
11.4.2 - PROBABILITY EVALUATION USING THE
STRUCTURE FUNCTION 239
11.4.2.1 - THE STRUCTURE FUNCTION 239
11.4.2.2 - THE STRUCTURE FUNCTION FOR
SIMPLE FAULT TREES 240
EXAMPLE 11-9 241
SOLUTION TO EXAMPLE 11-9 241
11.4.2.3 - PROBABILITY EVALUATION USING
THE STRUCTURE FUNCTION 242
EXAMPLE 11-10 242
SOLUTION TO EXAMPLE 11-10 243
11.4.2.4 - THE STRUCTURE FUNCTION
EXPRESSION IN TERMS OF THE
MINIMAL CUT SETS OR PATH SETS 244
EXAMPLE 11-11 244
SOLUTION TO EXAMPLE 11-11 245
PROBLEMS 245
REFERENCES 247
CHAPTER 12 - SYSTEM RELIABILITY PREDICTION AND
TARGET RELIABILITY 249
12.1 - TARGET RELIABILITY 249
12.2 - TARGET RELIABILITY ALLOCATION 250
12.3 - RELIABILITY PREDICTION METHODOLOGY 251
EXAMPLE 12-1 272
SOLUTIONS TO EXAMPLE 12-1 272
EXAMPLE 12-2 272
SOLUTIONS TO EXAMPLE 12-2 272
EXAMPLE 12-3 278
SOLUTIONS TO EXAMPLE 12-3 284
EXAMPLE 12-4 301
SOLUTIONS TO EXAMPLE 12-4 301
EXAMPLE 12-5 307
SOLUTIONS TO EXAMPLE 12-5 307
PROBLEMS 321
CHAPTER 13 - LIMIT LAW OF THE TIME-TO-FAILURE
DISTRIBUTION OF A COMPLEX SYSTEM:
DRENICK'S THEOREM 341
13.1 - DRENICK'S THEOREM 341
13.2 - PROOF OF DRENICK'S THEOREM 345
REFERENCES 349
CHAPTER 14 - RELIABILITY OF COMPONENTS WITH A
POLICY OF REPLACING THOSE THAT FAIL
BY A PRESCRIBED OPERATING TIME 351
14.1 - METHODOLOGY 351
EXAMPLE 14-1 353
EXAMPLE 14-2 358
PROBLEMS 361
CHAPTER 15 - RELIABILITY ALLOCATION:
APPORTIONMENT 363
15.1- INTRODUCTION 363
15.2 - WHY RELIABILITY ALLOCATION? 364
15.3 - HOW AND WHEN CAN RELIABILITY ALLOCATION
BE BEST USED? 365
15.4 - RELIABILITY ALLOCATION: APPORTIONMENT
METHODS 367
15.4.1 - BASIC METHOD FOR SERIES SYSTEMS 367
EXAMPLE 15-1 370
SOLUTION TO EXAMPLE 15-1 370
EXAMPLE 15-2 371
SOLUTION TO EXAMPLE 15 - 2 371
EXAMPLE 15-3 372
SOLUTIONS TO EXAMPLE 15-3 372
15.5 - AGREE ALLOCATION METHOD 374
15.5.1 - DESCRIPTION OF METHOD 374
15.5.2 - MATHEMATICAL MODEL FOR THE METHOD 375
15.5.3 - APPLICATION TO THE SERIES SYSTEM 375
15.5.4 - APPLICATION TO A PARALLEL SYSTEM 378
15.6 - KARMIOL METHOD USING PRODUCT OF
EFFECTS FACTORS 378
15.6.1 - DESCRIPTION OF THE METHOD 378
15.6.2 - MATHEMATICAL MODEL FOR THE METHOD 379
15.6.3 - APPLICATION TO A SERIES SYSTEM 382
15.6.4 - APPLICATION TO A PARALLEL SYSTEM 382
15.7 - KARMIOL METHOD UTILIZING SUM OF
WEIGHTING FACTORS 384
15.8 - DETERMINATION OF THE WEIGHTING FACTORS FOR
UNRELIABILITY AND SUBSEQUENTLY FOR
RELIABILITY APPORTIONMENT 387
15.8.1 - COMPLEXITY FACTOR 387
15.8.2 - STATE OF THE ART FACTOR 387
15.8.3 - OPERATIONAL PROFILE FACTOR 387
15.8.4 - CRITICALITY FACTOR 387
15.9 - THE BRACHA METHOD OF RELIABILITY
ALLOCATION 387
15.9.1 - DESCRIPTION OF METHOD 387
15.9.2 - MATHEMATICAL MODEL FOR THE METHOD 388
15.9.2.1 - INDEX OF THE STATE OF
THE ART 390
15.9.2.2 - INDEX OF COMPLEXITY 390
15.9.2.3 - INDEX OF ENVIRONMENT 391
15.9.2.4 - INDEX OF OPERATING TIME 391
15.9.2.5 - GENERAL PROCEDURE 391
15-9.3 - APPLICATION TO A SERIES SYSTEM 392
15.9.4 - APPLICATION TO A PARALLEL SYSTEM 394
15.9.5 - APPLICATION TO AN INACTIVE
REDUNDANT (STANDBY) SYSTEM 395
15.9.6 - MORE COMPLEX SYSTEM RELIABILITY
ALLOCATION 395
PROBLEMS 395
REFERENCES 396
CHAPTER 16 - RELIABILITY GROWTH 401
16.1 - INTRODUCTION 401
16.2 - RELIABILITY GROWTH MATH MODELS 406
16.2.1 - GOMPERTZ MODEL 406
EXAMPLE 16-1 408
SOLUTIONS TO EXAMPLE 16-1 408
16.2.2 - LLOYD-LIPOW MODEL 409
EXAMPLE 16-2 412
SOLUTIONS TO EXAMPLE 16-2 412
16.3 - METHODS TO ESTIMATE RELIABILITY GROWTH
FROM ATTRIBUTE DATA 415
METHOD 1 415
EXAMPLE 16-3 415
SOLUTIONS TO EXAMPLE 16-3 415
METHOD 2 418
EXAMPLE 16-4 419
SOLUTIONS TO EXAMPLE 16-4 419
16.4 - RELIABILITY GROWTH MODELS THAT GIVE S-SHAPED
CURVES 423
16.4.1 - S-SHAPED RELIABILITY GROWTH CURVES 425
16.4.1.1 - THE GOMPERTZ CURVE 425
16.4.1.2 - THE LOGISTIC RELIABILITY
GROWTH CURVE 426
EXAMPLE 16-5 426
SOLUTIONS TO EXAMPLE 16-5 430
16.4.2 - MODIFIED GOMPERTZ RELIABILITY
GROWTH CURVE 432
EXAMPLE 16-6 433
SOLUTION TO EXAMPLE 16-6 433
16.5 - MTBF GROWTH AND FAILURE RATE
IMPROVEMENT CURVES 434
a
16.5.1 - CURRENT OR INSTANTANEOUS l AND m 436
EXAMPLE 16-7 438
SOLUTION TO EXAMPLE 16-7 438
EXAMPLE 16-8 440
SOLUTIONS TO EXAMPLE 16-8 442
16.6 - THE AMSAA RELIABILITY GROWTH MODEL 443
16.6.1 INTRODUCTION 443
16.6.2 - GRAPHICAL ESTIMATION OF PARAMETERS 445
EXAMPLE 16-9 446
SOLUTION TO EXAMPLE 16-9 446
16.6.3 - STATISTICAL ESTIMATION OF PARAMETERS 446
16.6.3.1 - TIME TERMINATED TEST 449
16.6.3.2 - FAILURE TERMINATED TEST 449
EXAMPLE 16-10 450
SOLUTIONS TO EXAMPLE 16-10 450
EXAMPLE 16-11 452
SOLUTIONS TO EXAMPLE 16-11 452
PROBLEMS 456
REFERENCES 465
APPENDIX 16A DERIVATION OF EQUATIONS (16.2), (16.3)
AND (16.4) 466
APPENDIX 16B COMPUTER PROGRAM AND
OUTPUT FOR EXAMPLE 164 469
APPENDIX 16C RELATIONSHIP OF EQUATION (16.32)
AND THE WEIBULL FAILURE RATE 471
CHAPTER 17 - FAILURE MODES, EFFECTS, AND
CRITICALITY ANALYSIS 473
17.1 - INTRODUCTION 473
17.2 - METHOD I 473
17.2.1 - SYSTEMATIC TECHNIQUE 474
17.2.2 - COMPONENT FAILURE MODES ANALYSIS 474
17.2.2.1 - RESPONSIBILITIES OF VARIOUS
ENGINEERS IN CONDUCTING
A FAMECA 476
17.2.3 - REQUIREMENTS FOR SPECIAL HANDLING
AND TESTING OF CRITICAL COMPONENTS 486
17.3 - METHOD 2 487
17.3.1 - THE FAILURE MODES AND EFFECTS
ANALYSIS 487
17.3.2 - CRITICALITY ANALYSIS AND RANKING 500
PROBLEMS 505
17.3 - REFERENCES 505
APPENDICES 507
APPENDIX A - RANK TABLES 508
APPENDIX B - STANDARDIZED NORMAL
DISTRIBUTION'S AREA TABLES 522
APPENDIX C - STANDARDIZED NORMAL
DISTRIBUTION'S ORDINATE VALUES,
OR PROBABILITY DENSITIES 530
APPENDIX D - PERCENTAGE POINTS,
F DISTRIBUTION, FOR F(F) = 0.50 531
APPENDIX E - CRITICAL VALUES FOR
THE KOLMOGOROV-SMIRNOV
GOODNESS-OF- PIT TEST 533
INDEX 535
ABOUT THE AUTHOR 539
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Philip Koopman: koopman@cmu.edu