Notes on:

Reliability Engineering Handbook

Kececioglu

     

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).


Volume 1 Contents:

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

Volume 2 Contents:

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