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