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Bibliographic Details
Main Authors: Meeker, William Q. (Author), Escobar, Luis A. (Author)
Format: Book
Language:English
Published: New York, NY [u.a.] Wiley 1998
Series:Wiley series in probability and statistics : Applied probability and statistics section
A Wiley-interscience publication
Subjects:
Reliabilität
Reliability (Engineering) > Statistical methods
Links:http://www.loc.gov/catdir/description/wiley031/97039270.html
http://www.loc.gov/catdir/toc/onix01/97039270.html
http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008452651&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:XXII, 680 S. zahlr. graph. Darst.
ISBN:0471143286
Staff View

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Record in the Search Index

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adam_text IMAGE 1 STATISTICAL METHODS FOR RELIABILITY DATA WILLIAM Q. MEEKER DEPARTMENT OF STATISTICS IOWA STATE UNIVERSITY LUIS A. ESCOBAR DEPARTMENT OF EXPENMENTAL STATISTICS LOUISIANA STATE UNIVERSITY A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC. NEW YORK * CHICHESTER * WEINHEIM * BRISBANE * SINGAPORE * TORONTO IMAGE 2 CONTENTS PREFACE ACKNOWLEDGMENTS 1. RELIABILITY CONCEPTS AND RELIABILITY DATA 1.1. INTRODUCTION, 2 1.2. EXAMPLES OF RELIABILITY DATA, 4 1.3. GENERAL MODELS FOR RELIABILITY DATA, 15 1.4. REPAIRABLE SYSTEMS AND NONREPAIRABLE UNITS, 19 1.5. STRATEGY FOR DATA COLLECTION, MODELING, AND ANALYSIS, 20 2. MODELS, CENSORING, AND LIKELIHOOD FOR FAILURE-TIME DATA 2.1. MODELS FOR CONTINUOUS FAILURE-TIME PROCESSES, 27 2.2. MODELS FOR DISCRETE DATA FROM A CONTINUOUS PROCESS, 32 2.3. CENSORING, 34 2.4. LIKELIHOOD, 36 3. NONPARAMETRIC ESTIMATION 3.1. INTRODUCTION, 47 3.2. ESTIMATION FROM SINGLY CENSORED INTERVAL DATA, 47 3.3. BASIC IDEAS OF STATISTICAL INFERENCE, 48 3.4. CONNDENCE INTERVALS FROM COMPLETE OR SINGLY CENSORED DATA, 50 3.5. ESTIMATION FROM MULTIPLY CENSORED DATA, 52 3.6. POINTWISE CONFIDENCE INTERVALS FROM MULTIPLY CENSORED DATA, 54 3.7. ESTIMATION FROM MULTIPLY CENSORED DATA WITH EXACT FAILURES, 57 IMAGE 3 VIU CONTENTS 3.8. SIMULTANEOUS CONFIDENCE BANDS, 60 3.9. UNCERTAIN CENSORING TIMES, 64 3.10. ARBITRARY CENSORING, 65 4. LOCATION-SCALE-BASED PARAMETRIC DISTRIBUTIONS 75 4.1. INTRODUCTION, 76 4.2. QUANTITIES OF INTEREST IN RELIABILITY APPLICATIONS, 76 4.3. LOCATION-SCALE AND LOG-LOCATION-SCALE DISTRIBUTIONS, 78 4.4. EXPONENTIAL DISTRIBUTION, 79 4.5. NORMAL DISTRIBUTION, 80 4.6. LOGNORMAL DISTRIBUTION, 82 4.7. SMALLEST EXTREME VALUE DISTRIBUTION, 83 4.8. WEIBULL DISTRIBUTION, 85 4.9. LARGEST EXTREME VALUE DISTRIBUTION, 86 4.10. LOGISTIC DISTRIBUTION, 88 4.11. LOGLOGISTIC DISTRIBUTION, 89 4.12. PARAMETERS AND PARAMETERIZATION, 90 4.13. GENERATING PSEUDORANDOM OBSERVATIONS FROM A SPECIFIED DISTRIBUTION, 91 5. OTHER PARAMETRIC DISTRIBUTIONS 97 5.1. INTRODUCTION, 97 5.2. GAMMA DISTRIBUTION, 98 5.3. GENERALIZED GAMMA DISTRIBUTION, 99 5.4. EXTENDED GENERALIZED GAMMA DISTRIBUTION, 101 5.5. GENERALIZED F DISTRIBUTION, 102 5.6. INVERSE GAUSSIAN DISTRIBUTION, 103 5.7. BIRNBAUM-SAUNDERS DISTRIBUTION, 105 5.8. GOMPERTZ-MAKEHAM DISTRIBUTION, 108 5.9. COMPARISON OF SPREAD AND SKEWNESS PARAMETERS, 110 5.10. DISTRIBUTIONS WITH A THRESHOLD PARAMETER, 111 5.11. GENERALIZED THRESHOLD-SCALE DISTRIBUTION, 113 5.12. OTHER METHODS OF DERIVING FAILURE-TIME DISTRIBUTIONS, 115 6. PROBABILITY PLOTTING 122 6.1. INTRODUCTION, 122 6.2. LINEARIZING LOCATION-SCALE-BASED DISTRIBUTIONS, 123 6.3. GRAPHICAL GOODNESS OF FIT, 127 IMAGE 4 IX 6.4. PROBABILITY PLOTTING POSITIONS, 128 6.5. PROBABILITY PLOTS WITH SPECIFIED SHAPE PARAMETERS, 136 6.6. NOTES ON THE APPLICATION OF PROBABILITY PLOTTING, 141 7. PARAMETRIC LIKELIHOOD FITTING CONCEPTS: EXPONENTIAL DISTRIBUTION 153 7.1. INTRODUCTION, 153 7.2. PARAMETRIC LIKELIHOOD, 155 7.3. CONFIDENCE INTERVALS FOR 0, 159 7.4. CONFIDENCE INTERVALS FOR FUNCTIONS OF 9, 163 7.5. COMPARISON OF CONFIDENCE INTERVAL PROCEDURES, 164 7.6. LIKELIHOOD FOR EXACT FAILURE TIMES, 165 7.7. DATA ANALYSIS WITH NO FAILURES, 167 8. MAXIMUM LIKELIHOOD FOR LOG-LOCATION-SCALE DISTRIBUTIONS 173 8.1. INTRODUCTION, 173 8.2. LIKELIHOOD, 174 8.3. LIKELIHOOD CONFIDENCE REGIONS AND INTERVALS, 177 8.4. NORMAL-APPROXIMATION CONFIDENCE INTERVALS, 186 8.5. ESTIMATION WITH GIVEN A, 192 9. BOOTSTRAP CONFIDENCE INTERVALS 204 9.1. INTRODUCTION, 204 9.2. BOOTSTRAP SAMPLING, 205 9.3. EXPONENTIAL DISTRIBUTION CONFIDENCE INTERVALS, 208 9.4. WEIBULL, LOGNORMAL, AND LOGLOGISTIC DISTRIBUTION CONFIDENCE INTERVALS, 212 9.5. NONPARAMETRIC BOOTSTRAP CONFIDENCE INTERVALS, 217 9.6. PERCENTILE BOOTSTRAP METHOD, 226 10. PLANNING LIFE TESTS 231 10.1. INTRODUCTION, 232 10.2. APPROXIMATE VARIANCE OF ML ESTIMATORS, 236 10.3. SAMPLE SIZE FOR UNRESTRICTED FUNCTIONS, 238 10.4. SAMPLE SIZE FOR POSITIVE FUNCTIONS, 239 10.5. SAMPLE SIZES FOR LOG-LOCATION-SCALE DISTRIBUTIONS WITH CENSORING, 240 IMAGE 5 X CONTENTS 10.6. TEST PLANS TO DEMONSTRATE CONFORMANCE WITH A RELIABILITY STANDARD, 247 10.7. SOME EXTENSIONS, 250 11. PARAMETRIC MAXIMUM LIKELIHOOD: OTHER MODELS 254 11.1. INTRODUCTION, 255 11.2. FITTING THE GAMMA DISTRIBUTION, 256 11.3. FITTING THE EXTENDED GENERALIZED GAMMA DISTRIBUTION, 257 11.4. FITTING THE BISA AND IGAU DISTRIBUTIONS, 260 11.5. FITTING A LIMITED FAILURE POPULATION MODEL, 262 11.6. TRUNCATED DATA AND TRUNCATED DISTRIBUTIONS, 266 11.7. FITTING DISTRIBUTIONS THAT HAVE A THRESHOLD PARAMETER, 273 12. PREDICTION OF FUTURE RANDOM QUANTITIES 289 12.1. INTRODUCTION, 290 12.2. PROBABILITY PREDICTION INTERVALS (0 GIVEN), 292 12.3. STATISTICAL PREDICTION INTERVAL (0 ESTIMATED), 293 12.4. THE (APPROXIMATE) PIVOTAL METHOD FOR PREDICTION INTERVALS, 296 12.5. PREDICTION IN SIMPLE CASES, 298 12.6. CALIBRATING NAIVE STATISTICAL PREDICTION BOUNDS, 300 12.7. PREDICTION OF FUTURE FAILURES FROM A SINGLE GROUP OF UNITS IN THE FIELD, 304 12.8. PREDICTION OF FUTURE FAILURES FROM MULTIPLE GROUPS OF UNITS WITH STAGGERED ENTRY INTO THE FIELD, 308 13. DEGRADATION DATA, MODELS, AND DATA ANALYSIS 316 13.1. INTRODUCTION, 317 13.2. MODELS FOR DEGRADATION DATA, 317 13.3. ESTIMATION OF DEGRADATION MODEL PARAMETERS, 326 13.4. MODELS RELATING DEGRADATION AND FAILURE, 327 13.5. EVALUATION OFF(R), 328 13.6. ESTIMATION OFF(0, 331 13.7. BOOTSTRAP CONFIDENCE INTERVALS, 332 13.8. COMPARISON WITH TRADITIONAL FAILURE-TIME ANALYSES, 333 13.9. APPROXIMATE DEGRADATION ANALYSIS, 336 14. INTRODUCTION TO THE USE OF BAYESIAN METHODS FOR RELIABILITY DATA 343 14.1. INTRODUCTION, 344 14.2. USING BAYES S RULE TO UPDATE PRIOR INFORMATION, 344 IMAGE 6 CONTENTS XI 14.3. PRIOR INFORMATION AND DISTRIBUTIONS, 345 14.4. NUMERICAL METHODS FOR COMBINING PRIOR INFORMATION WITH A LIKELIHOOD, 350 14.5. USING THE POSTERIOR DISTRIBUTION FOR ESTIMATION, 356 14.6. BAYESIAN PREDICTION, 358 14.7. PRACTICAL ISSUES IN THE APPLICATION OF BAYESIAN METHODS, 362 15. SYSTEM RELIABILITY CONCEPTS AND METHODS 369 15.1. INTRODUCTION, 369 15.2. SYSTEM STRUCTURES AND SYSTEM FAILURE PROBABILITY, 370 15.3. ESTIMATING SYSTEM RELIABILITY FROM COMPONENT DATA, 380 15.4. ESTIMATING RELIABILITY WITH TWO OR MORE CAUSES OF FAILURE, 382 15.5. OTHER TOPICS IN SYSTEM RELIABILITY, 386 16. ANALYSIS OF REPAIRABLE SYSTEM AND OTHER RECURRENCE DATA 393 16.1. INTRODUCTION, 394 16.2. NONPARAMETRIC ESTIMATION OF THE MCF, 396 16.3. NONPARAMETRIC COMPARISON OF TWO SAMPLES OF RECURRENCE DATA, 404 16.4. PARAMETRIC MODELS FOR RECURRENCE DATA, 406 16.5. TOOLS FOR CHECKING POINT-PROCESS ASSUMPTIONS, 409 16.6. MAXIMUM LIKELIHOOD FITTING OF POISSON PROCESS, 412 16.7. GENERATING PSEUDORANDOM REALIZATIONS FROM AN NHPP PROCESS, 417 16.8. SOFTWARE RELIABILITY, 419 17. FAILURE-TIME REGRESSION ANALYSIS 427 17.1. INTRODUCTION, 428 17.2. FAILURE-TIME REGRESSION MODELS, 429 17.3. SIMPLE LINEAR REGRESSION MODELS, 432 17.4. STANDARD ERRORS AND CONFIDENCE INTERVALS FOR REGRESSION MODELS, 435 17.5. REGRESSION MODEL WITH QUADRATIC JU, AND NONCONSTANT A, 439 17.6. CHECKING MODEL ASSUMPTIONS, 443 17.7. MODELS WITH TWO OR MORE EXPLANATORY VARIABLES, 447 17.8. PRODUCT COMPARISON: AN INDICATOR-VARIABLE REGRESSION MODEL, 450 17.9. THE PROPORTIONAL HAZARDS FAILURE-TIME MODEL, 455 17.10. GENERAL TIME TRANSFORMATION FUNCTIONS, 459 IMAGE 7 XII CONTENTS 18. ACCELERATED TEST MODELS 466 18.1. INTRODUCTION, 466 18.2. USE-RATE ACCELERATION, 470 18.3. TEMPERATURE ACCELERATION, 471 18.4. VOLTAGE AND VOLTAGE-STRESS ACCELERATION, 479 18.5. ACCELERATION MODELS WITH MORE THAN ONE ACCELERATING VARIABLE, 484 18.6. GUIDELINES FOR THE USE OF ACCELERATION MODELS, 487 19. ACCELERATED LIFE TESTS 493 19.1. INTRODUCTION, 493 19.2. ANALYSIS OF SINGLE-VARIABLE ALT DATA, 495 19.3. FURTHER EXAMPLES, 504 19.4. SOME PRACTICAL SUGGESTIONS FOR DRAWING CONCLUSIONS FROM ALT DATA, 515 19.5. OTHER KINDS OF ACCELERATED TESTS, 517 19.6. POTENTIAL PITFALLS OF ACCELERATED LIFE TESTING, 522 20. PFENNING ACCELERATED LIFE TESTS 534 20.1. INTRODUCTION, 535 20.2. EVALUATION OF TEST PLANS, 538 20.3. PLANNING SINGLE-VARIABLE ALT EXPERIMENTS, 540 20.4. PLANNING TWO-VARIABLE ALT EXPERIMENTS, 547 20.5. PLANNING ALT EXPERIMENTS WITH MORE THAN TWO EXPERIMENTAL VARIABLES, 558 21. ACCELERATED DEGRADATION TESTS 563 21.1. INTRODUCTION, 564 21.2. MODELS FOR ACCELERATED DEGRADATION TEST DATA, 565 21.3. ESTIMATING ACCELERATED DEGRADATION TEST MODEL PARAMETERS, 566 21.4. ESTIMATION OF FAILURE PROBABILITIES, DISTRIBUTION QUANTILES, AND OTHER FUNCTIONS OF MODEL PARAMETERS, 567 21.5. CONFIDENCE INTERVALS BASED ON BOOTSTRAP SAMPLES, 568 21.6. COMPARISON WITH TRADITIONAL ACCELERATED LIFE TEST METHODS, 569 21.7. APPROXIMATE ACCELERATED DEGRADATION ANALYSIS, 574 22. CASE STUDIES AND FURTHER APPLICATIONS 582 22.1. DANGERS OF CENSORING IN A MIXED POPULATION, 583 22.2. USING PRIOR INFORMATION IN ACCELERATED TESTING, 586 IMAGE 8 CONTENTS XLLL 22.3. AN LFP/COMPETING RISK MODEL, 590 22.4. FATIGUE-LIMIT REGRESSION MODEL, 593 22.5. PLANNING ACCELERATED DEGRADATION TESTS, 597 EPILOGUE 602 APPENDIX A. NOTATION AND ACRONYMS 609 APPENDIX B. SOME RESULTS FROM STATISTICAL THEORY 617 B. 1. CDFS AND PDFS OF FUNCTIONS OF RANDOM VARIABLES, 617 B.2. STATISTICAL ERROR PROPAGATION-THE DELTA METHOD, 619 B.3. LIKELIHOOD AND FISHER INFORMATION MATRICES, 621 B.4. REGULARITY CONDITIONS, 621 B.5. CONVERGENCE IN DISTRIBUTION, 623 B.6. OUTLINE OF GENERAL ML THEORY, 625 APPENDIX C. TABLES 629 REFERENCES 645 AUTHOR INDEX 665 SUBJECT INDEX 671
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series2 Wiley series in probability and statistics : Applied probability and statistics section
A Wiley-interscience publication
spellingShingle Meeker, William Q.
Escobar, Luis A.
Statistical methods for reliability data
Reliabilität
Reliability (Engineering) -- Statistical methods
Reliabilität (DE-588)4213628-3 gnd
subject_GND (DE-588)4213628-3
title Statistical methods for reliability data
title_auth Statistical methods for reliability data
title_exact_search Statistical methods for reliability data
title_full Statistical methods for reliability data William Q. Meeker ; Luis A. Escobar
title_fullStr Statistical methods for reliability data William Q. Meeker ; Luis A. Escobar
title_full_unstemmed Statistical methods for reliability data William Q. Meeker ; Luis A. Escobar
title_short Statistical methods for reliability data
title_sort statistical methods for reliability data
topic Reliabilität
Reliability (Engineering) -- Statistical methods
Reliabilität (DE-588)4213628-3 gnd
topic_facet Reliabilität
Reliability (Engineering) -- Statistical methods
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