Statistical methods for reliability data:
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| Main Authors: | , |
|---|---|
| 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: | |
| Online Access: | Publisher description Table of Contents Inhaltsverzeichnis |
| Physical Description: | XXII, 680 S. zahlr. graph. Darst. |
| ISBN: | 0471143286 |
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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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| id | DE-604.BV012456301 |
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| indexdate | 2024-07-09T18:27:53Z |
| institution | BVB |
| isbn | 0471143286 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008452651 |
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| physical | XXII, 680 S. zahlr. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
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| publisher | Wiley |
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| series2 | Wiley series in probability and statistics : Applied probability and statistics section A Wiley-interscience publication |
| spelling | Meeker, William Q. Verfasser aut Statistical methods for reliability data William Q. Meeker ; Luis A. Escobar New York, NY [u.a.] Wiley 1998 XXII, 680 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics : Applied probability and statistics section A Wiley-interscience publication Reliabilität Reliability (Engineering) -- Statistical methods Reliabilität (DE-588)4213628-3 gnd rswk-swf Reliabilität (DE-588)4213628-3 s DE-604 Escobar, Luis A. Verfasser aut http://www.loc.gov/catdir/description/wiley031/97039270.html Publisher description http://www.loc.gov/catdir/toc/onix01/97039270.html Table of Contents GBV Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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 |
| url | 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 |
| work_keys_str_mv | AT meekerwilliamq statisticalmethodsforreliabilitydata AT escobarluisa statisticalmethodsforreliabilitydata |