Bayesian reliability:
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Springer
[2008]
|
| Schriftenreihe: | Springer series in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis Seite 413-425 |
| Beschreibung: | XVI, 436 Seiten Diagramme |
| ISBN: | 9780387779485 |
Internformat
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| 100 | 1 | |a Hamada, Michael |d 1955- |e Verfasser |0 (DE-588)1115204327 |4 aut | |
| 245 | 1 | 0 | |a Bayesian reliability |c Michael S. Hamada, Alyson G. Wilson, C. Shane Reese, Harry F. Martz |
| 264 | 1 | |a New York |b Springer |c [2008] | |
| 264 | 4 | |c © 2008 | |
| 300 | |a XVI, 436 Seiten |b Diagramme | ||
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| 490 | 0 | |a Springer series in statistics | |
| 500 | |a Literaturverzeichnis Seite 413-425 | ||
| 650 | 4 | |a Fiabilité - Méthodes statistiques | |
| 650 | 4 | |a Statistique bayésienne | |
| 650 | 4 | |a Bayesian statistical decision theory | |
| 650 | 4 | |a Reliability (Engineering) |x Statistical methods | |
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Datensatz im Suchindex
| _version_ | 1804137905542660096 |
|---|---|
| adam_text | Contents
Preface........................................................VII
1 Reliability Concepts....................................... 1
1.1 Defining Reliability...................................... 1
1.2 Measures of Random Variation............................ 2
1.3 Examples of Reliability Data.............................. 1(1
1.3.1 Bernoulli Success/Failure Data...................... 10
1.3.2 Failure Count Data................................ 10
1.3.3 Lifetime/Failure Time Data ........................ 11
1.3.4 Degradation Data................................. 12
1.4 Censoring.............................................. 13
1.5 Bayesian Reliability Analysis.............................. 15
1.6 Related Reading ........................................ 18
1.7 Exercises for Chapter 1 .................................. 19
2 Bayesian Inference......................................... 21
2.1 Introductory Concepts................................... 21
2.1.1 Maximum Likelihood Estimation.................... 24
2.1.2 Classical Point and Interval Estimation
for a Proportion................................... 26
2.2 Fundamentals of Bayesian Inference........................ 27
2.2.1 The Prior Distribution............................. 28
2.2.2 Combining Data with Prior Information.............. 30
2.3 Prediction.............................................. 35
2.4 The Marginal Distribution of the Data and Bayes Factors .... 36
2.5 A Lognormal Example................................... 39
2.6 More on Prior Distributions .............................. 46
2.6.1 Noninformative and Diffuse Prior Distributions ....... 46
2.6.2 Conjugate Prior Distributions....................... 47
2.6.3 Informative Prior Distributions...................... 47
2.7 Related Reading ........................................ 49
2.8 Exercises for Chapter 2 .................................. 49
XII Contents
3 Advanced Bayesian Modeling
and Computational Methods .............................. 51
3.1 Introduction to Markov Chain Monte Carlo (MCMC)........ 51
3.1.1 Metropolis-Hastings Algorithms..................... 52
3.1.2 Gibbs Sampler.................................... 60
3.1.3 Output Analysis .................................. 64
3.2 Hierarchical Models...................................... 68
3.2.1 MCMC Estimation of Hierarchical Model Parameters . . 71
3.2.2 Inference for Launch Vehicle Probabilities ............ 71
3.3 Empirical Bayes......................................... 73
3.4 Goodness of Fit......................................... 76
3.5 Related Reading ........................................ 82
3.6 Exercises for Chapter 3 .................................. 82
4 Component Reliability..................................... 85
4.1 Introduction............................................ 85
4.2 Discrete Data Models for Reliability....................... 86
4.2.1 Success/Failure Data .............................. 86
4.2.2 Failure Count Data................................ 87
4.3 Failure Time Data Models for Reliability................... 90
4.3.1 Exponential Failure Times.......................... 91
4.3.2 Weibull Failure Times.............................. 97
4.3.3 Lognormal Failure Times...........................102
4.3.4 Gamma Failure Times .............................104
4.3.5 Inverse Gaussian Failure Times .....................105
4.3.6 Normal Failure Times..............................106
4.4 Censored Data..........................................107
4.5 Multiple Units and Hierarchical Modeling ..................Ill
4.6 Model Selection.........................................116
4.6.1 Bayesian Information Criterion......................116
4.6.2 Deviance Information Criterion .....................117
4.6.3 Akaike Information Criterion .......................120
4.7 Related Reading ........................................120
4.8 Exercises for Chapter 4 ..................................120
5 System Reliability.........................................125
5.1 System Structure........................................125
5.1.1 Reliability Block Diagrams .........................126
5.1.2 Structure Functions................................126
5.1.3 Minimal Path and Cut Sets.........................129
5.1.4 Fault Trees.......................................131
5.2 System Analysis.........................................135
5.2.1 Calculating System Reliability......................135
5.2.2 Prior Distributions for Systems .....................138
5.2.3 Fault Trees with Bernoulli Data.....................141
Contents XIII
5.2.4 Fault Trees with Lifetime Data......................145
5.2.5 Bayesian Network Models..........................147
5.2.6 Models for Dependence ............................155
5.3 Related Reading ........................................158
5.4 Exercises for Chapter 5 ..................................159
Repairable System Reliability .............................161
6.1 Introduction............................................161
6.1.1 Types of Data....................................162
6.1.2 Characteristics of System Repairs ...................162
6.2 Renewal Processes.......................................163
6.3 Poisson Processes........................................165
6.3.1 Homogeneous Poisson Processes (HPPs)..............167
6.4 Nonhomogeneous Poisson Processes (NHPPs)...............170
6.4.1 Power Law Processes (PLPs) .......................170
6.4.2 Log-Linear Processes ..............................176
6.5 Alternatives to NHPPs...................................176
6.5.1 Modulated Power Law Processes (MPLPs) ...........176
6.5.2 Piecewise Exponential Model (PEXP)................179
6.6 Goodness of Fit and Model Selection.......................180
6.7 Current Reliability and Other Performance Criteria..........181
6.7.1 Current Reliability ................................181
6.7.2 Other Performance Criteria.........................182
6.8 Multiple-Unit Systems and Hierarchical Modeling ...........183
6.9 Availability.............................................192
6.9.1 Other Data Types for Availability...................194
6.9.2 Complex System Availability .......................196
6.10 Related Reading ........................................198
6.11 Exercises for Chapter 6 ..................................199
Regression Models in Reliability...........................203
7.1 Introduction............................................203
7.1.1 Covariate Types...................................204
7.1.2 Covariate Relationships............................205
7.2 Logistic Regression Models for Binomial Data...............205
7.3 Poisson Regression Models for Count Data..................215
7.4 Regression Models for Lifetime Data.......................221
7.5 Model Selection.........................................228
7.6 Residual Analysis .......................................229
7.7 Accelerated Life Testing..................................235
7.7.1 Common Accelerating Variables and Relationships.....237
7.8 Reliability Improvement Experiments......................243
7.9 Other Regression Situations ..............................258
7.10 Related Reading ........................................259
7.11 Exercises for Chapter 7 ..................................259
XIV Contents
8 Using Degradation Data to Assess Reliability..............271
8.1 Introduction............................................271
8.1.1 Comparison with Lifetime Data.....................278
8.2 More Complex Degradation Data Models...................279
8.2.1 Reliability Function................................281
8.3 Diagnostics for Degradation Data Models...................283
8.4 Incorporating Covariates .................................287
8.4.1 Accelerated Degradation Testing....................288
8.4.2 Improving Reliability Using Designed Experiments .... 295
8.5 Destructive Degradation Data.............................298
8.6 An Alternative Degradation Data Model Using Stochastic
Processes...............................................306
8.7 Related Reading ........................................309
8.8 Exercises for Chapter 8 ..................................310
9 Planning for Reliability Data Collection...................319
9.1 Introduction............................................319
9.2 Planning Criteria, Optimization, and Implementation........320
9.2.1 Optimization in Planning...........................321
9.2.2 Implementing the Simulation-Based Framework.......323
9.3 Planning for Binomial Data...............................324
9.4 Planning for Lifetime Data...............................327
9.5 Planning Accelerated Life Tests...........................328
9.6 Planning for Degradation Data............................330
9.7 Planning for System Reliability Data.......................331
9.8 Related Reading ........................................339
9.9 Exercises for Chapter 9 ..................................339
10 Assurance Testing.........................................343
10.1 Introduction............................................343
10.1.1 Classical Risk Criteria.............................345
10.1.2 Average Risk Criteria..............................345
10.1.3 Posterior Risk Criteria.............................346
10.2 Binomial Testing........................................348
10.2.1 Binomial Posterior Consumer s and Producer s Risks . . 349
10.2.2 Hybrid Risk Criterion..............................353
10.3 Poisson Testing .........................................354
10.4 Weibull Testing.........................................358
10.4.1 Single Weibull Population Testing...................360
10.4.2 Combined Weibull Accelerated/Assurance Testing.....364
10.5 Related Reading ........................................368
10.6 Exercises for Chapter 10 .................................369
A Acronyms and Abbreviations..............................375
Contents XV
Special Functions and Probability Distributions ...........377
B.I Greek Alphabet.........................................377
B.2 Special Functions........................................377
B.2.1 Beta Function ....................................377
B.2.2 Binomial Coefficient...............................378
B.2.3 Determinant......................................378
B.2.4 Factorial.........................................378
B.2.5 Gamma Function..................................378
B.2.6 Incomplete Beta Function..........................378
B.2.7 Incomplete Beta Function Ratio.....................378
B.2.8 Indicator Function.................................379
B.2.9 Logarithm........................................379
B.2.10 Lower Incomplete Gamma Function .................379
B.2.11 Standard Normal Cumulative Density Function .......379
B.2.12 Standard Normal Probability Density Function........379
B.2.13 Trace............................................379
B.2.14 Upper Incomplete Gamma Function.................379
B.3 Probability Distributions.................................380
B.3.1 Bernoulli.........................................380
B.3.2 Beta.............................................380
B.3.3 Binomial.........................................382
B.3.4 Bivariate Exponential..............................382
B.3.5 Chi-squared ......................................383
B.3.6 Dirichlet .........................................383
B.3.7 Exponential ......................................386
B.3.8 Extreme Value....................................386
B.3.9 Gamma..........................................389
B.3.10 Inverse Chi-squared................................389
B.3.11 Inverse Gamma...................................392
B.3.12 Inverse Gaussian..................................392
B.3.13 Inverse Wishart...................................392
B.3.14 Logistic..........................................396
B.3.15 Lognormal........................................396
B.3.16 Multinomial......................................399
B.3.17 Multivariate Normal...............................399
B.3.18 Negative Binomial.................................399
B.3.19 Negative Log-Gamma..............................401
B.3.20 Normal ..........................................403
B.3.21 Pareto...........................................403
B.3.22 Poisson ..........................................403
B.3.23 Poly-Weibull......................................403
B.3.24 Student s t .......................................406
B.3.25 Uniform..........................................408
B.3.26 Weibull..........................................408
B.3.27 Wishart..........................................411
XVI Contents
References.....................................................413
Author Index..................................................427
Subject Index .................................................431
|
| adam_txt |
Contents
Preface.VII
1 Reliability Concepts. 1
1.1 Defining Reliability. 1
1.2 Measures of Random Variation. 2
1.3 Examples of Reliability Data. 1(1
1.3.1 Bernoulli Success/Failure Data. 10
1.3.2 Failure Count Data. 10
1.3.3 Lifetime/Failure Time Data . 11
1.3.4 Degradation Data. 12
1.4 Censoring. 13
1.5 Bayesian Reliability Analysis. 15
1.6 Related Reading . 18
1.7 Exercises for Chapter 1 . 19
2 Bayesian Inference. 21
2.1 Introductory Concepts. 21
2.1.1 Maximum Likelihood Estimation. 24
2.1.2 Classical Point and Interval Estimation
for a Proportion. 26
2.2 Fundamentals of Bayesian Inference. 27
2.2.1 The Prior Distribution. 28
2.2.2 Combining Data with Prior Information. 30
2.3 Prediction. 35
2.4 The Marginal Distribution of the Data and Bayes' Factors . 36
2.5 A Lognormal Example. 39
2.6 More on Prior Distributions . 46
2.6.1 Noninformative and Diffuse Prior Distributions . 46
2.6.2 Conjugate Prior Distributions. 47
2.6.3 Informative Prior Distributions. 47
2.7 Related Reading . 49
2.8 Exercises for Chapter 2 . 49
XII Contents
3 Advanced Bayesian Modeling
and Computational Methods . 51
3.1 Introduction to Markov Chain Monte Carlo (MCMC). 51
3.1.1 Metropolis-Hastings Algorithms. 52
3.1.2 Gibbs Sampler. 60
3.1.3 Output Analysis . 64
3.2 Hierarchical Models. 68
3.2.1 MCMC Estimation of Hierarchical Model Parameters . . 71
3.2.2 Inference for Launch Vehicle Probabilities . 71
3.3 Empirical Bayes. 73
3.4 Goodness of Fit. 76
3.5 Related Reading . 82
3.6 Exercises for Chapter 3 . 82
4 Component Reliability. 85
4.1 Introduction. 85
4.2 Discrete Data Models for Reliability. 86
4.2.1 Success/Failure Data . 86
4.2.2 Failure Count Data. 87
4.3 Failure Time Data Models for Reliability. 90
4.3.1 Exponential Failure Times. 91
4.3.2 Weibull Failure Times. 97
4.3.3 Lognormal Failure Times.102
4.3.4 Gamma Failure Times .104
4.3.5 Inverse Gaussian Failure Times .105
4.3.6 Normal Failure Times.106
4.4 Censored Data.107
4.5 Multiple Units and Hierarchical Modeling .Ill
4.6 Model Selection.116
4.6.1 Bayesian Information Criterion.116
4.6.2 Deviance Information Criterion .117
4.6.3 Akaike Information Criterion .120
4.7 Related Reading .120
4.8 Exercises for Chapter 4 .120
5 System Reliability.125
5.1 System Structure.125
5.1.1 Reliability Block Diagrams .126
5.1.2 Structure Functions.126
5.1.3 Minimal Path and Cut Sets.129
5.1.4 Fault Trees.131
5.2 System Analysis.135
5.2.1 Calculating System Reliability.135
5.2.2 Prior Distributions for Systems .138
5.2.3 Fault Trees with Bernoulli Data.141
Contents XIII
5.2.4 Fault Trees with Lifetime Data.145
5.2.5 Bayesian Network Models.147
5.2.6 Models for Dependence .155
5.3 Related Reading .158
5.4 Exercises for Chapter 5 .159
Repairable System Reliability .161
6.1 Introduction.161
6.1.1 Types of Data.162
6.1.2 Characteristics of System Repairs .162
6.2 Renewal Processes.163
6.3 Poisson Processes.165
6.3.1 Homogeneous Poisson Processes (HPPs).167
6.4 Nonhomogeneous Poisson Processes (NHPPs).170
6.4.1 Power Law Processes (PLPs) .170
6.4.2 Log-Linear Processes .176
6.5 Alternatives to NHPPs.176
6.5.1 Modulated Power Law Processes (MPLPs) .176
6.5.2 Piecewise Exponential Model (PEXP).179
6.6 Goodness of Fit and Model Selection.180
6.7 Current Reliability and Other Performance Criteria.181
6.7.1 Current Reliability .181
6.7.2 Other Performance Criteria.182
6.8 Multiple-Unit Systems and Hierarchical Modeling .183
6.9 Availability.192
6.9.1 Other Data Types for Availability.194
6.9.2 Complex System Availability .196
6.10 Related Reading .198
6.11 Exercises for Chapter 6 .199
Regression Models in Reliability.203
7.1 Introduction.203
7.1.1 Covariate Types.204
7.1.2 Covariate Relationships.205
7.2 Logistic Regression Models for Binomial Data.205
7.3 Poisson Regression Models for Count Data.215
7.4 Regression Models for Lifetime Data.221
7.5 Model Selection.228
7.6 Residual Analysis .229
7.7 Accelerated Life Testing.235
7.7.1 Common Accelerating Variables and Relationships.237
7.8 Reliability Improvement Experiments.243
7.9 Other Regression Situations .258
7.10 Related Reading .259
7.11 Exercises for Chapter 7 .259
XIV Contents
8 Using Degradation Data to Assess Reliability.271
8.1 Introduction.271
8.1.1 Comparison with Lifetime Data.278
8.2 More Complex Degradation Data Models.279
8.2.1 Reliability Function.281
8.3 Diagnostics for Degradation Data Models.283
8.4 Incorporating Covariates .287
8.4.1 Accelerated Degradation Testing.288
8.4.2 Improving Reliability Using Designed Experiments . 295
8.5 Destructive Degradation Data.298
8.6 An Alternative Degradation Data Model Using Stochastic
Processes.306
8.7 Related Reading .309
8.8 Exercises for Chapter 8 .310
9 Planning for Reliability Data Collection.319
9.1 Introduction.319
9.2 Planning Criteria, Optimization, and Implementation.320
9.2.1 Optimization in Planning.321
9.2.2 Implementing the Simulation-Based Framework.323
9.3 Planning for Binomial Data.324
9.4 Planning for Lifetime Data.327
9.5 Planning Accelerated Life Tests.328
9.6 Planning for Degradation Data.330
9.7 Planning for System Reliability Data.331
9.8 Related Reading .339
9.9 Exercises for Chapter 9 .339
10 Assurance Testing.343
10.1 Introduction.343
10.1.1 Classical Risk Criteria.345
10.1.2 Average Risk Criteria.345
10.1.3 Posterior Risk Criteria.346
10.2 Binomial Testing.348
10.2.1 Binomial Posterior Consumer's and Producer's Risks . . 349
10.2.2 Hybrid Risk Criterion.353
10.3 Poisson Testing .354
10.4 Weibull Testing.358
10.4.1 Single Weibull Population Testing.360
10.4.2 Combined Weibull Accelerated/Assurance Testing.364
10.5 Related Reading .368
10.6 Exercises for Chapter 10 .369
A Acronyms and Abbreviations.375
Contents XV
Special Functions and Probability Distributions .377
B.I Greek Alphabet.377
B.2 Special Functions.377
B.2.1 Beta Function .377
B.2.2 Binomial Coefficient.378
B.2.3 Determinant.378
B.2.4 Factorial.378
B.2.5 Gamma Function.378
B.2.6 Incomplete Beta Function.378
B.2.7 Incomplete Beta Function Ratio.378
B.2.8 Indicator Function.379
B.2.9 Logarithm.379
B.2.10 Lower Incomplete Gamma Function .379
B.2.11 Standard Normal Cumulative Density Function .379
B.2.12 Standard Normal Probability Density Function.379
B.2.13 Trace.379
B.2.14 Upper Incomplete Gamma Function.379
B.3 Probability Distributions.380
B.3.1 Bernoulli.380
B.3.2 Beta.380
B.3.3 Binomial.382
B.3.4 Bivariate Exponential.382
B.3.5 Chi-squared .383
B.3.6 Dirichlet .383
B.3.7 Exponential .386
B.3.8 Extreme Value.386
B.3.9 Gamma.389
B.3.10 Inverse Chi-squared.389
B.3.11 Inverse Gamma.392
B.3.12 Inverse Gaussian.392
B.3.13 Inverse Wishart.392
B.3.14 Logistic.396
B.3.15 Lognormal.396
B.3.16 Multinomial.399
B.3.17 Multivariate Normal.399
B.3.18 Negative Binomial.399
B.3.19 Negative Log-Gamma.401
B.3.20 Normal .403
B.3.21 Pareto.403
B.3.22 Poisson .403
B.3.23 Poly-Weibull.403
B.3.24 Student's t .406
B.3.25 Uniform.408
B.3.26 Weibull.408
B.3.27 Wishart.411
XVI Contents
References.413
Author Index.427
Subject Index .431 |
| any_adam_object | 1 |
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| author | Hamada, Michael 1955- Wilson, Alyson G. Reese, C. Shane Martz, Harry F. |
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| author_facet | Hamada, Michael 1955- Wilson, Alyson G. Reese, C. Shane Martz, Harry F. |
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| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV023479750 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:37:31Z |
| indexdate | 2024-07-09T21:19:43Z |
| institution | BVB |
| isbn | 9780387779485 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016661929 |
| oclc_num | 225427570 |
| open_access_boolean | |
| owner | DE-824 DE-92 DE-384 DE-11 |
| owner_facet | DE-824 DE-92 DE-384 DE-11 |
| physical | XVI, 436 Seiten Diagramme |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Hamada, Michael 1955- Verfasser (DE-588)1115204327 aut Bayesian reliability Michael S. Hamada, Alyson G. Wilson, C. Shane Reese, Harry F. Martz New York Springer [2008] © 2008 XVI, 436 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Literaturverzeichnis Seite 413-425 Fiabilité - Méthodes statistiques Statistique bayésienne Bayesian statistical decision theory Reliability (Engineering) Statistical methods Reliabilität (DE-588)4213628-3 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Reliabilität (DE-588)4213628-3 s Bayes-Entscheidungstheorie (DE-588)4144220-9 s DE-604 Wilson, Alyson G. Verfasser (DE-588)1115207032 aut Reese, C. Shane Verfasser (DE-588)1115208942 aut Martz, Harry F. Verfasser (DE-588)1115209108 aut Erscheint auch als Online-Ausgabe 978-0-387-77950-8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016661929&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hamada, Michael 1955- Wilson, Alyson G. Reese, C. Shane Martz, Harry F. Bayesian reliability Fiabilité - Méthodes statistiques Statistique bayésienne Bayesian statistical decision theory Reliability (Engineering) Statistical methods Reliabilität (DE-588)4213628-3 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| subject_GND | (DE-588)4213628-3 (DE-588)4144220-9 |
| title | Bayesian reliability |
| title_auth | Bayesian reliability |
| title_exact_search | Bayesian reliability |
| title_exact_search_txtP | Bayesian reliability |
| title_full | Bayesian reliability Michael S. Hamada, Alyson G. Wilson, C. Shane Reese, Harry F. Martz |
| title_fullStr | Bayesian reliability Michael S. Hamada, Alyson G. Wilson, C. Shane Reese, Harry F. Martz |
| title_full_unstemmed | Bayesian reliability Michael S. Hamada, Alyson G. Wilson, C. Shane Reese, Harry F. Martz |
| title_short | Bayesian reliability |
| title_sort | bayesian reliability |
| topic | Fiabilité - Méthodes statistiques Statistique bayésienne Bayesian statistical decision theory Reliability (Engineering) Statistical methods Reliabilität (DE-588)4213628-3 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| topic_facet | Fiabilité - Méthodes statistiques Statistique bayésienne Bayesian statistical decision theory Reliability (Engineering) Statistical methods Reliabilität Bayes-Entscheidungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016661929&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hamadamichael bayesianreliability AT wilsonalysong bayesianreliability AT reesecshane bayesianreliability AT martzharryf bayesianreliability |