Accelerated life models: modeling and statistical analysis
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton
Chapman & Hall
2002
|
| Schriftenreihe: | Monographs on statistics and applied probability
94 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Angekündigt als: Bagdonavičius, Vilijandas: Models of accelerated life |
| Beschreibung: | XIX, 334 S. |
| ISBN: | 1584881860 |
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| 245 | 1 | 0 | |a Accelerated life models |b modeling and statistical analysis |c Vilijandas Bagdonavičius ; Mikhail Nikulin |
| 246 | 1 | 3 | |a Models of accelerated life |
| 264 | 1 | |a Boca Raton |b Chapman & Hall |c 2002 | |
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| 490 | 1 | |a Monographs on statistics and applied probability |v 94 | |
| 500 | |a Angekündigt als: Bagdonavičius, Vilijandas: Models of accelerated life | ||
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| 650 | 4 | |a Accelerated life testing -- Mathematical models | |
| 650 | 4 | |a Accelerated life testing -- Statistical methods | |
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Datensatz im Suchindex
| _version_ | 1804128854335291392 |
|---|---|
| adam_text | Titel: Accelerated life models
Autor: Bagdonavičius, Vilijandas
Jahr: 2002
Contents
Preface xvii
1 Failure time distributions 1
1.1 Introduction 1
1.2 Parametric classes of failure time distributions 2
1.2.1 Constant hazard rate 3
1.2.2 Monotone hazard rate 3
1.2.3 H-shaped hazard rate 11
1.2.4 U-shaped hazard rate 16
2 Accelerated life models 19
2.1 Introduction 19
2.2 Generalized Sedyakin s model 20
2.2.1 Definition of the model 20
2.2.2 GS model for step-stresses 21
2.3 Accelerated failure time model 24
2.3.1 Definition of the model for constant stresses 24
2.3.2 Definition of the model for time-varying stresses 25
2.3.3 AFT model for step-stresses 27
2.3.4 Relations between the means and the quantiles 27
2.4 Proportional hazards model 29
2.4.1 Definition of the model for constant stresses 29
2.4.2 Definition of the model for time-varying stresses 30
2.4.3 PH and MPH models for simple step-stresses 32
2.4.4 PH and MPH models for general step-stresses 33
2.4.5 Relations between the PH and the AFT models 34
2.4.6 Relations between the GS and the PH models 37
2.5 Generalized proportional hazards models 38
2.5.1 Introduction 38
2.5.2 Definitions of the generalized proportional hazards
models 38
2.5.3 Interpretation of the GPH and AFT models in terms
of resource usage 40
2.5.4 Characterization of the GPH1 model with constant
stresses 42
CONTENTS
2.5.5 Relations with the frailty models 43
2.5.G Relations with the linear transformation models 44
2.5.7 The main classes of the GPH models 44
2.5.8 Modification of the GPH1 models when the time-
shift rule holds 50
2.5.9 Relations between the survival functions under
constant and non-constant stresses. 51
2.5.10 GPH1 and MGPH1 models for simple step-stresses 52
2.5.11 General step-stresses 52
2.C GAH and GAMH models 53
2.7 Changing shape and scale models 54
2.7.1 Definition of the model for constant stresses 54
2.7.2 Definition of the model for time-varying stresses 54
2.7.3 CHSS and MCHSS models for simple step-stresses 55
2.7.4 CHSS and MCHSS models for general step-stresses 56
2.8 Generalizations 5G
2.8.1 AFT model with time dependent regression coeffi-
cients 57
2.8.2 PH model with time dependent regression coefficients 59
2.8.3 Partly parametric additive risk and Aalen s models 59
2.9 Models including switch-up and cycling effects 59
2.10 Heredity hypothesis CO
2.11 Summary 62
Accelerated degradation models 67
3.1 .Introduction 67
3.2 Degradation models 68
3.2.1 General degradation path model 69
3.2.2 Gamma-process 69
3.2.3 Shock processes 70
3.3 Modeling the influence of explanatory variables 72
3.4 Modeling the traumatic event process 74
Maximum likelihood estimation for FTR data 79
4.1 Censored failure time data 79
4.2 Parametric likelihood function for right censored FTR data 80
4.3 Score function §2
4.4 Asymptotic properties of the maximum likelihood estimators 83
4.5 Approximate confidence intervals 87
4.6 Some remarks on serniparainetric estimation 89
Parametric AFT model 91
5.1 Parametrization of the AFT model 91
5.1.1 Interval valued explanatory variables 92
5.1.2 Discrete and categorical explanatory variables. 94
CONTENTS Xi
5.2 Interpretation of the regression coefficients 95
5.2.1 Models without interactions 95
5.2.2 Models with interactions 96
5.2.3 Time dependent regression coefficients 97
5.3 FTR data analysis: scale-shape families of distributions 98
5.3.1 Model and data 98
5.3.2 Maximum likelihood estimation of the regression
parameters 100
5.3.3 Estimators of the main reliability characteristics 101
5.3.4 Asymptotic distribution of the regression parameters
estimators 103
5.3.5 Approximate confidence intervals for the main
reliability characteristics 104
5.3.6 Tests for nullity of the regression coefficients 106
5.3.7 Residual plots 108
5.4 FTR data analysis: generalized Weibull distribution 110
5.4.1 Model 110
5.4.2 Maximum likelihood estimation for the regression
parameters 111
5.4.3 Estimators of the main reliability characteristics 112
5.4.4 Asymptotic distribution of the regression parameters 113
5.4.5 Approximate confidence intervals for the main
reliability characteristics 114
5.4.6 Tests for nullity of the regression coefficients 115
5.4.7 Residual plots 116
5.5 FTR data analysis: exponential distribution 117
5.5.1 Model 117
5.5.2 Maximum likelihood estimation of the regression
parameters 117
5.5.3 Estimators of the main reliability characteristics 118
5.5.4 Asymptotic properties of the regression parameters 118
5.5.5 Approximate confidence intervals for the main
reliability characteristics 118
5.5.6 Tests for nullity of the regression coefficients 119
5.5.7 Residual plots 120
5.6 Plans of experiments in accelerated life testing 120
5.6.1 First plan of experiments 120
5.6.2 Second plan of experiments 121
5.6.3 Third plan of experiments 122
5.6.4 Fourth plan of experiments 123
5.7 Parametric estimation in ALT under the AFT model 124
5.7.1 Maximum likelihood estimation 124
5.7.2 Estimators of the main reliability characteristics
under the usual stress 127
5.7.3 Asymptotic distribution of the regression parameters 129
CONTENTS
i.7,4 Confidence intervals for the main reliability charac-
teristics
132
135
135
0 Semiparametric AFT model
0.1 FTR data analysis
6.1.1 Introduction 333
0.1.2 Semiparametric estimation of the regression param-
eters 130
0.1.3 Estimators of the main reliability characteristics 139
0.1.4 Asymptotic distribution of the regression parameters
estimators 140
0.1.5 Tests for nullity of the regression coefficients. 142
0.2 Semiparametric estimation in ALT 143
G.2.1 First plan of experiments: parametrized r and
unknown So 143
G.2.2 Third plan of experiments: unspecified So and r 143
0.2.3 Asymptotic properties of the estimators 145
0.2.4 Approximate confidence intervals 150
0.2.5 Case of random moments of switcli-up of stresses 150
7 The Cox or PH model 155
7.1 Introduction 155
7.2 Parametrization of the PH model 155
7.3 Interpretation of the regression coefficients 156
7.3.1 Interval valued explanatory variables 156
7.3.2 Discrete and categorical explanatory variables 158
7.3.3 Models without interactions 158
7.3.4 Models with interactions 159
7.3.5 Time dependent regression coefficients 160
7.4 Semiparametric FTR data analysis for the PH model 160
7.4.1 Model and data 160
7.4.2 Semiparametric estimation of the regression param-
eters 161
7.4.3 Estimators of the main reliability characteristics 164
7.4.4 Asymptotic distribution of the regression parameters
estimators 105
7.4.o Asymptotic distribution of the main reliability
characteristics 109
7.4.6 Tests for nullity of the regression coefficients 171
7.4.7 Graphical test for the PH model 173
7.4.8 Stratified PH model 173
8 GPH models: FTR analysis 175
8.1 Introduction -,-r
Q o o • f 5
8.2 Semiparametric FTR data analysis for the GPHl models 175
CONTENTS xiii
8.2.1 Models 175
8.2.2 Data 176
8.2.3 Semiparametric estimation of the parameters 9 177
8.2.4 Algorithm for computing the score functions 179
8.2.5 Expressions of the score functions for specified GPH1
models 181
8.2.6 Case of ex aequo 182
8.2.7 Estimators of the main reliability characteristics 182
8.2.8 Some remarks on asymptotic distribution estimators 183
8.2.9 Graphical tests for the GPH1 models 185
8.3 Semiparametric FTR data analysis: intersecting hazards 185
8.3.1 Model and data 185
8.3.2 Semiparametric estimation of the parameters 9 186
8.3.3 Algorithm for computing the score functions 187
8.3.4 Case of ex aequo 188
8.3.5 Estimators of the main reliability characteristics 189
9 Changing scale and shape model 191
9.1 Parametric FTR data analysis 191
9.2 Semiparametric FTR data analysis 192
9.2.1 Semiparametric estimation of the regression param-
eters 192
9.2.2 Estimators of the main reliability characteristics 194
9.3 Semiparametric estimation in ALT 194
9.3.1 First plan of experiments 194
9.3.2 Case of unspecified functions r and a 195
10 GAH and GAMH models 197
10.1 GAH model 197
10.2 GAMH model 200
10.3 AAR model 201
10.4 PPAR model 203
11 Estimation when a process of production is unstable 207
11.1 Application of the AFT model 207
11.2 Application of the GPH1 model 208
12 Goodness-of-fit for accelerated life models 213
12.1 Goodness-of-fit for the GS model 213
12.1.1 Test statistic for the GS model 214
12.1.2 Asymptotic distribution of the test statistic 215
12.1.3 The test 220
12.1.4 Consistency and the power of tire test against
approaching alternatives 220
12.2 Goodness-of-fit for the model with absence of memory 224
CONTENTS
226
229
229
12.2.1 Logrank-typc test statistic for the AM model 225
12.2.2 Asymptotic distribution of the logrank-typc test
statistic
12.2.3 Logrank-typc test
12.2.4 Consistency and the power of the test against the
approaching alternatives
12.2.5 Kolmogorov-type test 232
12.3 Goodness-of-fit for the AFT model 23^
12.4 Goodness-of-fit for the PH model 237
12.4.1 Score tests 237
12.4.2 Tests based on estimated score process 242
12.4.3 Tests based on linear combinations of martingale
residuals with two variable weights 245
12.5 Goodness-of-fit for the GPH models 246
12.5.1 Estimators used for goodness-of-fit test construction 246
12.5.2 Tests for the models with specified q 248
12.5.3 Tests for the models witli specified or parametrized
q 250
12.G Goodness-of-fit for parametric regression models 252
12.6.1 Likelihood ratio tests 252
12.6.2 Numerical methods for assessing goodncss-of-fit 253
13 Estimation in degradation models 259
13.1 Introduction 259
13.2 Linear patli models 260
13.2.1 Model without explanatory variables 260
13.2.2 Nonparametric estimation of the cumulative intensi-
ties 261
13.2.3 Nonparametric estimation of unconditional reliabil-
ity characteristics 263
13.2.4 Prediction of the residual reliability characteristics 264
13.2.5 Prediction of the ideal reliability characteristics 266
13.2.6 Prediction of the reliability characteristics related
with elimination of particular failure modes 267
13.2.7 Semiparametric and parametric estimation 269
13.2.8 Right censored data 272
13.2.9 Model with explanatory variables 273
13.2.10 Nonparametric estimation of the cumulative intensi-
tics 273
13.2.11 Estimation and prediction of the reliability under
given explanatory variables 278
13.3 Gannua and shock processes 279
13.3.1 Data and likelihood structure when the form of the
mean degradation form is specified 279
CONTENTS
xv
13.3.2 Estimation of degradation characteristics and re-
liability when traumatic events do not depend on
degradation 281
13.3.3 Estimation of reliability and degradation character-
istics when traumatic events depend on degradation 284
13.3.4 Estimation when the form of the mean degradation
is unknown 286
A Some results from stochastic process theory 289
A.l Stochastic process. Filtration 289
A.2 Counting process 290
A.3 Stochastic integral 290
A.4 Conditional expectation 291
A.5 Martingale 292
A.6 Predictable process and Doob-Meycr decomposition 293
A.7 Predictable variation and predictable covariation 295
A.8 Stochastic integrals with respect to martingales 297
A.9 Localization 300
A.10 Stochastic integrals with respect to martingales (continuation) 300
A. 11 Weak convergence 301
A.12 Central limit theorem for martingales 303
A. 13 Nonparametric estimators of the cumulative hazard and the
survival function 305
A.14 Product-integral 306
A.15 Delta method 307
References 311
Author index 327
Subject index 331
|
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| author | Bagdonavičius, Vilijandas Nikulin, Michail S. |
| author_GND | (DE-588)134042727 (DE-588)131649515 |
| author_facet | Bagdonavičius, Vilijandas Nikulin, Michail S. |
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| id | DE-604.BV013999870 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:55:51Z |
| institution | BVB |
| isbn | 1584881860 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009583742 |
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| physical | XIX, 334 S. |
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| spelling | Bagdonavičius, Vilijandas Verfasser (DE-588)134042727 aut Accelerated life models modeling and statistical analysis Vilijandas Bagdonavičius ; Mikhail Nikulin Models of accelerated life Boca Raton Chapman & Hall 2002 XIX, 334 S. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 94 Angekündigt als: Bagdonavičius, Vilijandas: Models of accelerated life Mathematisches Modell Accelerated life testing -- Mathematical models Accelerated life testing -- Statistical methods Zuverlässigkeitstheorie (DE-588)4195525-0 gnd rswk-swf Statistische Analyse (DE-588)4116599-8 gnd rswk-swf Zuverlässigkeitstheorie (DE-588)4195525-0 s Statistische Analyse (DE-588)4116599-8 s DE-604 Nikulin, Michail S. Verfasser (DE-588)131649515 aut Monographs on statistics and applied probability 94 (DE-604)BV002494005 94 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009583742&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bagdonavičius, Vilijandas Nikulin, Michail S. Accelerated life models modeling and statistical analysis Monographs on statistics and applied probability Mathematisches Modell Accelerated life testing -- Mathematical models Accelerated life testing -- Statistical methods Zuverlässigkeitstheorie (DE-588)4195525-0 gnd Statistische Analyse (DE-588)4116599-8 gnd |
| subject_GND | (DE-588)4195525-0 (DE-588)4116599-8 |
| title | Accelerated life models modeling and statistical analysis |
| title_alt | Models of accelerated life |
| title_auth | Accelerated life models modeling and statistical analysis |
| title_exact_search | Accelerated life models modeling and statistical analysis |
| title_full | Accelerated life models modeling and statistical analysis Vilijandas Bagdonavičius ; Mikhail Nikulin |
| title_fullStr | Accelerated life models modeling and statistical analysis Vilijandas Bagdonavičius ; Mikhail Nikulin |
| title_full_unstemmed | Accelerated life models modeling and statistical analysis Vilijandas Bagdonavičius ; Mikhail Nikulin |
| title_short | Accelerated life models |
| title_sort | accelerated life models modeling and statistical analysis |
| title_sub | modeling and statistical analysis |
| topic | Mathematisches Modell Accelerated life testing -- Mathematical models Accelerated life testing -- Statistical methods Zuverlässigkeitstheorie (DE-588)4195525-0 gnd Statistische Analyse (DE-588)4116599-8 gnd |
| topic_facet | Mathematisches Modell Accelerated life testing -- Mathematical models Accelerated life testing -- Statistical methods Zuverlässigkeitstheorie Statistische Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009583742&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494005 |
| work_keys_str_mv | AT bagdonaviciusvilijandas acceleratedlifemodelsmodelingandstatisticalanalysis AT nikulinmichails acceleratedlifemodelsmodelingandstatisticalanalysis AT bagdonaviciusvilijandas modelsofacceleratedlife AT nikulinmichails modelsofacceleratedlife |