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Statistical Modeling for Degradation Data.

By: Chen, Ding-Geng (Din).
Contributor(s): Lio, Yuhlong | Ng, Hon Keung Tony | Tsai, Tzong-Ru.
Material type: TextTextSeries: eBooks on Demand.ICSA Book Series in Statistics Ser: Publisher: Singapore : Springer, 2017Copyright date: ©2017Description: 1 online resource (382 pages).Content type: text Media type: computer Carrier type: online resourceISBN: 9789811051944.Subject(s): Research--Data processingGenre/Form: Electronic books.Additional physical formats: Print version:: Statistical Modeling for Degradation DataDDC classification: 519.5 LOC classification: QA276-280Online resources: Click here to view this ebook.
Contents:
Intro -- Preface -- Part 1: Review and Theoretical Framework (Chaps. 1, 2, 3, 4, 5, and 6) -- Part 2: Modeling and Experimental Designs (Chaps. 7, 8, 9, and 10) -- Part 3: Applications (Chaps. 11, 12, 13, 14, 15, 16, and 17) -- List of Chapter Reviewers -- Contents -- Contributors -- About the Editors -- Part I Review and Theoretical Framework -- 1 Stochastic Accelerated Degradation Models Based on a Generalized Cumulative Damage Approach -- 1.1 Introduction -- 1.2 Basic Properties for Stochastic Cumulative Damage Process -- 1.3 The Distribution of the Failure Time and the Degradation -- 1.3.1 Degradation Model Based on Brownian Motion Process -- 1.3.2 Degradation Model Based on Geometric Brownian Motion Process -- 1.3.3 Degradation Model Based on Shifted Gamma Motion Process -- 1.3.4 General Likelihood for Hard and Soft Failures -- 1.4 Degradation Models with Several Accelerating Variables -- 1.5 Likelihood Construction with Accelerating Variables and Model Selection -- 1.6 Concluding Remarks -- References -- 2 Hierarchical Bayesian Change-Point Analysis for Nonlinear Degradation Data -- 2.1 Introduction -- 2.2 Degradation Analysis Using Change-Point Regression -- 2.2.1 Change-Point Regression -- 2.2.2 Hierarchical Bayesian Change-Point Degradation Model -- 2.2.3 Deriving the Failure-Time Distribution -- 2.3 Degradation-Based Burn-in Optimization -- 2.3.1 Reliability Criterion -- 2.3.2 Cost Criterion -- 2.3.3 Incorporation of Pre-burn-in Data -- 2.4 Results and Discussion -- 2.4.1 Degradation Modeling and Failure-Time Distribution Estimation -- 2.4.1.1 Individual Degradation Modeling -- 2.4.1.2 Hierarchical Bayesian Degradation Modeling -- 2.4.2 Burn-in Test Planning -- 2.4.2.1 Planning Burn-in Without Inspection -- 2.4.2.2 Planning Burn-In with Inspection -- 2.5 Conclusion -- References.
3 Degradation Modeling, Analysis, and Applications on Lifetime Prediction -- 3.1 Introduction -- 3.1.1 Traditional Reliability Analysis -- 3.1.2 Degradation Data -- 3.1.3 Accelerated Degradation Testing -- 3.1.3.1 Three Types of ADTs -- 3.1.3.2 Accelerated Degradation Models -- 3.1.4 Overview -- 3.2 Acceleration Models -- 3.2.1 Usage Rate Acceleration Models -- 3.2.2 Temperature Acceleration Models -- 3.2.2.1 Arrhenius Relationship -- 3.2.2.2 Eyring Relationship -- 3.2.3 Voltage Acceleration Models -- 3.2.4 Other Acceleration Models -- 3.3 Degradation Modeling and Analysis -- 3.3.1 General Path Models -- 3.3.1.1 Two Basic Methods of Model Application -- 3.3.1.2 Incorporation of Accelerated Models -- 3.3.2 Stochastic Processes Models -- 3.3.2.1 The Wiener Process -- 3.3.2.2 The Gamma Process -- 3.3.2.3 The Inverse Gaussian Process -- 3.3.3 Estimation of Model Parameters -- 3.3.4 Lifetime Prediction -- 3.4 Initial Degradation Levels -- 3.4.1 Motivating Examples -- 3.4.2 Mixed-Effect General Path Model -- 3.5 Discussions on Future Study -- References -- 4 On Some Shock Models with Poisson and Generalized Poisson Shock Processes -- 4.1 Introduction -- 4.2 Definition of the GPP -- 4.3 Extreme Shock Model -- 4.4 Delayed Failures and Shot-Noise Processes -- 4.5 GPP for the Preventive Maintenance Model -- 4.6 Concluding Remarks -- References -- 5 Degradation-Based Reliability Modeling of Complex Systems in Dynamic Environments -- 5.1 Introduction -- 5.2 Dynamic Environments -- 5.2.1 Characterization of Dynamic Environments -- 5.2.2 Incorporation of Dynamic Environments -- 5.3 Multiple Degradation Processes Under Static Environments -- 5.3.1 Multivariate Gaussian Distribution Based Model -- 5.3.2 Multivariate Birnbaum-Saunders Distribution Based Model -- 5.3.3 Degradation Rate Interaction Model -- 5.3.4 Copula Based Multivariate Degradation Process Model.
5.4 Multiple Degradation Processes Under Dynamic Environments -- 5.4.1 Multiple Degradation Process and Random Shock Models -- 5.4.2 Multiple Degradation Process and Dynamic Covariate Models -- 5.5 Conclusions -- References -- 6 A Survey of Modeling and Application of Non-destructive and Destructive Degradation Tests -- 6.1 Introduction -- 6.2 Nondestructive Degradation Model -- 6.2.1 Fixed or Random Effect Degradation Model -- 6.2.2 Stochastic Process Degradation Models -- 6.2.2.1 Wiener Process -- 6.2.2.2 Gamma Process -- 6.2.2.3 Inverse Gaussian Process -- 6.2.3 Mixed Random Effect and Stochastic Process -- 6.2.3.1 Random-Effect Wiener Process -- 6.2.3.2 Random-Effect Gamma Process -- 6.2.3.3 Random-Effect Inverse Gaussian Process -- 6.2.4 Other Degradation Models -- 6.3 Destructive Degradation Model -- 6.4 Applications on Degradation Model -- 6.5 Concluding Remarks -- References -- Part II Modeling and Experimental Designs -- 7 Degradation Test Plan for a Nonlinear Random-CoefficientsModel -- 7.1 Introduction -- 7.2 The Degradation Model -- 7.2.1 Nonlinear Random-Coefficients Model -- 7.2.2 The Fisher Information Matrix -- 7.2.2.1 The FO Method -- 7.2.2.2 Simulation-Based FOCE Method -- 7.3 Failure-Time Distribution -- 7.4 Optimal Degradation Test Plan Under Cost Functions -- 7.4.1 Specification of the Degradation Test -- 7.4.2 Cost Functions -- 7.4.2.1 Experimental Cost -- 7.4.2.2 Information Loss Cost -- 7.4.3 The Cost Optimization Problem -- 7.5 Practical Application: PDP Example -- 7.5.1 The Cost-Effective optimal plan for PDP Degradation Test -- 7.5.2 Sensitivity Analysis -- 7.5.2.1 The Effect of Cost Factors -- 7.5.2.2 The Effect of Estimated Model Parameters -- 7.5.2.3 The Effect of pth Quantiles -- 7.6 Conclusion -- References -- 8 Optimal Designs for LED Degradation Modeling -- 8.1 Introduction.
8.2 Constant-Stress Accelerated Degradation Model -- 8.3 Statistical Inference -- 8.4 Optimal Strategy -- 8.5 Illustration Example -- 8.5.1 Statistical Inference -- 8.5.2 Optimal Strategy -- 8.6 Conclusion and Discussion -- Appendix -- References -- 9 Gamma Degradation Models: Inference and Optimal Design -- 9.1 Introduction -- 9.2 Degradation Model Based on Gamma Process -- 9.2.1 Definition of Gamma Process -- 9.2.2 Distribution of Product's Lifetime -- 9.3 Design and Inference of Degradation Experiment -- 9.3.1 Degradation Tests -- 9.3.2 Accelerated Degradation Tests -- 9.3.3 Step-Stress Accelerated Degradation Tests -- 9.4 Extensions and Some Applications -- 9.4.1 Multiple Quality Characteristics -- 9.4.2 Inspection Model and Maintenance Decision -- 9.4.3 Burn-In Test -- 9.5 Concluding Remarks -- References -- 10 Misspecification Analysis of Gamma with Inverse Gaussian Degradation Processes -- 10.1 Introduction -- 10.2 A Motivating Example -- 10.3 Misspecifying Gamma Process as Inverse Gaussian Process When δ Is Known -- 10.4 Misspecifying Gamma Process as Inverse Gaussian Process When δ Is Unknown -- 10.5 Data Analysis -- 10.6 Conclusions -- References -- Part III Applications -- 11 Practical Applications of a Family of Shock-Degradation Failure Models -- 11.1 Introduction -- 11.2 Shock-Degradation Failure Models -- 11.2.1 The Shock Process -- 11.2.2 The Degradation Process -- 11.2.3 The Shock-Degradation Survival Distribution -- 11.3 Data Structures -- 11.3.1 Direct Readings on the Degradation Process -- 11.3.2 Observations on Failure Times, System Strength and Shocks -- 11.4 Joint Observation of Survival and Degradation -- 11.5 Case Applications -- 11.5.1 Osteoporotic Hip Fractures -- 11.5.2 Norwegian Divorces -- 11.5.3 Survival Times for Cystic Fibrosis Patients -- 11.6 Discussion and Concluding Remarks -- References.
12 Statistical Methods for Thermal Index Estimation Based on Accelerated Destructive Degradation Test Data -- 12.1 Introduction -- 12.1.1 Background -- 12.1.2 Related Literature -- 12.1.3 Overview -- 12.2 Accelerated Tests and Thermal Index -- 12.2.1 Test Plans -- 12.2.2 Data and Notation -- 12.2.3 Thermal Index -- 12.3 Statistical Methods for Thermal Index Estimations -- 12.3.1 The Traditional Method -- 12.3.2 The Parametric Method -- 12.3.3 The Semiparametric Method -- 12.4 An Illustration of Thermal Index Estimation -- 12.4.1 Degradation Path Modeling -- 12.4.2 TI Estimation -- 12.5 Simulation Studies -- 12.5.1 Simulation Settings -- 12.5.2 Results Under the Correct Model -- 12.5.3 Results Under a Misspecified Model -- 12.6 Discussions -- References -- 13 Inference on Remaining Useful Life Under Gamma Degradation Models with Random Effects -- 13.1 Introduction -- 13.2 Gamma Degradation Model with Random Effects -- 13.3 Remaining Useful Life -- 13.4 Statistical Inference on Remaining Useful Life -- 13.5 Monto Carlo Simulation Study -- 13.6 Illustrative Example: LED Degradation Data -- 13.7 Concluding Remarks -- Appendix -- References -- 14 ADDT: An R Package for Analysis of Accelerated Destructive Degradation Test Data -- 14.1 Introduction -- 14.2 The Statistical Methods -- 14.2.1 Data -- 14.2.2 The Traditional Method -- 14.2.3 The Parametric Method -- 14.2.4 The Semiparametric Method -- 14.3 Data Analysis -- 14.4 Concluding Remarks -- References -- 15 Modeling and Inference of CD4 Data -- 15.1 Introduction -- 15.2 Exploratory Data Analysis -- 15.3 Statistical Inference -- 15.3.1 Inferential Model -- 15.3.2 False Discovery Rate (FDR) -- 15.4 Conclusion -- References -- 16 State Space Models Based Prognostic Methods for Remaining Useful Life Prediction of Rechargeable Batteries -- 16.1 Introduction.
16.2 A Particle Filtering Based State Space Model for Battery Remaining Useful Life Prediction at a Constant Discharge Rate.
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Intro -- Preface -- Part 1: Review and Theoretical Framework (Chaps. 1, 2, 3, 4, 5, and 6) -- Part 2: Modeling and Experimental Designs (Chaps. 7, 8, 9, and 10) -- Part 3: Applications (Chaps. 11, 12, 13, 14, 15, 16, and 17) -- List of Chapter Reviewers -- Contents -- Contributors -- About the Editors -- Part I Review and Theoretical Framework -- 1 Stochastic Accelerated Degradation Models Based on a Generalized Cumulative Damage Approach -- 1.1 Introduction -- 1.2 Basic Properties for Stochastic Cumulative Damage Process -- 1.3 The Distribution of the Failure Time and the Degradation -- 1.3.1 Degradation Model Based on Brownian Motion Process -- 1.3.2 Degradation Model Based on Geometric Brownian Motion Process -- 1.3.3 Degradation Model Based on Shifted Gamma Motion Process -- 1.3.4 General Likelihood for Hard and Soft Failures -- 1.4 Degradation Models with Several Accelerating Variables -- 1.5 Likelihood Construction with Accelerating Variables and Model Selection -- 1.6 Concluding Remarks -- References -- 2 Hierarchical Bayesian Change-Point Analysis for Nonlinear Degradation Data -- 2.1 Introduction -- 2.2 Degradation Analysis Using Change-Point Regression -- 2.2.1 Change-Point Regression -- 2.2.2 Hierarchical Bayesian Change-Point Degradation Model -- 2.2.3 Deriving the Failure-Time Distribution -- 2.3 Degradation-Based Burn-in Optimization -- 2.3.1 Reliability Criterion -- 2.3.2 Cost Criterion -- 2.3.3 Incorporation of Pre-burn-in Data -- 2.4 Results and Discussion -- 2.4.1 Degradation Modeling and Failure-Time Distribution Estimation -- 2.4.1.1 Individual Degradation Modeling -- 2.4.1.2 Hierarchical Bayesian Degradation Modeling -- 2.4.2 Burn-in Test Planning -- 2.4.2.1 Planning Burn-in Without Inspection -- 2.4.2.2 Planning Burn-In with Inspection -- 2.5 Conclusion -- References.

3 Degradation Modeling, Analysis, and Applications on Lifetime Prediction -- 3.1 Introduction -- 3.1.1 Traditional Reliability Analysis -- 3.1.2 Degradation Data -- 3.1.3 Accelerated Degradation Testing -- 3.1.3.1 Three Types of ADTs -- 3.1.3.2 Accelerated Degradation Models -- 3.1.4 Overview -- 3.2 Acceleration Models -- 3.2.1 Usage Rate Acceleration Models -- 3.2.2 Temperature Acceleration Models -- 3.2.2.1 Arrhenius Relationship -- 3.2.2.2 Eyring Relationship -- 3.2.3 Voltage Acceleration Models -- 3.2.4 Other Acceleration Models -- 3.3 Degradation Modeling and Analysis -- 3.3.1 General Path Models -- 3.3.1.1 Two Basic Methods of Model Application -- 3.3.1.2 Incorporation of Accelerated Models -- 3.3.2 Stochastic Processes Models -- 3.3.2.1 The Wiener Process -- 3.3.2.2 The Gamma Process -- 3.3.2.3 The Inverse Gaussian Process -- 3.3.3 Estimation of Model Parameters -- 3.3.4 Lifetime Prediction -- 3.4 Initial Degradation Levels -- 3.4.1 Motivating Examples -- 3.4.2 Mixed-Effect General Path Model -- 3.5 Discussions on Future Study -- References -- 4 On Some Shock Models with Poisson and Generalized Poisson Shock Processes -- 4.1 Introduction -- 4.2 Definition of the GPP -- 4.3 Extreme Shock Model -- 4.4 Delayed Failures and Shot-Noise Processes -- 4.5 GPP for the Preventive Maintenance Model -- 4.6 Concluding Remarks -- References -- 5 Degradation-Based Reliability Modeling of Complex Systems in Dynamic Environments -- 5.1 Introduction -- 5.2 Dynamic Environments -- 5.2.1 Characterization of Dynamic Environments -- 5.2.2 Incorporation of Dynamic Environments -- 5.3 Multiple Degradation Processes Under Static Environments -- 5.3.1 Multivariate Gaussian Distribution Based Model -- 5.3.2 Multivariate Birnbaum-Saunders Distribution Based Model -- 5.3.3 Degradation Rate Interaction Model -- 5.3.4 Copula Based Multivariate Degradation Process Model.

5.4 Multiple Degradation Processes Under Dynamic Environments -- 5.4.1 Multiple Degradation Process and Random Shock Models -- 5.4.2 Multiple Degradation Process and Dynamic Covariate Models -- 5.5 Conclusions -- References -- 6 A Survey of Modeling and Application of Non-destructive and Destructive Degradation Tests -- 6.1 Introduction -- 6.2 Nondestructive Degradation Model -- 6.2.1 Fixed or Random Effect Degradation Model -- 6.2.2 Stochastic Process Degradation Models -- 6.2.2.1 Wiener Process -- 6.2.2.2 Gamma Process -- 6.2.2.3 Inverse Gaussian Process -- 6.2.3 Mixed Random Effect and Stochastic Process -- 6.2.3.1 Random-Effect Wiener Process -- 6.2.3.2 Random-Effect Gamma Process -- 6.2.3.3 Random-Effect Inverse Gaussian Process -- 6.2.4 Other Degradation Models -- 6.3 Destructive Degradation Model -- 6.4 Applications on Degradation Model -- 6.5 Concluding Remarks -- References -- Part II Modeling and Experimental Designs -- 7 Degradation Test Plan for a Nonlinear Random-CoefficientsModel -- 7.1 Introduction -- 7.2 The Degradation Model -- 7.2.1 Nonlinear Random-Coefficients Model -- 7.2.2 The Fisher Information Matrix -- 7.2.2.1 The FO Method -- 7.2.2.2 Simulation-Based FOCE Method -- 7.3 Failure-Time Distribution -- 7.4 Optimal Degradation Test Plan Under Cost Functions -- 7.4.1 Specification of the Degradation Test -- 7.4.2 Cost Functions -- 7.4.2.1 Experimental Cost -- 7.4.2.2 Information Loss Cost -- 7.4.3 The Cost Optimization Problem -- 7.5 Practical Application: PDP Example -- 7.5.1 The Cost-Effective optimal plan for PDP Degradation Test -- 7.5.2 Sensitivity Analysis -- 7.5.2.1 The Effect of Cost Factors -- 7.5.2.2 The Effect of Estimated Model Parameters -- 7.5.2.3 The Effect of pth Quantiles -- 7.6 Conclusion -- References -- 8 Optimal Designs for LED Degradation Modeling -- 8.1 Introduction.

8.2 Constant-Stress Accelerated Degradation Model -- 8.3 Statistical Inference -- 8.4 Optimal Strategy -- 8.5 Illustration Example -- 8.5.1 Statistical Inference -- 8.5.2 Optimal Strategy -- 8.6 Conclusion and Discussion -- Appendix -- References -- 9 Gamma Degradation Models: Inference and Optimal Design -- 9.1 Introduction -- 9.2 Degradation Model Based on Gamma Process -- 9.2.1 Definition of Gamma Process -- 9.2.2 Distribution of Product's Lifetime -- 9.3 Design and Inference of Degradation Experiment -- 9.3.1 Degradation Tests -- 9.3.2 Accelerated Degradation Tests -- 9.3.3 Step-Stress Accelerated Degradation Tests -- 9.4 Extensions and Some Applications -- 9.4.1 Multiple Quality Characteristics -- 9.4.2 Inspection Model and Maintenance Decision -- 9.4.3 Burn-In Test -- 9.5 Concluding Remarks -- References -- 10 Misspecification Analysis of Gamma with Inverse Gaussian Degradation Processes -- 10.1 Introduction -- 10.2 A Motivating Example -- 10.3 Misspecifying Gamma Process as Inverse Gaussian Process When δ Is Known -- 10.4 Misspecifying Gamma Process as Inverse Gaussian Process When δ Is Unknown -- 10.5 Data Analysis -- 10.6 Conclusions -- References -- Part III Applications -- 11 Practical Applications of a Family of Shock-Degradation Failure Models -- 11.1 Introduction -- 11.2 Shock-Degradation Failure Models -- 11.2.1 The Shock Process -- 11.2.2 The Degradation Process -- 11.2.3 The Shock-Degradation Survival Distribution -- 11.3 Data Structures -- 11.3.1 Direct Readings on the Degradation Process -- 11.3.2 Observations on Failure Times, System Strength and Shocks -- 11.4 Joint Observation of Survival and Degradation -- 11.5 Case Applications -- 11.5.1 Osteoporotic Hip Fractures -- 11.5.2 Norwegian Divorces -- 11.5.3 Survival Times for Cystic Fibrosis Patients -- 11.6 Discussion and Concluding Remarks -- References.

12 Statistical Methods for Thermal Index Estimation Based on Accelerated Destructive Degradation Test Data -- 12.1 Introduction -- 12.1.1 Background -- 12.1.2 Related Literature -- 12.1.3 Overview -- 12.2 Accelerated Tests and Thermal Index -- 12.2.1 Test Plans -- 12.2.2 Data and Notation -- 12.2.3 Thermal Index -- 12.3 Statistical Methods for Thermal Index Estimations -- 12.3.1 The Traditional Method -- 12.3.2 The Parametric Method -- 12.3.3 The Semiparametric Method -- 12.4 An Illustration of Thermal Index Estimation -- 12.4.1 Degradation Path Modeling -- 12.4.2 TI Estimation -- 12.5 Simulation Studies -- 12.5.1 Simulation Settings -- 12.5.2 Results Under the Correct Model -- 12.5.3 Results Under a Misspecified Model -- 12.6 Discussions -- References -- 13 Inference on Remaining Useful Life Under Gamma Degradation Models with Random Effects -- 13.1 Introduction -- 13.2 Gamma Degradation Model with Random Effects -- 13.3 Remaining Useful Life -- 13.4 Statistical Inference on Remaining Useful Life -- 13.5 Monto Carlo Simulation Study -- 13.6 Illustrative Example: LED Degradation Data -- 13.7 Concluding Remarks -- Appendix -- References -- 14 ADDT: An R Package for Analysis of Accelerated Destructive Degradation Test Data -- 14.1 Introduction -- 14.2 The Statistical Methods -- 14.2.1 Data -- 14.2.2 The Traditional Method -- 14.2.3 The Parametric Method -- 14.2.4 The Semiparametric Method -- 14.3 Data Analysis -- 14.4 Concluding Remarks -- References -- 15 Modeling and Inference of CD4 Data -- 15.1 Introduction -- 15.2 Exploratory Data Analysis -- 15.3 Statistical Inference -- 15.3.1 Inferential Model -- 15.3.2 False Discovery Rate (FDR) -- 15.4 Conclusion -- References -- 16 State Space Models Based Prognostic Methods for Remaining Useful Life Prediction of Rechargeable Batteries -- 16.1 Introduction.

16.2 A Particle Filtering Based State Space Model for Battery Remaining Useful Life Prediction at a Constant Discharge Rate.

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