Statistical Modeling for Degradation Data 1st Edition by Ding Geng Chen, Yuhlong Lio, Hon Keung Tony Ng, Tzong Ru Tsai 9811051933 9789811051937

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ISBN-10 :  9811051933 

ISBN-13 :  9789811051937

Author:  Ding-Geng Chen, Yuhlong Lio, Hon Keung Tony Ng, Tzong-Ru Tsai 

This book focuses on the statistical aspects of the analysis of degradation data. In recent years, degradation data analysis has come to play an increasingly important role in different disciplines such as reliability, public health sciences, and finance. For example, information on products’ reliability can be obtained by analyzing degradation data. In addition, statistical modeling and inference techniques have been developed on the basis of different degradation measures. The book brings together experts engaged in statistical modeling and inference, presenting and discussing important recent advances in degradation data analysis and related applications. The topics covered are timely and have considerable potential to impact both statistics and reliability engineering.

Statistical Modeling for Degradation Data 1st Table of contents:

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 Tes
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
16.1 Introduction
16.2 A Particle Filtering Based State Space Model for Battery Remaining Useful Life Prediction at a
16.3 A Spherical Cubature Particle Filtering Based State Space Model for Battery Remaining Useful Li
16.4 A Particle Filtering Based State Space Model for Battery Remaining Useful Life Prediction at Di
16.5 Discussions
16.6 Conclusion Remarks
References
17 On System Identification for Accelerated Destructive Degradation Testing of Nonlinear Dynamic Sys
17.1 Introduction
17.2 System Identification
17.2.1 NARX Models
17.2.2 Hammerstein-Wiener Models
17.3 Data Set Generation
17.3.1 Road Profile Generation
17.3.2 Nonlinear Quarter Car Model
17.3.3 Quarter Vehicle Road Simulator
17.4 Spanning Basis Transformation Regression for Time Domain System Identification
17.4.1 SBTR
17.4.2 An Alternative View of Time Series Data
17.4.3 Feature Lengths and Regularisation
17.4.4 Visualising Model Performance
17.5 System Identification for Nonlinear Systems
17.6 Data Generation Strategies
17.6.1 Initial Data Generation Signal
17.6.2 Nonparametric Bootstrapping
17.6.3 Parametric Bootstrapping
17.6.4 Prototype Bootstrapping with K-means Clustering
17.7 Discussion and Conclusion

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Tags: Statistical Modeling, Degradation Data, Ding Geng Chen, Yuhlong Lio, Hon Keung Tony Ng, Tzong Ru Tsai