Degradation Processes in Reliability 1st Edition by Kahle, Waltraud 9781119307525 111930752X

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ISBN 10: 111930752X
ISBN 13: 9781119307525
Author: Kahle, Waltraud

“Degradation process” refers to many types of reliability models, which correspond to various kinds of stochastic processes used for deterioration modeling.  This book focuses on the case of a univariate degradation model with a continuous set of possible outcomes. The envisioned univariate models have one single measurable quantity which is assumed to be observed over time. The first three chapters are each devoted to one degradation model. The last chapter illustrates the use of the previously described degradation models on some real data sets. For each of the degradation models, the authors provide probabilistic results and explore simulation tools for sample paths generation. Various estimation procedures are also developed.

Degradation Processes in Reliability 1st Table of contents:

I.1. From lifetime data to degradation path observations

I.2. A few real data sets

I.3. A brief overview of classical degradation models

I.4. The mathematical framework

I.5. Outline of the book

1 Wiener Processes

1.1. Gaussian distribution

1.2. Brownian motion

1.3. Constructions and simulation methods

1.4. Wiener process (Brownian motion with drift)

1.5. First passage time (time to failure)

1.6. Statistical inference

1.7. Extension and related models

2 Gamma Processes

2.1. Gamma distribution

2.2. Poisson random measures

2.3. Definition and basic properties of a gamma process

2.4. Series representations

2.5. Simulation

2.6. Hitting time (time-to-failure) and overshoot

2.7. Statistical inference in parametric models

2.8. Statistical inference in the semi-parametric model

2.9. Statistical inference for models with random effects (frailty model)

2.10. Extensions and related models

3 Doubly Stochastic Marked Poisson Processes

3.1. Modeling degradation by marked point processes

3.2. Statistical inference

4 Model Selection and Application to Real Data Sets

4.1. Takeda device data

4.2. Laser data

4.3. Hudak crack growth data

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Degradation Processes,Reliability,Kahle, Waltraud