Degradation processes in reliability / Waltraud Kahle, Sophie Mercier, Christian Paroissin.

Format:

Book

Author/Creator:

Kahle, Waltraud, author.

Mercier, Sophie, author.

Paroissin, Christian, author.

Series:

Mathematical models and methods in reliability set ; Volume 3.

Mathematical Models and Methods in Reliability Set ; Volume 3

Language:

English

Subjects (All):

Materials--Deterioration--Mathematical models.

Materials.

Stochastic processes.

Reliability (Engineering)--Mathematical models.

Reliability (Engineering).

Physical Description:

1 online resource (243 p.)

Edition:

1

Place of Publication:

Wiley 2016

Summary:

"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.

Contents:

Cover; Title Page; Copyright; Contents; Abbreviations and Notations; Introduction; 1: Wiener Processes; 2: Gamma Processes; 3: Doubly Stochastic Marked Poisson Processes; 4: Model Selection and Application to Real Data Sets; Bibliography; Index; Other titles from ISTE in Mathematics and Statistics; ELUA; 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; 1.1. 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; 2.1. Gamma distribution; 2.2. Poisson random measures; 2.3. Definition and basic properties of a gamma process; 2.4. Series representations; 2.5. Simulation; 2.7. 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; 3.1. Modeling degradation by marked point processes

3.2. Statistical inference4.1. Takeda device data; 4.2. Laser data; 4.3. Hudak crack growth data; 1.3.1. Random walk approximation; 1.3.2. Brownian bridge sampling; 1.3.3. Karhunen-Loève approximation; 1.6.1. Statistical inference for degradation data; 1.6.2. Statistical inference for time to failure data; 1.6.3. Statistical inference for both degradation and time to failure data; 1.7.1. Time-scaled Wiener processes; 1.7.2. Brownian motion with nonlinear drift; 2.5.1. Random walk approximation; 2.5.2. Gamma bridge sampling; 2.5.3. Compound Poisson process approximations

3.2.1. Maximum likelihood estimations3.2.2. Confidence estimations; 3.2.3. Moment estimates; 3.2.4. Comparison of maximum likelihood and moment estimates; 4.2.1. Parameter estimation; 4.2.2. Comparison of the estimations for the average degradation and the time to failure; 4.2.3. Procedures for selection model; 2.6.1. Introduction; 2.6.2. Theoretical results; 2.6.3. Simulation; 2.7.1.1. Maximum likelihood estimator; 2.7.1.2. Moments method estimator; 2.7.2.1. Estimation based only on failure data; 2.7.2.2. Estimation based on both degradation and failure data

2.7.2.3. Mixture of various cases

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781119307495

111930749X

9781119307488

1119307481