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Degradation Processes in Reliability

By: Waltraud Kahle, Sophie Mercier, Christian Paroissin

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Hardcover | 18 May 2016 | Edition Number 1

At a Glance

Hardcover
240 Pages

Dimensions(cm)
24.13 x 16.51 x 1.78

Hardcover

RRP $325.55

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Since a few decades, industrialists are collecting more and more online degradation data. This can be of great importance for highly reliable systems, for which failures are seldom observable. Consecutive deterioration measurements can be seen as the observation of a stochastic process, which is meant to represent the random evolution of the system deterioration level with time. In this setting, failure times correspond to the first passage time of the system deterioration level beyond a threshold.

In the book, the key concepts of degradation modeling by popular classes of stochastic processes (Wiener process, Gamma process, marked point processes) are developed. For each model, probabilistic properties of first passage times are provided, as well as simulation procedures. The statistical inference of the process from deterioration data is also addressed. Examples are used to illustrate the advantages and the differences between the different models.

The topic is very important for applications, and a reference book on this topic is missing. Most results are already published in scientific journals or in books collecting chapters from several authors. This book aims at gathering these results, jointly with a few additional new results, within a unified and rigorous mathematical framework. Examples with detailed explanations will illustrate the theory all along the book, to make the theory applicable.

Industry Reviews

"The main focus of the book is on parametric models. In such a case likelihood maximization is recommended as the main estimation method. The form of the likelihood function is always rigorously derived and the procedure of its maximization is discussed. If the covariance matrix of ML estimates is sufficiently simple, it is also presented. For some models, estimation by the method of moments is described; the corresponding equations are then also rigorously derived. The book also contains very detailed descriptions of various methods for simulation of considered degradation processes." (Mathematical Reviews/MathSciNet April 2017)

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