Book Image

Dynamic System Reliability

By : Liudong Xing, Gregory Levitin, Chaonan Wang
Book Image

Dynamic System Reliability

By: Liudong Xing, Gregory Levitin, Chaonan Wang

Overview of this book

This book focuses on hot issues of dynamic system reliability, systematically introducing the reliability modeling and analysis methods for systems with imperfect fault coverage, systems with function dependence, systems subject to deterministic or probabilistic common-cause failures, systems subject to deterministic or probabilistic competing failures, and dynamic standby sparing systems. It presents recent developments of such extensions involving reliability modeling theory, reliability evaluation methods, and features numerous case studies based on real-world examples. The presented dynamic reliability theory can enable a more accurate representation of actual complex system behavior, thus more effectively guiding the reliable design of real-world critical systems. The book begins by describing the evolution from the traditional static reliability theory to the dynamic system reliability theory and provides a detailed investigation of dynamic and dependent behaviors in subsequent chapters. Although written for those with a background in basic probability theory and stochastic processes, the book includes a chapter reviewing the fundamentals that readers need to know in order to understand the contents of other chapters that cover advanced topics in reliability theory and case studies.
Table of Contents (14 chapters)
Free Chapter
1 Introduction
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3.4 Multi‐State System

MSSs are systems in which the system and/or its components can exhibit multiple states or performance levels [21]. Particularly, consider an MSS with n multi‐state components and w different system states or performance levels. Each component j under the IPCM has mj + 1 states (j = 1, …, n). Among these states, state 0 corresponds to the UF of component j, state 1 corresponds to the covered failure of component j, states 2, …, mj correspond to different performance levels of the component operational state. Let xj denote the state indicator variable of component j, imagespj,kIt--j is in state k at time t under the IPCM, i.e. imagespj,kIt=Pxj=k--Table 3.1 illustrates the state and probability space of multi‐state component j under IPCM.

Table 3.1 State space of multi‐state component j [22].

Operational states Failed states
different performance levels imagesPxj=mj=pj,mjIt--