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)
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1 Introduction
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10.4 Approximation Method

This section presents fast approximation models based on the central limit theorem (CLT) for reliability analysis of 1‐out‐of‐n homogeneous and heterogeneous cold standby systems. Refer to [39] for the extension of the approximate model to a more general k‐out‐of‐n cold‐standby system requiring k primary and online components. Refer to [40] for another extension of the approximate method for reliability analysis of warm standby systems.

10.4.1 Homogeneous Cold Standby System

Consider a homogeneous cold standby system with n s‐identical components with A1 being the primary component and A2, …, An being cold standby spares, which are used in the order of their indices. Specifically, when A1 fails at time T1, it is replaced by A2; when A2 fails at time T1 + T2, it is replaced by A3, and so on. The replacement is assumed to happen instantaneously. The time durations T1, T2, … are assumed to be...