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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4.3 Repairable Hierarchical System

For HSs with components subject to independent repair, a separable approach similar to that in Section 4.2 is combined with the Markov method for the system availability analysis [2] .

The possible states for each component A located at layer i of a repairable HS include: operational state (AiO), covered failure state (AiC), layer i UF state (AiUi), layer (i + 1) UF state (imagesAiUi+1--L UF state (imagesAiUL--Figure 4.7 shows the continuous time Markov chain (CTMC) modeling the failure and repair behavior of component A at layer i.

FT of CTMC for component A at layer i displaying node AiO linked by exchange arrows with nodes labeled AiC, AiUL, AiUi+1, and AiUi.

Figure 4.7 CTMC for component A at layer i [2] .

Solving the CTMC of Figure 4.7 , the state occupation probability for each state P(AiO), P(AiC), P(AiUi), P(AiUi + 1), ..., P(AiUL) can be obtained. The separable approach presented in Section 4.2 can then be similarly applied to separate the consideration of layer i UF from the combinatorics of the solution to evaluating the unavailability of a...