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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8.3 Single‐Phase System with Single FDEP Group

Based on the PFGE method, a combinatorial methodology is discussed in this section for analyzing reliability of a single‐phase system subject to competing failures involved in a single FDEP group or multiple independent (nonoverlapped) FDEP groups. The method is applicable to any arbitrary ttf distributions for the system components.

8.3.1 Combinatorial Method

Given that the trigger component(s) can only experience LFs. The method contains the following three steps:

  • Step 1: Define FDEP‐related events and evaluate event occurrence probabilities. Three events representing different occurrence sequences of the trigger event and PFGE events of the corresponding dependent components are defined as follows:
    • E1: the trigger event does not take place (i.e. the trigger component does not fail locally). Assume that the unconditional LF event of trigger component, e.g. A is YAl. P(E1) is calculated as:
      (8.7)equation P E 1 = P ...