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.

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Table of Contents (14 chapters)
Preface
Preface
Free Chapter
1
Nomenclature
Nomenclature
2
1 Introduction
1 Introduction
References
3
2 Fundamental Reliability Theory
2 Fundamental Reliability Theory
2.1 Basic Probability Concepts
2.2 Reliability Measures
2.3 Fault Tree Modeling
2.4 Binary Decision Diagram
2.5 Markov Process
2.6 Reliability Software
References
4
3 Imperfect Fault Coverage
3 Imperfect Fault Coverage
3.1 Different Types of IPC
3.2 ELC Modeling
3.3 Binary‐State System
3.4 Multi‐State System
3.5 Phased‐Mission System
3.6 Summary
References
5
4 Modular Imperfect Coverage
4 Modular Imperfect Coverage
4.1 Modular Imperfect Coverage Model
4.2 Nonrepairable Hierarchical System
4.3 Repairable Hierarchical System
4.4 Summary
References
6
5 Functional Dependence
5 Functional Dependence
5.1 Logic OR Replacement Method
5.2 Combinatorial Algorithm
5.3 Case Study 1: Combined Trigger Event
5.4 Case Study 2: Shared Dependent Event
5.5 Case Study 3: Cascading FDEP
5.6 Case Study 4: Dual Event and Cascading FDEP
5.7 Summary
References
7
6 Deterministic Common‐Cause Failure
6 Deterministic Common‐Cause Failure
6.1 Explicit Method
6.2 Efficient Decomposition and Aggregation Approach
6.3 Decision Diagram–Based Aggregation Method
6.4 Universal Generating Function–Based Method
6.5 Summary
References
8
7 Probabilistic Common‐Cause Failure
7 Probabilistic Common‐Cause Failure
7.1 Single‐Phase System
7.2 Multi‐Phase System
7.3 Impact of PCCF
7.4 Summary
References
9
8 Deterministic Competing Failure
8 Deterministic Competing Failure
8.1 Overview
8.2 PFGE Method
8.3 Single‐Phase System with Single FDEP Group
8.4 Single‐Phase System with Multiple FDEP Groups
8.5 Single‐Phase System with PFs Having Global and Selective Effects
8.6 Multi‐Phase System with Single FDEP Group
8.7 Multi‐Phase System with Multiple FDEP Groups
8.8 Summary
References
10
9 Probabilistic Competing Failure
9 Probabilistic Competing Failure
9.1 Overview
9.2 System with Single Type of Component Local Failures
9.3 System with Multiple Types of Component Local Failures
9.4 System with Random Failure Propagation Time
9.5 Summary
References
11
10 Dynamic Standby Sparing
10 Dynamic Standby Sparing
10.1 Types of Standby Systems
10.2 CTMC‐Based Method
10.3 Decision Diagram−Based Method
10.4 Approximation Method
10.5 Event Transition Method
10.6 Overview of Optimization Problems
10.7 Summary
References
12
Index
Index
13
End User License Agreement
End User License Agreement

9.4 System with Random Failure Propagation Time

The methods presented in Sections 9.2 and 9.3 assume that any failure propagation originating from a system component instantaneously takes effect, which is often not true in real‐world cases [8]. In this section, a combinatorial method is presented for addressing random propagation time (PT) in the reliability analysis of single‐phase systems subject to the competing probabilistic failure isolation and failure propagation effects.

9.4.1 Combinatorial Method

The method involves a six‐step procedure described as follows:

  • Step 1: Separate effects of PFGEs from the trigger component. According to the PFGE approach (Section 8.2), the system unreliability is evaluated as
    (9.39)equation UR system t = 1 − P u t + Q t · P u t , --

    where Pu(t) = P(no PFGEs from the trigger, e.g. R), imagesQt=PXSFt|XRpCt--t (denoted by XSF(t)) given that the trigger undergoes no PFGEs (denoted by imagesXRpCt-- evaluated through...

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