#### 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.
Preface
Free Chapter
Nomenclature
1 Introduction
2 Fundamental Reliability Theory
3 Imperfect Fault Coverage
4 Modular Imperfect Coverage
5 Functional Dependence
6 Deterministic Common‐Cause Failure
7 Probabilistic Common‐Cause Failure
9 Probabilistic Competing Failure
10 Dynamic Standby Sparing
Index

# 9.2 System with Single Type of Component Local Failures

A combinatorial methodology is presented for reliability analysis of nonrepairable single‐phase systems subject to the PFD behavior. Each system component undergoes PFGEs and a single or identical type of LFs.

## 9.2.1 Combinatorial Method

The method involves a five‐step procedure described as follows.

• Step 1: Separate effects of PFGEs from the trigger component. According to the PFGE approach (Section 8.2), particularly (8.1), the system unreliability is evaluated as
(9.1) UR system t = 1 P u t + Q t · P u t , --

where Pu(t) = P (no PFGEs from the trigger component T take place during the mission) = 1 − qTp(t). Q(t) in (9.1) is evaluated through the following steps.

• Step 2: Define probabilistic functional dependence cases (PFDCs). PFDCs are identified to cover all possible isolation relationships between the trigger component and related PDEP‐components belonging...