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
End User License Agreement

10.2 CTMC‐Based Method

As discussed in Section 2.5, system states and state transitions are two essential concepts of the Markov‐based method [29]. A system state is defined by a specific combination of component state variables at a given instant of time. A state transition occurs due to the failure or repair of a system component [30]. The CTMC‐based methods assume exponential time‐to‐failure and time‐to‐repair distributions for the system components.

The solution to a CTMC model with n different states includes the probability of the system being in each state, particularly, Pj(t) that denotes the probability that the system is in state j at time t (j = 1,…,n). They can be obtained by solving a set of differential equations in the form of (2.26), which is

(10.1)equation α 11 α 21 α 31 α n 1 α 12 α 22 α 32 α n 2 ...