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

2.1 Basic Probability Concepts

Random experiment is an experiment with its outcome being unknown ahead of time but all of its possible individual outcomes being known [1]. The set of all possible outcomes of a random experiment constitutes its sample space, denoted by Ω. Each individual outcome in the sample space is referred to as a sample point.

A subset of a sample space associated with a random experiment is defined as an event that occurs if the experiment is performed and the outcome observed is in the subset defining the event. There are two special events: a certain event (sample space itself Ω) that occurs with probability ONE (1) and an impossible event (empty set ∅) that occurs with probability ZERO (0). Because events are sets, the operations in the set theory like complement, union, and intersection can be applied to generate new events.

If two events A and B do not share any common sample points, i.e. A ∩ B = ∅, then A and B...