Mathematical Models for Systems Reliability

Evolved from the lectures of a recognized pioneer in developing the theory of reliability, this text provides a rigorous treatment of the required probability background for understanding reliability theory. It introduces statistical estimation theory and measures of system effectiveness and applies results of general continuous-time Markov chains to n-unit repairable systems. It also presents several methods for computing the transition probabilities matrix and shows how certain techniques can be applied to a range of reliability problems, including preventive maintenance. The text includes numerous examples and exercises, along with a solutions manual for qualifying instructors.

This classroom-tested text begins by discussing the Poisson process and its associated probability laws. It then uses a number of stochastic models to provide a framework for life length distributions and presents formal rules for computing the reliability of nonrepairable systems that possess commonly occurring structures. The next two chapters explore the stochastic behavior over time of one- and two-unit repairable systems. After covering general continuous-time Markov chains, pure birth and death processes, and transitions and rates diagrams, the authors consider first passage-time problems in the context of systems reliability. The final chapters show how certain techniques can be applied to a variety of reliability problems.

Illustrating the models and methods with a host of examples, this book offers a sound introduction to mathematical probabilistic models and lucidly explores how they are used in systems reliability problems.