Evolved from the lectures of a recognized pioneer in developing the theory of reliability, Mathematical Models for Systems Reliability provides a rigorous treatment of the required probability background for understanding reliability theory.
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.
Preliminaries. Statistical Life Length Distributions. Reliability of Various Arrangements of Units. Reliability of a One-Unit Repairable System. Reliability of a Two-Unit Repairable System. Continuous-Time Markov Chains. First Passage Time for Systems Reliability. Embedded Markov Chains and Systems Reliability. Integral Equations in Reliability Theory. References. Index.