Accurate reliability modeling using Markov Analysis with non-constant hazard rates

Abstract

This paper combines the concepts of Markov analysis and the approximation of the failure characteristics of wear out components with Weibull distribution to arrive at an accurate and practical method for solving complex system reliability modeling problems. Present reliability models in the most part are based on constant failure rates wherein the probability of a component failure remains independent of the past history of the component operation. However, many complex systems have components with wear out failure characteristics. For such components the failure rates are not constant rather these change with the period of operation of the component. The most common method currently utilized in practice for handling the reliability predictions of systems having components with non constant failure rates are based on Monte Carlo simulations. However, to obtain the required high accuracies for moderately complex system reliability models, Monte Carlo simulations may require excessive computer time. In contrast, the solution of the mathematical models developed in this paper requires relatively insignificant computer time while achieving high prediction accuracies. The paper also presents some examples of systems of practical interest.