MATHEMATICAL ANALYSIS OF SYSTEM RELIABILITY USING MARKOV CHAINS

Paper Title

MATHEMATICAL ANALYSIS OF SYSTEM RELIABILITY USING MARKOV CHAINS

Abstract

In contrast, the solution of the mathematical models developed in this study requires relatively insignificant computer time while achieving high prediction accuracies. This facilitates the need for software tools such as Relex Software to handle the systems’ reliability. Many engineering systems are subject to failure after a given amount of time, and just how long a system will not fail depends on its design. Thus, a client of the Statistical Consulting Collaboratory requested an analysis of the reliability of his telecommunications system. One very useful useful technique in finding the reliability of a system is Markov modeling. This technique involves analytically finding the probability of the system being in each of its potential states, and when summed appropriately these state probabilities lead to the overall reliability of a system. However, for systems with a large number of states, solving for the reliability becomes increasingly tedious and complex. 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.
KEYWORDS : Markov chain, probability, Markov modeling, Monte Carlo, Relex Software.