The Effect of Correlation on the Reliability of Series Systems with Joint Normally Distributed Component Failure Times

Abstract

A practice in systems reliability studies has been to assume that the components making up these systems fail independently, i.e., correlation effects are ignored. As a result, the reliability computations are somewhat simplified. Correlation among the system components, however, will in fact result in a system reliability which may be quite different from that computed under the assumption of independence. For serial systems, distributions are developed for the multivariate normal. The reliability of serial systems undergoing these failure distributons is then investigated for selected values of correlation. Comparison is made with reliability values assuming independent failure, computed using the 'product rule' by multiplying the component reliabilities. The differences between these two estimates are tabulated and graphed. An analysis of the results indicates that increasing system complexity and correlation is accompanied by a corresponding increase in the reliability difference, and for certain parametric values the effect of correlation can be quite important.