A universal generating function-based multi-state system performance model subject to correlated failures

Multi-state system (MSS) reliability modeling is a paradigm that allows both systems and components to exhibit more than two performance levels. While several researchers have introduced correlation or dependence into MSS models to assess its negative influence on performance and associated measures, these methods exhibit complexity that is exponential or worse in the worst case. To overcome this limitation, this paper proposes an extension to the discrete universal generating function approach for MSS to allow correlation between the elements comprising a multi-state component. We subsequently generalize to the continuous case and allow failures to follow any life distribution. The approach possesses an analytical form and therefore enables efficient performance and reliability assessment as well as sensitivity analysis on the impact of correlation. This sensitivity analysis can be applied to a wide range of measures including performance, reliability, the density function, hazard rate, mean time to failure, availability, and mean residual life. The approach is illustrated through a series of examples, demonstrating the efficiency of the approach to assess performance and reliability as well as to conduct sensitivity analysis. The results indicate that the approach can identify the impact of correlation on performance, reliability, and the many measures of interest.