A Monte Carlo approach to the estimation of importance measures of multi-state components

A generalization of some frequently used importance measures has been proposed by the authors in a previous paper to characterize the importance that a multi-state component achieves a given level of performance for the overall multi-state system performance. The definitions of the measures are based on the conditional probabilities that a component reaches at most or at least a given level of performance. The present paper proposes a new Monte Carlo approach which allows estimating in a single simulation the importance of the various components achieving given levels of performance. This is done by means of properly devised counters for the simultaneous estimation of the system performance when all of the components evolve through all of their reachable performance levels, and of the system performance when the components are restricted to have at most or at least a given level of performance. The flexibility of the Monte Carlo method is exploited to account for the load-sharing dependencies among parallel components. The approach is tested on a sample multi-state transmission system of literature.