Fast Simulation of Highly Dependable Systems with General Failure and Repair Processes

Abstract

Computing dependability measures of repairable systems with general failure and repair processes is difficult, in general, using either analytical or numerical methods. Monte Carlo simulation could be used to solve this problem; however, in highly dependable systems standard simulation takes a very long time to estimate system reliability and availability with reasonable accuracy because typically’ the system failure is a rare event. When all failure and repair time distributions are exponential, importance sampling has been used successfully to reduce simulation run lengths. In this paper, we extend the applicability of importance sampling to non-Markovian models with general failure and repair time distributions. We show that by carefully selecting a heuristic for importance sampling, orders of magnitude reduction in simulation run lengths can be obtained. We study the effect of periodic maintenance on systems with components having increasing and decreasing failure rate. Also, we study the effect of the component’s lifetime distribution on the component’s redundancy needed to satisfy a particular system reliability goal. For general failure and repair processes, such studies are not possible with any of the conventional methods known from the literature; simulation is the only alternative and importance sampling makes it feasible. © 1993 IEEE