State-Transition Monte Carlo for Evaluating Large, Repairable Systems

Abstract

This paper presents a new Monte Carlo method to estimate unreliabilities of large, repairable systems which can be modeled by a stationary Markov transition diagram. Sequences of state transitions ending at absorbing states are generated, using random numbers. Times to transitions related to the state-sequences are not generated. Next, the probability of system failure occurring in a mission time along each state-sequence is calculated. Finally, the arithmetic mean of these probabilities estimates the system unreliability. This state-transition Monte Carlo method yields better estimates in fewer trials than direct Monte Carlo methods. A cold-standby problem with non-identical units is also solved as a by-product of this paper. Copyright © 1980 by The Institute of Electrical and Electronics Engineers, Inc.