State-Transition Monte Carlo for Evaluating Large, Repairable Systems

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.