Distribution of Maximum Flow with Application to Multi-State Reliability Systems

摘要

This paper describes an efficient Monte Carlo sampling plan for estimating the distribution of maximum flow in a directed network whose arcs have random capacities. Such a network can be used to represent a multistate system whose multistate components are subject to deterioration in capacity by random amounts at random points in time. The proposed sampling plan uses an easily computed a priori upper bound on the complementary distribution function to obtain an unbiased point estimator with smaller variance than crude Monte Carlo sampling allows. The paper also describes procedures for interval estimation and for assessing when the sampling experiment has achieved a specified accuracy. To facilitate sampling, the paper presents a characterization of deterioration based on cumulative processes, leading to the treatment of arc capacities as being multinormally distributed. A technique is described for checking the appropriateness of this model with regard to lower and upper bounds on capacity. A procedure is also described for deriving a confidence interval on the measure used to assess variance reduction. An example illustrates the sampling plan and a concise summary gives all steps needed to implement the plan.