An Allocation Scheme for Estimating the Reliability of a Parallel-Series System

Abstract

We give a hybrid two-stage design which can be useful to estimate the reliability of a parallel-series and/or by duality a series-parallel system. When the components' reliabilities are unknown, one can estimate them by sample means of Bernoulli observations. Let T be the total number of observations allowed for the system. When T is fixed, we show that the variance of the system reliability estimate can be lowered by allocation of the sample size T at components' level. This leads to a discrete optimization problem which can be solved sequentially, assuming T is large enough. First-order asymptotic optimality is proved systematically and validated T Monte Carlo simulation.