Bayesian sequential estimation of the reliability of a parallel-series system

We give a risk-averse solution to the problem of estimating the reliability of a parallel-series system. We adopt a beta-binomial model for components reliabilities. Assuming that the total sample size for the experiment is fixed, the allocation at subsystems or components level may be random. Based on the sampling schemes for parallel and series systems separately, we propose a hybrid sequential scheme for the parallel-series system. Asymptotic optimality of the Bayes risk associated with quadratic loss is proved with the help of martingale convergence properties. A comparison is given with the best fixed design with numerical examples.