  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, and assume that the total sample size for the experience 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.
