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

TL;DR

This paper presents a Bayesian sequential method for estimating the reliability of parallel-series systems using a beta-binomial model, optimizing sampling schemes to minimize risk asymptotically.

Contribution

It introduces a hybrid sequential sampling scheme for complex systems and proves its asymptotic optimality under quadratic loss.

Findings

Proposed a hybrid sequential sampling scheme for parallel-series systems

Proved asymptotic optimality of the Bayes risk with martingale convergence

Applicable to fixed total sample size with random component allocation

Abstract

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.