Reliability Estimation in Coherent Systems

TL;DR

This paper develops Bayesian and parametric methods for estimating the reliability of complex coherent systems, including series-parallel and parallel-series configurations, even with unknown component reliabilities.

Contribution

It introduces nonparametric Bayesian estimators for sub-distribution functions and Weibull-based parametric estimators for component reliabilities in complex systems.

Findings

Nonparametric Bayesian estimators for sub-distribution functions.

Weibull model-based parametric reliability estimators.

Discussion of reliability estimation with masked data.

Abstract

Usually, methods evaluating system reliability require engineers to quantify the reliability of each of the system components. For series and parallel systems, there are some options to handle the estimation of each component's reliability. We will treat the reliability estimation of complex problems of two classes of coherent systems: series-parallel, and parallel-series. In both of the cases, the component reliabilities may be unknown. We will present estimators for reliability functions at all levels of the system (component and system reliabilities). Nonparametric Bayesian estimators of all sub-distribution and distribution functions are derived, and a Dirichlet multivariate process as a prior distribution is presented. Parametric estimator of the component's reliability based on Weibull model is presented for any kind of system. Also, some ideas in systems with masked data are discussed.