Bayesian reliability analysis of a products of probabilities model for parallel systems with dependent components

Abstract

In a Bayesian reliability analysis of a system with dependent components, an aggregate analysis (i.e. system-level analysis) or a simplified disaggregate analysis with independence assumptions may be preferable if the estimations obtained from employing these two approaches do not deviate substantially from those derived through a disaggregate analysis, which is generally considered the most accurate method. This study was conducted to identify the key factors and their range of values that lead to estimation errors of great magnitude. In particular, a copula-based Bayesian reliability model was developed to formulate the dependence structure for a products of probabilities model of a simple parallel system. Monte Carlo simulation, regionalised sensitivity analysis and classification tree learning were employed to investigate the key factors. The resulting classification tree achieved favourable predictive accuracy. Several decision rules suggesting the optimal approach under different combinations of conditions were also extracted. This study has made a methodological contribution in laying the groundwork for investigating systems with dependent components using copula-based Bayesian reliability models. With regard to practical implications, this study also derived useful guidelines for selecting the most appropriate analysis approach under different scenarios with different magnitude of dependence.