A High-Order Saddlepoint Method for Bayesian System Evaluation

Abstract

How to evaluate the system reliability through the test data of components is one of the key challenges in the field of reliability. In this study, the authors focus on calculating the Bayesian lower credible limit. Although the approximation methods are widely used in reliability evaluation, how to apply them to the Bayesian context remains to be solved. Some previous studies have attempted to address this issue. However, their approaches might result in instability, and they have imposed significant constraints on component and system structures. A high-order saddlepoint approximation method for high accuracy is proposed, as well as a feasible procedure for determining the saddlepoint method’s asymptotic variable. The proposed framework allows us to analyze the components following various posterior distributions without limiting the system structure. Numerical experiments on various systems are presented to demonstrate the effectiveness and accuracy of the proposed method. In comparison, it consistently outperforms other commonly used approximation approaches.