Bayesian prior information fusion for power law process via evidence theory

The power law process (PLP) is widely used to analyze the failures of repairable systems, and the PLP parameter estimation is the primary concern for reliability assessment or maintenance decision making. Although the Bayesian estimation of the PLP has been studied in existing research, little attention has been paid to how to obtain its prior distribution, especially when the prior information is coming from multiple sources. To address this problem, a framework for Bayesian prior information fusion using evidence theory is proposed in this paper. This framework first uses evidence theory to represent the prior information from multiple sources or experts and then combines them into fused information. Based on the belief and plausibility functions of the fused information, the prior distribution is bounded by an upper and lower probability density functions which are derived by moment equivalence. A case study is also carried out to verify and illustrate the proposed method. The results show that this proposed approach is beneficial for the Bayesian estimation of the power law process.