Research on Bayesian Reliability Evaluation Method of Repairable Systems Based on Power Law Process under Interval Uncertain Information

Bayesian method is commonly used in the reliability assessment of repairable systems with small samples in fields such as aerospace.The knowledge about the informative prior and/or failure data from repairable systems may not be collected as precisely as possible due to uncertain factors,but can be obtained in terms of lower and upper bounds.For the case of such interval uncertainty information,the Bayesian reliability analysis method of multiple repairable whose failure process can follow the power law process(PLP)is studied in this paper.Under the informative priors,the interval-based Bayesian posterior analysis of the PLP is essentially transformed into solving the constrained optimization problem in which the objective function is just the traditional Bayesian posterior analysis result of the PLP under the informative priors.The feasibility and effectiveness of the proposed method is verified with specific enginee-ring examples.The results show that the proposed interval-based Bayesian method of the PLP can provide a refe-rence method for the reliability assessment of repairable systems with small samples in consideration of the influence of uncertain factors.