Bayesian analysis of optimal burn-in policy for heterogeneous components with minimal repair

This study develops a Bayesian method to analyze optimal burn-in policy for heterogeneous components with minimal repair. We use the non-homogeneous Poisson processes with different power law intensity functions to model the minimal repair processes for heterogeneous components. Since the component from the weak subpopulation may fail more frequently, the total number of minimal repairs can be used for establishing a screening rule. By screening, we can decide whether the component after burn-in should be eliminated or not. Considering the uncertainty of model parameters, we generate a minimally repaired data set of components by simulation. Then, we obtain the model parameters estimators by using Bayesian method combined with the existing data. We further analyze and get the optimal burn-in settings under cost and performance optimization model. A numerical example is used to verify the effectiveness of the Bayesian method.