An Adaptive Bayesian Replacement Policy with Minimal Repair

In this study, an adaptive Bayesian decision model is developed to determine the optimal replacement age for the systems maintained according to a general age replacement policy. It is assumed that when a failure occurs, it is either critical with probability p or non-critical with probability 1− p, independently. A maintenance policy is considered where the non-critical failures are corrected with minimal repair and the system is replaced either at the first critical failure or at age τ whichever occurs first. The aim is to find the optimal value of τ which minimizes the expected cost per unit time. Two adaptive Bayesian procedures which utilize different levels of information are proposed for sequentially updating the optimal replacement times. Posterior density/mass functions of the related variables are derived when the time to failure for the system can be expressed as a Weibull random variable. Some simulation results are also presented for illustration purposes.