AN ADAPTIVE AGE REPLACEMENT POLICY

Abstract
Under an age replacement policy we replace at failure or at the end of a specified time interval, whichever occurs first. This makes sense if a failure replacement costs more than a planned replacement and the failure rate is strictly increasing. We assume that the failure distribution is a Weibull distribution with known shape parameter (greater than one) and unknown scale parameter. Moreover, we assume that a natural conjugate prior distribution with specified parameters is at hand which we modify after each stage according to Bayes' rule. Our policy adapts to the changing prior. We see intuitively that the larger the replacement interval set, the more information we are likely to obtain. We take account of this in a precisely defined manner via dynamic programming. The optimal policy is partially characterized and various limiting results are obtained.

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