Change of Life Distribution Via a Hazard Transformation: An Inequality with Application to Minimal Repair

We introduce a general transformation of hazard rates and discuss the corresponding change of a life length distribution. Minimal repair transformations are shown to be special cases of this framework which builds on general results concerning likelihood ratios for point processes, and in particular on the Girsanov theorem for point processes. We then study the role of the available information and the consequent definition of “state” in the change of distributions. By using the general notion of F-minimal repair, where F stands for the information which identifies the state of the considered device, we show that the “black box”-minimal repair modeling leads to a stochastically longer total life length than the more realistic one based on internal state information. Thus the former forms a potential source of bias in minimal repair modeling.