Modeling discrete bathtub and upside-down bathtub mean residual-life functions

A general modeling approach is presented that allows parametric modeling of the mean residual life so that maximum-likelihood estimation of models can be done. This will enable such parametric models to be estimated for complete discrete data as well as right-censored discrete data. A simple example is presented where the mean residual life increases, then decreases; however, the hazard rate also increases, drops suddenly at one cycle, and then increases again. Two reasonable industrial explanations of such unusual behavior are discussed.>