Aging property of unimodal failure rate models

There is a family of statistical models, whose failure rate is unimodal or reverse bathtub shaped. For the situations where the failure is mainly caused by fatigue or corrosion, the time to failure is often represented by such models. This paper studies the aging property of such a class of models. It shows that a unimodal failure rate can be effectively viewed as increasing, decreasing, or constant, depending on the model parameters. Relevant quantitative measures are developed to identify to which case a given unimodal failure rate model belongs. Such two models, lognormal and inverse Weibull distributions, are analyzed.