Useful Periods for Lifetime Distributions With Bathtub Shaped HazardRate Functions

Abstract

We propose computationally tractable formal mathematical definitions for the 'useful period' of lifetime distributions with bathtub shaped hazard rate functions. Detailed analysis of the reduced additive Weibull hazard rate function illustrates its utility for identifying such useful periods. Examples of several other bathtub shaped hazard rate functions are also presented with applications to lifetime data. The suggestion is made of defining and considering analogous 'stable periods' in the case of the corresponding upside-down bathtub shaped mean residual life functions.