A general approach to the shape of failure rate and mean residual life functions

Failure rate and mean residual life are two important characteristics for studying reliability of products. In literature, some work studied the shape of failure rate function based on the knowledge of the associated probability density function; some other work investigated the shape of mean residual life function based on the shape of the associated failure rate function separately for continuous case and discrete case. In this article, a general approach is developed which can be applied to the aforementioned studies.