Monotonicity of failure rate and mean residual life function of a gamma-type model

In reliability studies, the sense of variation of the hazard rate is of major concern since it indicates system wear out or burn in or in some cases a non-monotonic hazard rate. In this paper, we consider a generalized gamma distribution and study, in detail, the monotonicity of its failure rate and the mean residual life function. This involves the investigation of the monotonic structure of a transform function and then using this structure, we study the monotonic structure of the failure rate and the mean residual life function. Some of the known results follow as special cases of our results.