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Reliability Bounds for Exponential Mixtures

We obtain some new reliability bounds for the class of life distributions which are exponential mixtures. It is shown that our bounds often improve on the usual DFR upper bound as well as those contained in the recent results of Shaked, Heyde and Leslie, Hall , and Brown. Simple sufficient conditions, under which such is the case, are developed. The main thrust of our findings is that our bounds are tighter for moderate to heavy departures from exponentiality. Among other results, it is shown that every DFR survival probability with a finite mean is stochastically strictly dominated by an exponential mixture. An application of our methods yields a new bound on the tail of the equilibrium distribution of a DFR renewal process, which can be tighter than the corresponding results of Brown.