TP2-Orderings and the IFR Property with Applications

Abstract

In this paper, TP2 orderings of distributions and of survival functions are considered. It is shown that the first passage time of a Markov process with TP2- ordered transition distributions has an increasing failure rate (IFR). Conditions are also given for which mixtures of IFR distributions are IFR. A formula is obtained for the failure rate when the strength distribution is a function of both load and strength. This formula, in conjunction with the TP2-ordering on the strength survival functions and log-concavity of the strength and load variables, leads to an increasing failure rate for the strength distribution. Finally, two models based on this theory are presented which explain the IFR character of the strength distribution of fibrous composite materials.