Applications of Duality and Stochastic Dominance in Reliability Theory.

摘要

In this paper we discuss a notion which is the dual of the failure rate and is defined as f(t)/F(t). This concept has come up several times in the literature, but has never been investigated in detail. In this paper the name survival rate is used. We show that in many models of practical interest the survival rates of certain random variables have nice properties. This makes it possible to obtain bounds on the distribution functions of these random variables. Moreover, we show that a form of stochastic dominance based on the survival rates of the random variables has some interesting applications. (Author)