Variance residual life function in reliability studies

摘要

In life testing situations, the additional life time given that the component has survived upto time t is called the residual life function (RLF) of the component. More specifically, if X is the life of a component, then the random variable X_t = X — t∣X > t is called the residual life function. In this paper we study the Var(X_t), its monotonicity and the associated aging classes of distributions. It is shown that, under mild conditions, Var(X_t) determines the distribution. Some characterization results of the class of decreasing (increasing) variance residual life function are presented and the closure of these classes under some reliability operations is studied.