Properties of classes of life distribution based on the conditional variance

Abstract

We consider two classes of life distribution, VD and VI, the members of which are defined in terms of the conditional variance σ2(t) of the remaining lifetime of a system: a life distribution F belongs to VD if is a decreasing function and to VI if is increasing. We study closure properties of these classes under relevant reliability operations such as mixing, convolution and formation of coherent systems. We show, for example, that the class VD is not closed under convolution or mixing, and that the class VI is not closed under formation of coherent systems.