Dependence and Aging Aspects of Multivariate Survival

Abstract

Abstract The basic reliability concept of monotone failure rate is presented, and extensions to n variables are considered. We analyze Harris' multivariate extension of increasing failure rate, in particular his right corner set increasing property, which is a type of positive dependence. But we think that multivariate monotone failure rate need not involve dependence. Hence, increasing failure rate as extended in this article requires merely that the residual life of all subsets of a set of n survival times must be increasing. Decreasing failure rate is defined analogously and it is found that the multivariate exponential distribution forms the “boundary” between.