WBF PROPERTY AND STOCHASTICAL MONOTONICITY OF THE MARKOV PROCESS ASSOCIATED TO SCHUR-CONSTANT SURVIVAL FUNCTIONS

We concentrate attention on non-negative absolutely continuous random variables with a Schuu-constant joint survival function. Such a proper ty defines a special case of exchangeability, corresponding to a multi variate no aging condition, in a Bayesian set-up. In the longitudinal observation of our random variables, the pair (Number of failures, Tot al time on test) is a Markov process which has a central role. Our mai n result result shows that such a process is stochastically increasing if and only if the variables are WBF (Weakened By Failure). (C) 1996 Academic Press, Inc.