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 Schur-constant joint survival function. Such a property defines a special case of exchangeability, corresponding to a multivariate no aging condition, in a Bayesian set-up. In the longitudinal observation of our random variables, the pair (Number of failures, Total time on test) is a Markov process which has a central role. Our main result result shows that such a process is stochastically increasing if and only if the variables are WBF (Weakened By Failure).