On some properties of the IDMRL class of life distributions

In this paper we consider some properties of the IDMRL class of life distributions, which have not been addressed in the literature thus far. Specifically we show that the IDMRL class of life distributions are closed under weak convergence. The second result concerns preservation under the Poisson shock model. We know that if shocks arrive according to a homogeneous Poisson process and P ¯ k is the probability of surviving the first k shocks, then H ¯ ( t ) = ∑ k = 0 ∞ P ¯ k P [ N ( t ) = k ] is the probability that the device survives beyond time. We show that if P ¯ k has the discrete IDMRL property, then H ¯ ( t ) is continuous IDMRL. We also investigate some closure properties of IDMRL distributions.