A note on two preservation properties of homogeneous Poisson shock models (Q1605828)

Given the probability density \(p\) for some device to survive the first \(k\) shocks and that shocks arrive in a Poisson stream. Then it is proved by direct computations that if \(p\) is unimodal about 0, i.e. nonincreasing, then the survival density of the device has this property as well. Under an additional restriction the order of mode, median, and mode of \(p\) is preserved by the mixing via the shock model representation.