Bounds for the failure rate in heterogeneous populations
South African Statistical Journal, 41:1, 23–37 (2007)
We derive bounds for the mixture failure rate in the multiplicative (proportional hazards) model. We explicitly show that the corresponding proportionality in subpopulations does not result in proportionality for a whole population. We analyze the shape of the mixture failure rate in an environment with a stress change point and also discuss the effect of shocks which change a mixing distribution.