Two notions of positive ageing based on stochastic dominance

The negative effects of age on the life length of a device or positive ageing are commonly used criteria for classifying life distributions. In this paper two notions of positive ageing are considered. These are the new better (worse) than used in average conditional survival probability and harmonic new better (worse) than used in upper tail. Closure of these notions under mixture and convolution are studied. The survivals of a device subject to discrete shocks of these notions of ageing which occur according to homogeneous Poisson processes are studied. A cumulative damage model is considered. Two test statistics are proposed for the two notions of ageing.