FAILURE DISTRIBUTIONS OF GENERALIZED SHOCK MODELS AND THEIR APPLICATION

A generalized shock model is studied. The probability $\bar{P}_k(t)$ of surviving k shocks at time t depends not only on k, but also on the age of the system. So the survival probability can be written as: $\bar{H}(s)=\sum_{k=0}^{\infty} \bar{P}_k(t) P\{N(t)=k\}$. For generalized Poisson shock process and the continuous wear process with stationary independent nonnegative increments, we studied some appropriate conditions under which the survival probabilities are IFR, IFRA, NBU, NBUE respectively. For instance under the condition that $\bar{P}_k(t)$ is bivariate IFR（NBU） and other conditions, H is IFR （NBU）. We give some applications of the theory.