Discrete time shock model with varying success probability

Abstract

Let us consider a system fails when the time between two consecutive shocks falls below a fixed threshold $\delta \in N$ and the system's lifetime is measured as the time up to the occurrence of this event. In this paper, we consider the interarrival times between $(i-1)$ i-th and $i$- th successive shocks follow a geometric distribution with mean 1/pi ,where pi =theta*pi-1, i=1,2,..., ,0<theta<1, 0<p<1. Under the above considerations, the distribution of system lifetime is obtained. Probability generating function and than also moments of system are derived. The proportion estimates of distribution parameters are studied. A numerical example is also presented buy using real data.