Discrete time shock model with varying success probability

Year 2019, Volume: 12 Issue: 1, 13 - 24, 31.07.2019

Kadir Karakaya , Yunus Akdoğan , Fatih Şahin İsmail Kınacı , Coşkun Kuş

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/p_i ,where p_i =theta*p^i-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.

Keywords

q-distributions, delta-Shock model, probabilty generating function

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