On the distribution of state of the system subject to random shock

Abstract

Most of the systems come to break down as time goes by. We assume the deteriorating process from the initial state of the system to breakdown as the shock occurrence process. The shock comes to the system according to a Poisson process and deteriorate the system state by random amount. The repairman randomly visits the system to observe the state of the system. The system is repaired by (β,α) policy. The objective of this thesis is to derive the distribution function of the state of the system having the random shock. To begin with, we analyzed the system under the exponential repair time. We got the characteristic functions of the state of the system and meaningful probability values through cycle analysis. Also, we got the explicit distribution function of the state of the system using the renewal function. And, we generalized the repairman visit process.