Shock model approach to change points with ERLANG threshold

Abstract

Cumulative damage process is related to shock models in reliability theory. The threshold or withstanding capacity of the system can be considered to be any one of the constant level, cumulative shock random threshold level, maximum shock random threshold etc. In this paper, cumulative shock random threshold level is considered wherein a system undergoes a shock and encounters random amount of damage but the system survives with the damages. Successive shocks at random epochs lead to the cumulative damages and when the cumulative damage crosses the threshold level of the system, the system fails. Assuming threshold level undergoes a change in the form of distribution after the change points are taken to be ERLANG random variable, the distribution function for the threshold level is obtained by taking exponential distribution as the threshold levels are before, in between and after the change points respectively. Using this distribution function for the threshold level, the expected time to the breakdown of the system and its variance are obtained by using shock model and cumulative damage process approach.