Reliability of a system under a new mixed shock model

Abstract

In this paper, we investigate the lifetime reliability of a system under a new mixed shock model. Consider a system whose efficiency is $k.$ If the magnitude of the shock is greater than $d$ or the interarrival time between two consecutive shocks is less than δ, the efficiency of the system reduces by one unit. If $k_1$ denotes the number of shocks that have the magnitude greater than $d$ and $k_2$ demonstrates the number of the interarrival times between two consecutive shocks is less than δ while, $k_1+k_2=k,$ as a results, the system loses its efficiency and fails. The system lifetime reliability function, the reliability of system lifetime in a perfectly functioning state and the reliability of system lifetime in partially working states have been calculated. The effect of critical points values on the reliability function of the system lifetime has been studied by using the simulation.

Keywords:

• Mixed shock model
• extreme shock model
• $\delta$-shock model
• reliability function

Acknowledgement

The authors are grateful to the reviewers for their valuable encouraging comments and suggestions.

Additional information

Funding

This work is supported by the Shahid Chamran University of Ahvaz (grant number: SCU.MS99.118).