Mean residual lifetime assessment approach for a multi-state standby system

In this paper, a new MRL assessment approach for a multi-state standby system is considered. The three-state system is backed up with a binary cold standby unit. Given that the system is at a specific state at time t, obtaining the MRL is worth considering in conducting the maintenance and repair plans of the system. For different degradation rates and time points, MRL results are examined. An HCTMP is considered for the degradation. Therefore, when the system is observed to be at its perfect state, the MRL decrease with an increase in all the failure rates of the system. However, when the system is observed to be at its partial state, the MRL is not affected by the increase in the failure rate pertained to the perfect state. The MRL when the system has known to be failed before time t and backed up with the standby unit increases with the time increase whereas the MRL when the system is at its perfect(or partial) state is constant when time increases. Moreover, cost evaluation of the system is analyzed. The results are supported with numerical examples and graphical representations.

Automated summary

This paper presents a new MRL assessment approach for a multi-state standby system with a binary cold standby unit. The MRL results are examined for different degradation rates and time points using an HCTMP model. The study finds that when the system is in a perfect state, the MRL decreases with an increase in all failure rates. However, when the system is in a partial state, the MRL is not affected by an increase in failure rates related to the perfect state. The paper also analyzes the cost evaluation of the system and provides numerical examples and graphical representations to support the results.