Reliability Analysis of a Two Nonidentical Unit Parallel System with Optional Vacations under Poisson Shocks

In this article, we study the impact of some system parameters on an industrial system consisting of two nonidentical parallel units with one repairer. The active unit may fail due to essential factors such as aging or deterioration, or due to external phenomena such as Poisson shocks occurring at different time periods. Whenever the value of a shock is greater than the specified threshold of the active unit, the active unit fails. The article assumes that the repairman can make one of two decisions at the beginning of system operation: either he takes a vacation when the two units are operating normally, or he remains in the system to monitor it until the first failure of the system. If a failure occurs in either unit during the repairman’s absence, the failed unit must wait until the repairman is called back to work. We assume that the value of each shock is i.i.d. with a known distribution. The length of the repairman’s vacation, the repair time, and the recall time are arbitrary distributions. Various reliability measures were calculated using the supplementary variable technique and the theory of Markov vector processes. Sensitivity and relative sensitivity analyses were also performed for the system parameters. Finally, numerical calculations and graphical analyses were performed to validate the derived indices.