Assessment of the Availability and Reliability of a Repairable L-out-of-M: G Retrial Feedback System Considering Bernoulli Vacation, Preventive Maintenance, and Two-Phase Repair

This paper examines an [Formula: see text]-out-of-[Formula: see text] repairable retrial feedback system with an unreliable repairman, operating under preventive maintenance and Bernoulli vacation policies. The repair process is characterized by two heterogeneous phases: a compulsory first-phase repair followed by an optional second-phase repair. Upon completion of the first-phase repair, a unit may either proceed to the optional second-phase repair or enter a vacation (idle) state. Components with unsatisfactory repairs from both phases or the first phase may re-enter the retrial orbit as feedback units requiring further repair. A failed component receives immediate attention if the repairman is idle; otherwise, it joins the orbit if the repairman is engaged in preventive maintenance, already busy, or on vacation. The system’s long-run probabilities are calculated using Cramer’s rule, and key reliability indices including availability and reliability are evaluated. The Laplace transform method is used for transient analysis. To comprehend the behavior of the system, we perform a graphical analysis of its availability and dependability. We also study how the system parameters affect these functions. The cost-benefit ratio is computed to understand how feedback affects the system.