Evaluation of the availability and reliability of a standby repairable system incorporating imperfect switchovers and working breakdowns

This study involves the evaluation of the availability and reliability of a repairable system containing warm standby components and undergoing switching failure under a Markovian environment. A single repairperson is responsible for repairing failed components. As soon as the system is free of failed components, the repairperson takes multiple vacations. The repairperson is also subject to breakdown while repairing failed components. When the repairperson experiences a breakdown, there is a probability of 1 - delta that he/she is sent for recovery, or a probability of delta that he/she continues to work at a lower rate. For the Markov model, we establish a finite set of differential equations governing the repairable system. A numerical approach based on the Runge-Kutta method is employed to solve the differential equations. Numerical solutions for the time-dependent availability can then be obtained. For the reliability model, we use the Laplace transform method to find the explicit form of the reliability function and the mean time to failure (MTTF) of the system. Finally, we conduct a numerical sensitivity analysis of the time-dependent availability, system reliability and MTTF with respect to various system parameters.