Transient analysis of a machine repair system with standby, two modes of failure, discouragement and switching failure

The present study is concerned with a machine repair problem with mixed standbys, permanent and additional repairmen. To deal with the realistic situation, the concepts of balking and reneging are also included. The operating units as well as standby units are assumed to fail in two modes. The units have exponential life time and repair time distributions. It is also assumed that there is a probability of a switching failure of the standby units to the operating state. The transient state probabilities are obtained by Runge‐Kutta method. Some performance indices such as expected number of failed units, expected number of standby units, machine availability, etc., are obtained. To determine the expected total cost per unit time, a cost function has been facilitated. The numerical experiment is carried out to validate the analytical results of the developed model. The sensitivity analysis is also performed to explore the effect of different parameters on the performance indices.