Machine repairing systems with standby switching failure

• We model a machine repairing system with general repair times and standby switching failure.
• We derive simpler computational forms of the lognormal and Weibull distributions.
• The supplementary variable method with a recursive procedure is used to develop the stationary probabilities.
• A total expected cost function is given to search the optimal parameters using an efficient approach.

This paper attempts to explore the performance measures and optimization analysis of machine repairing systems with standby switching failure. The time between failures and time-to-repair of failed machines are assumed to be exponential and general distributions, respectively. The standby is switched over to the operating mode when an operating machine fails, and the switch is subject to failure with probability qq. A recursive method based on the supplementary variable technique is used to derive the steady-state probabilities of failed machines in the system. We then develop various performance measures of the system and construct the expected cost function per unit time. The probabilistic global search Lausanne method is employed to determine the optimal number of standbys and the optimal repair rate, wherein the expected cost per unit time is minimized. Finally, some numerical examples are provided for illustrative purposes.