Machine Repair System with F-Policy, Two Unreliable Servers, and Warm Standbys

Abstract

Abstract This investigation deals with machine repair problems with F-policy and a repair facility that has two unreliable servers and the provision of warm standbys. F-policy implies that when the number of failed machines reaches a maximum capacity K of the system, the next arrival of failed machines is not allowed into the system until the number of failed machines again decreases to a fixed level F. The first server repairs the failed machines as soon as they fail, but the second server starts the repair service only when there are more than a prespecified number of failed machines available in the system to minimize the work load of failed machines in the system. Both servers may be broken down during the repair of failed machines and, after repair, again return to the system for service to the failed machines. We developed a Markov model for the machine repair problem, which consists of the combination of operating and standby machines using the birth-death process. The matrix method is employed to determine the transient probabilities of the number of failed machines in the system, throughput of the system, and some other performance measures. The cost function is also provided for the determination of optimal service rates to depict the system utility at optimum cost.