N-Policy for M/G/1 Machine Repair Model with Mixed Standby Components, Degraded Failure and Bernoulli Feedback

Abstract

In this paper, we study N-policy for a finite population Bernoulli feedback queueing model for machine repair problem with degraded failure. The running times of the machines between breakdowns have an exponential distribution. The repair times of the machines are independent and identically distributed random variables. If at any time a machine fails, it is sent to the repairman for repairing, the repairman restores the machine to the state as before failure. When the failed machine finds the repairman busy upon its failure, it has to wait until its turn as repairman stores only one machine at a time. When all the standby components are used, the failure of components occurs in a degraded fashion. To obtain the steady-state probabilities, the supplementary variable is introduced and a recursive method is employed. Some performance measures viz. expected number of down machines, expected number of machines waiting for repair in the queue, expected number of operating machines, expected number of spare machines, machine availability, etc. are established. Some special cases are deduced that match with the earlier existing results. To provide sensitivity analysis, numerical experiment is performed.