Transient analysis of machining system with spare provisioning and geometric reneging

Abstract

In this investigation, we deal with the transient analysis of repairable machining system having multi identical online and warm standby machines. There is facility of repair of failed machines rendered by an unreliable server who is prone to failure and follows the threshold policy in rendering the service and being repaired. The failed machines waiting in the queue may renege and opt sequentially whether to leave the queue or remain in the queue in geometric fashion at the epochs of availability of secondary server. By constructing the transient differential difference equations, the probabilities associated with the system states are determined using the numerical method based on Runge-Kutta method. Various queueing and reliability indices viz. expected number of failed machines in the system, throughput, reliability, mean time to failure, failure frequency, etc., are established and numerically computed by taking illustration. The sensitivity analysis and numerical simulation are performed for exploring the effects of parameters on some performance measures.