Cost Analysis for N-Policy Machining System With Spares, Service Halt, Set Up and Common Cause Failure

Abstract

In the present study we consider N-Policy for machining system with mixed standbys (warm and cold). The life times of on-line units and standby units are assumed to be exponentially distributed. There may be the case when all or some units fail simultaneously due to any common cause. When both types of standbys are exhausted the operating unit fails in degraded fashion. The failed units are repaired by the single server in exponential fashion, which activates only when queue size of failed units becomes N (³1). The server may also face sudden halt due to breakdown, which is immediately repaired. The server failure, set up duration taken by the repairman before he starts repairing of service and repair times of repairman are also exponentially distributed. The solution for steady state probabilities of the number of failed units in the system is obtained using recursive method. Expressions for various performance indices viz. expected number of failed units in the system and queue, the probability of server being idle, busy, breakdown or in set up state etc. are determined. Cost analysis is done by taking cost factors related to different situations.

Keywords: Common cause failure, Cost analysis, Mixed standby, N-Policy, Queue size, Recursive method, Server breakdown, Set up, State dependent rates.

View PDF