Common Cause Failure

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 (³ 1). 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.

This paper models a complex system to analyse its reliability characteristics. The system has two possible modes-normal and failed with two types of repair facilities-major and minor. The system can fail due to failure of any units which can fail in n-mutually exclusive ways or common cause failure. Each component of the system has a constant failure rate. The system can be repaired with two different distributions viz. exponential and arbitrary. By employing supplementary variable technique and Gumbel- Hougaard family copula, Laplace transformation of various transition state probabilities, availability and cost analysis (expected profit) along with steady-state behaviour of the system and their plots have been obtained. Numerical examples with a way to highlight the important results have been appended at last.