Reliability Measures of a Cold Standby System with Preventive Maintenance and Server Failure during Repair

A stochastic model for a cold standby system is developed by introducing the concepts of preventive maintenance and server failure. The repair and preventive maintenance of the system are conducted by a single server who is subjected to failure while performing jobs. The unit undergoes for preventive maintenance after a specific operating time‘t’. Repair of the unit is done at its complete failure. Treatment to the failed server is given in order to resume the jobs. The unit works as new after repair. The random variable associated with the failure rate of the unit, failure rate of the server, repair and preventive maintenance rates of the unit and treatment of the server are statistically independent. The distribution of failure time of the unit &server and the rate by which unit undergoes for preventive maintenance are exponentially distributed whereas, the distributions of repair, treatment and preventive maintenance rates are arbitrary. The semi-Markov process and regenerative point technique are used to derive the expressions for some important reliability measures. Graphical study of these measures has also been made for arbitrary values of various parameters and costs.