The up and down time distribution in a 1 out of n system with general life time and repair time distributions

In repairable systems with redundancy, failed units can be replaced by spare units in order to reduce system down time. The failed units are sent to a repair shop or manufacturer for maintenance and are subsequently returned for re-use. s paper we consider a 1 out of n system with cold standby and we assume that repaired machines are as ‘good-as-new’. We derive an approximation method for the distribution of the up time and the down time of the system in case of a general failure distribution and a general repair time distribution. This allows the model to be used in a wide variety of applications.