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Reliability Modeling of a 2- Out-of-3 Redundant System with Alternate Repair

Gitanjali ., S. Kumari


Here, the method for improving the effectiveness through repairing of the industrial and manufacturing systems has been extracted and so called a repair-replacement problem.  For this purpose, a three unit redundant system in which two units work in parallel and one unit is taken as spare in cold standby is considered and a reliability model is developed by using semi-Markov process and regenerative point technique.  This system is known as 2-out-of-3 redundant system. All the units are identical in nature. On the failure of operative unit, standby takes some time (called activation time) to become operative. After the completion of activation time, the failed unit is undertaken for repairing by a usual repairperson (server). However, after getting let down in repairing the unit in precise time, the ordinary server takes the responsibility of doing inspection of the failed unit. If there is probability of further repairing the unit, to improve the system performance, an expert server does its repair in the presence of regular server. Otherwise, the unit is replaced by new one with some replacement time. All random variables are assumed as independent and uncorrelated. The distributions of failure times, maximum operation and repair times are taken as negative exponential while the distributions of activation, inspection, repair and replacement times are assumed as arbitrary with different probability density functions. The numerical representation of mean time to system failure (MTSF), availability and profit with respect to replacement rate has also been shown for a particular case.

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