International Journal of Statistics and Reliability Engineering

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Vol 7, No 2 :

openaccess

Stochastic Analysis of a Non-Identical Repairable System of Three Units with Priority for Operation and Simultaneous Working of Cold Standby Units

Sweety Kadyan , M S Barak , Gitanjali .

Abstract

Here, we study stochastically a repairable system of three units in which one unit(say main unit) is initially operative and the other two identical units(say duplicate units) are kept as spare in cold standby. The duplicate cold standby units work simultaneously at the failure of main unit. The priority is given to the main unit for its operation. The repair activities of both types of units are handled by a single server who calls on the system promptly whenever needed. The repair activities on the part of the server are considered as perfect and thus the repaired unit works as new with the same lifetime distribution as the original. The failure time of the units (main and duplicate) is taken as constant while the repair time distributions of the units are assumed as arbitrary. The reliability characteristics such as mean sojourn times(MST), transition probabilities(TP), mean time to system failure(MTSF), availability, expected number of repairs (for both main and duplicate units), busy period of the server, expected number of visits of the server and finally the profit function is obtained in steady state by making use of semi-Markov process(SMP) and regenerative point technique (RPT). The values of these measures are obtained for arbitrary values of the parameters and accordingly their behaviour has been observed graphically. The power supply system can be considered as one of the practical applications of the work.

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ISSN(P) 2350-0174

ISSN(O) 2456-2378

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