Stochastic Analysis of Non-Identical Repairable Systems with Priority and Simultaneous
Working of ‘n’ Cold Standby Units
S. Kadyan
, S. C. Malik
Abstract
The present study emphasizes on the stochastic analysis of a non- identical repairable system with a total (n+1) units. The units are non-identical and classified as type I and type II units. In type I, there is a single unit which works initially and the remaining ‘n’ units are in cold standby considered as type II units. The type II units work simultaneously at the failure of type I unit. The system is analyzed in two ways- with or without the provision of priority for operation and repair for type I unit. The system model without priority is called 1st model while the model with priority for operation and repair to type I unit is taken as 2nd model. Reliability characteristics such as transition probabilities, mean sojourn times, mean time to system failure, long run availability, expected number of repairs in long run, expected number of visits paid by the server, busy period analysis of the server and profit are determined using regenerative point technique and semi-Markov process of both the system models. The effect of number of type-II units is examined on some significant reliability characteristics. The profit comparison of the models has been done for different values of type II units and other parameters which follow negative exponential distribution. The results are shown graphically in figures to give more clarification regarding the variation in reliability characteristics with respect to the parameters. The system so studied is applicable in surveillance exercises of some crucial places.
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