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Stochastic Analysis of a Two-Unit Cold Standby System with Arbitrary Distributions for Life, Repair and Waiting Times

Volume 11, Number 3, May 2015 - Paper 9 - pp. 293-299


1 Department of Mathematics, T.I.T.S. Bhiwani, Haryana, INDIA
2 Department of Mathematics, M.D. University Rohtak, Haryana, INDIA


El-Said and El-Sherbeny [5] analyzed two-identical-unit cold standby system with two stages of repair. The whole repairing process of failed unit is supposed to be completed only in the second stage. The elapsed time between two-stages of repair is called the waiting time. Authors of [5] developed a model and claimed that the results obtained by them are for the case when all the time distributions are general. But they did not get any non-regenerative state in their model which indicates that they could not take care of their claim. The claim has been taken care of in the present paper, wherein a stochastic model is developed considering all the distributions as general. Expressions for various measures of the system effectiveness are obtained by making use of semi-Markov processes and regenerative point technique. A particular case has also been discussed where all the distributions of times have been taken as exponential. Various conclusions and bounds pertaining to the profit of the system have also been obtained.


References: 8

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