A MATHEMATICAL MODEL ON STOCHASTIC BEHAVIOR OF A SINGLE UNIT REPAIRABLE SYSTEM WITH RANDOM FAILURE

Pradeep K Joshi Chitaranjan Sharma D.S.Sharma

Abstract


The reliability of any engineering system was analyzed by using probabilistic techniques. This paper is emphasizing on the analysis of reliability measures of a single unit repairable system. The system fails randomly, and then in each random failure time, it is attended by a repairman and gets repair. The three types of failures are: Minor failure-Type I and Type II category failure, Major failure- Type III and Type IV category failure, Partial failure – Type V category failure. All failure times and repair times are assumed exponential distribution and general distribution respectively. After each repair, the system regenerate and works like a new one. The various reliability measures such as transition probability, mean sojourn time, reliability, mean time to system failure, steady state availability are obtained using semi Markov analysis and regenerative point techniques.

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