A Stochastic system with possible maintenance of Standby before operation and inspection over replacement of the failed unit

This paper discusses with profit analysis of a stochastic system consisting of two identical units by considering the occurrence to repair the faults during system operation and possibility of maintenance of the cold standby unit before getting it into operation. On failure of the unit of the system, the repairman first inspect whether the fault is repairable or non repairable and accordingly carry out repair or replacement of the components involved. All random variables are statistically independent. The failure time of the unit follows negative exponential distribution while the distributions for maintenance, inspection and repair times are taken as arbitrary with different probability density functions. The maintenance and repair of the unit are unadulterated. MTSF, Availability, Busy period and profit function are obtained by using semi-Markov process and regeneration point technique have been followed by special cases and graphs.