Stochastic Analysis of a System with Replacement Time and Inspection of The Failed Unit By Possible Maintenance of Standby Unit

A stochastic system of two identical units has been probed by conducting inspection of the standby unit to examine its possible goodness for operation at the failure of operating unit. There is a single server who visits the system immediately to rectify the faults which occur during system operation. The inspection of the failed unit is done to see the feasibility of its repair. If repair of the unit is not feasible to the system, it is replaced by new one after a time ‘t’. All random variables are statistically independent. The expressions for the time to failure of the unit follows negative exponential distribution while the distributions for maintenance, inspection repair and replacement times are taken as arbitrary with different probability density functions. The maintenance and repair of the unit are perfect. The semi-Markov process and regenerative point technique are used to derive the expressions for some reliability measures of vital significance. The graphical behavior of MTSF, availability and profit function have been observed for particular values of different parameters and costs.