A Parallel System with Arrival Time of Expert Server Subject to Maximum Repair and Inspection times of Ordinary Server

A parallel system of two identical units has been analyzed stochastically considering two types of servers. Initially, the unit is repaired by the ordinary sever who visits the system immediately. And, when ordinary server is unable to do repair of that unit in a given maximum repair time, the unit undergoes for inspection to see the feasibility of its repair by an expert server. If inspection reveals that repair of the unit is also not possible by the expert server, then it is replaced by new unit. The expert server takes some time to arrive at the system. The failure rate of each unit and rate by which unit undergoes for inspection by the ordinary server are taken as constant while the distributions of arrival, inspection, repair and replacement times are assumed as arbitrary with different probability density functions. All random variables are statistically independent. The expressions for several reliability measures are derived using semi-Markov process and regenerative point technique. Graphs are drawn to depict the behavior of MTSF, availability and profit for different values of the parameters.