Profit Analysis of One Out of Two System with Duplicate Standby and Priority to Repair

In the present paper, we discuses a reliability model of a one-out-of-two system with one duplicate unit as a standby. This system consists of two operating units (main units) and one duplicate unit as a cold standby. The system is considered to be in an up-state if at least one of the two main units is operating mode and it fails when both main units fail. After failure of one main unit reaming one main unit does not fulfill our requirement smoothly that's why we arranged a duplicate cold standby unit for shearing load of main unit and fulfill our requirement. Each unit is in either operative or complete failure mode. A single server is available to attend to the system immediately when needed. Repair time distributions are taken to be random with various probability density functions, whereas the unit(s) failure time is exponentially distributed. The formulations for the models' mean time to system failure, availability, and profit have been derived using the semiMarkov process and regenerative point technique.