Profit Analysis of a System of Non-identical Units with Degradation and Replacement

This paper presents the profit analysis of a system of two non-identical units in which one unit is original which is initially operative and the other is duplicate kept in cold standby. The units may fail completely directly from normal mode. There is a single server who visits the system immediately when required. The original unit undergoes for repair upon failure while only replacement of the duplicate unit is made by similar new one. The original unit does not work as new after repair and so called degraded unit. The system is considered in up-state if any one of new/duplicate/degraded unit is operative. The server inspects the degraded unit at its failure to see the feasibility of repair. The failure time of the units are exponentially distributed whereas the distributions of inspection time, replacement time of the duplicate unit and repair time of the original/duplicate/degraded unit are taken as arbitrary with different probability density functions. Some reliability characteristics of the system model are evaluated using semi-Markov process and regenerative point technique. The numerical results for a particular case are also obtained to depict the behavior of Mean Time to System Failure (MTSF), availability and profit function graphically.