Cost-Benefit Analysis of a System with Server Failure and Replacement of the Unit at Different Failure Modes Subject to Inspection

This paper deals with a reliability model developed for a single-unit system which may fail completely either directly from normal mode or via partial failure. There is a single server who inspects the unit at its partial and complete failure to examine the feasibility of repair. If repair of the unit at these stages is not feasible, it is replaced immediately by new one. The system remains operative with partially failed unit. The server is subjected to failure while conducting inspection and repair of the unit. Treatment is given to the server upon failure. The repair of the unit and treatment given to the server are considered as perfect. The failure time of the unit and server follow negative exponential while the distributions of inspection and repair times of the unit as well as the distribution of treatment time of the server are taken as arbitrary. To carry out cost-benefit analysis, the expressions for several measures of system effectiveness are derived using semi-Markov process and regenerative point technique. The graphical behavior of MTSF, availability and profit has been shown with respect to treatment rate of the server keeping fixed values of other parameters.