Cost Benefit Analysis of a Two Unit System Model with the Concept with Service Facility-FCFS: Analyzing the Cost Benefit of a Two Unit System Model with a Service Facility and Cold Standby (Journal of Advances and Scholarly Researches in Allied Education, 2019)
The present study seeks to explore cost benefit analysis of a cold standby system with conditional failure of a server. The model consists of two identical units one unit is in operative mode and other in cold standby. The cold standby unit becomes active when operative unit breaks down. The failure of the server may happen during any service activity which produces unpleasant results in terms of safety as well as economic losses. In this system model we assume that there is a single server for repair activity, who may go for refreshmenttreatment to increase his efficiency whenever required. But in case of repair of cold standby unit, server is not allowed to take refreshmenttreatment. The server works afresh after taking refreshment with full efficiency. The time to take refreshment and repair activity follows negative exponential distribution whereas the distributions of unit and server failure are taken as arbitrary with different probability density functions. The expressions for various reliability measures such as transition probabilities, mean sojourn times, mean time to system failure, steady state availability etc. are deduced by using semi-Markov process and regenerative point technique. The numerical behaviour of some important performance measures to check the efficacy of the system model under such situations is delineated for arbitrary values of the parameters in the tables respectively.