Stochastic analysis of two-unit redundant system with priority to inspection over repair

Due to a human being the server can perform his duty without failure/tiredness seems to be unrealistic. The importance of water supply systems that work punctually without any delayed know by the common man. The same situation simulated here, with two unit cold standby system with the facility that the server inspects the failed unit before repair/replacement of the unit and refreshment is provided to server whenever required has been discussed. The priority is given to inspection of the unit over repair of the unit. This model is applicable in the water supply system. In this model, operative unit may fail, directly from normal mode and the cold standby unit may get failed owing to remain unused for a longer period of time or any other reason. There is a single server who visits the system immediately whenever required for the dual purpose of inspection and repair activities. Also, the server may eventually perform the better service efficiently after having refreshment. It is assumed that, time to take refreshment and repair activity follows negative exponential distribution whereas the distributions of unit failure and server failure are taken as arbitrary with different probability density functions. For concluding the study of such model, various stochastic measures are analyzed in steady state using semi-Markov process and regenerative point technique. The tables are structured for arbitrary values of the parameters to exhibit the behaviour of some important performance measures to check the efficacy of the system model under such situations.