Stochastic analysis of a two-unit system with standby and server failure subject to inspection

It is not necessary that the server can perform its duty without failure/tiredness. While, a common man also know the importance of water supply system that works punctually without any delay. 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. 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 remaining 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, after having refreshment, the server may eventually perform the better service efficiently. It is assumed that time for 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.