MTSF and Profit Analysis of a Cold-Standby System with Unstable Switching Device and Weibull Distribution

A stochastic model for a cold standby system is developed by taking two identical units, single server and a switch device. The standby unit has to switch into operation, at the failure of the operative unit, with the help of some switching device. The switching device is in the random state i.e. may or may not found operable. The cold standby fails after surpassing a threshold time limit, called a maximum redundancy time. At its failure, the cold standby is taken under inspection for deciding about repair or replacement. A single server carries out all restoration activities. The semi-Markov theory of stochastic processes and regenerative point technique are used to develop the system model and to derive the expressions for various measures of system performance. The measures of system effectiveness are discussed by assuming Weibull distribution for the parameters. The findings of the study are shown graphically to highlight the impact of parameters on the system performance.