Profit analysis of two-unit standby system with rest period for the operator and correlated failures and repairs

Abstract This paper analyses a two-unit cold standby system with the provision of rest for the operator. After working a random amount of time, the operator needs to rest for a random amount of time and during the rest period the system comes down, but does not fail. Also, the failure and repair times of each unit are assumed to be correlated, by taking their joint density as a bivariate exponential. The system is observed at suitable regenerative epochs to obtain various reliability characteristics of interest to system designers as well as operations managers. Numerical results pertaining to a particular case are also presented.