Stochastic Analysis of a Standby System With Waiting Repair Strategy

Abstract

This paper investigates the reliability of a standby system incorporating waiting time to repair. The considered system consists of two units, namely, the main unit and the standby unit. Whenever the main unit fails, the whole load is transferred to the standby unit instantaneously by a switching-over device. As regards to the repairing of the main unit, it has to wait for repair whenever it fails due to unavailability of repair facility. When both the main and standby units fail, then the system goes to the complete failure mode. The system may also fail due to incorrect start of the system, which can occur due to an untrained and inexperience operator. The repair of the main and standby units follows general distribution, whereas repair due to human error is obtained with the help of Gumbel-Hougaard family copula. The system is analyzed by supplementary variable technique and Laplace transformation. Various reliability measures like availability, mean time to failure, and profit function have been evaluated for the considered system. A numerical example with a way to illustrate the utility of the model has also been presented.