Availability and cost analysis of a standby complex system with different types of failure under waiting repair discipline using Gumbel-Hougaard family copula distribution

This paper deals with the reliability and cost analysis of two unit standby redundant complex system under different repair facility. The system consists of two units´ main unit and standby unit connected in standby redundancy. The main units as well as standby unit are assumed to go under two types of failure - partial failure and complete failure. Whenever main unit fails completely, the standby unit takes its load via switch over device. The failed unit goes under repair, if repair facility is available or waits for repair if facility is not available. The system will completely break down if the main unit is under repair and standby unit fails. The failure rates are constant and assumed to follow exponential distribution. Repair follows two types of distribution- general distribution and Gumbel-Hougaard family copula distribution. The system is studied by using supplementary variable technique and Laplace transform. The various measure of reliability has been discussed. Evaluations for some special cases have also been highlighted.