Study of Reliability Measures of a Two Units Standby System Under the Concept of Switch Failure Using Copula Distribution

摘要

This paper deals with the study of standby complex system which consists of a main unit and two standby units. The standby units are connected to the main unit via an automatic switch and the system is operated by a human operator. The standby units are connected with the main via a switch in such a way that they can perform the task immediately after failure of main unit. When the standby unit performs the task, the main unit goes for repair and as soon as it is repaired, the load of standby unit again goes to the main unit. In case main unit is not repaired and the first standby unit fails, the second standby unit starts and performs the task. A human operator operates the system and therefore the human failure can appear in state where system is in operational mode. The failure rates are constants and assume to follow exponential distribution but repairs follows two types of distribution (general and Gumbel-Hougaard family copula) distribution. The system is studied by supplementary variable techniques. Some important measures of reliability such as availability, MTTF, sensitivity and profit function have been discussed. Some particular cases have been discussed for different values of different variables.