Performance assessment of repairable system in series configuration under different types of failure and repair policies using copula linguistics

This paper deals with the study of reliability measures of a complex system consisting two subsystems, subsystem-1 and subsystem-2 in a series configuration. The subsystem-1 has three units that are working under the policy 2-out-of-3: F; policy, and the subsystem-2 has two units that are working under 1-out-of-2: G; policy. Failure rates of units of subsystems are constant and assumed to follow an exponential distribution, but their repair supports two types of distribution, general distribution, and Gumbel-Hougaard family copula distribution. Two types of repair (general repair and copula repair) have been employed for partially failed and completely failed states. The system is analysed using the supplementary variable technique. Some important measures of reliability such as availability of system, reliability of the system, MTTF and profit analysis have been discussed. Computations have taken a particular case by evaluating availability, reliability, MTTF and profit of operation of the system.