Performance assessment of a complex repairable system with k-out-of-n: G operational scheme and copula repair approach

The present study is a complex system with three subsystems connected in a series configuration. The first subsystem has n identical units and is ascribed to be operable by a k-out-of-n: G scheme, and the second subsystem, which has three indistinguishable parts, is capable of being operational if at least two of them are operable. The third subsystem has an independent unit and all subsystems are connected in a series in the sequence of subsystem 1, subsystem 2, and subsystem 3. The units of subsystem 1 and subsystem 2 are controlled by the auto changeover switches and the switch failure led to the complete failed state. The units' failure rates of subsystems are constant and follow an exponential distribution, however, there are two types of repair facilities: general and copula repair. Minor repair dealt with the general repair but complete failure needs copula repair. Traditional reliability measures have been studied for different values of failure and repair through supplementary variable and copula approaches.