Stochastic Assessment of k Operational State System with k-out-of-n:G Working Scheme with Employing Copula Repair Approach

This paper is a probabilistic performance study of a repairable complex system with three subsystems coupled in a series configuration. All three subsystems have been differently configured and also have different operational schemes. The first subsystem has n units and works under the k-out-of-n:G scheme, the second subsystem has four identical units and associates with a defined work scheme 2-out-of-4:G, however, the third subsystem has two indistinguishable units and works under the 1-out-of-2:G policy. The units' failure rates of the subsystems are different but constant and follow an exponential distribution, however, there are two types of repair facilities available for repair general and copula repair. Under the consideration of the system with the operational duration, the failed unit was replaced with a new one and it was assigned for repair. In the complete shutdown condition, a copula repair has been employed to repair the system. Traditional reliability measures have been studied for different values of failure and repair through supplementary variable and copula approaches. The numerical computations for securing different values of k and n have been exhibited and tables and graphs predict the future behavior of the system performance. In the conclusion section, the effect of reliability measures has been highlighted.