This paper focused on the study of reliability measures of the complex system consist of two subsystems, (subsystem-1 and subsystem-2), both connected in series. Subsystem-1 has four units in a parallel configuration and working under 2-out-of-4: G; policy. The subsystem-2 has one unit; both the subsystems are connected in a series configuration. The system has three types of failure, minor partial failure, major partial failure, and complete failure. It is assumed that the minor and major partial failures bring the system in the degraded state, while the complete failure mode stops working of the system. All failure rates are constant and assumed to follow an exponential distribution, but the repair follows two types of distribution, general distribution, and Gumbel-Hougaard family copula (Joint probability distribution). The system is analyzed by employing supplementary variable and Laplace transform. The various measures of system reliability such as Availability, Reliability, and Mean time to failure (MTTF), profit analysis have been obtained. Critical examinations of the system have been made throughout the work. The computed results have been demonstrated by graph and utility of analysis have been conveyed through conclusion section.
Mathematics Subject Classification: 62N05; 60K05
Keywords: Availability; Reliability; Sensitivity; Mean time to system failure (MTTF); Gumbel-Hougaard family copula; Supplementary variables
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