Repair machines play a critical role in military, communication, industrial, and manufacturing settings. This study investigates the performance of a system that utilizes repair machines with human operators, employing Copula's attributes for estimation. The research focuses on a serial system composed of two subsystems, each consisting of two active components running in parallel. Both subsystems are manned by two human operators and assigned two repair machines for operation and maintenance, where the repair machines are considered failure-prone systems. The system experiences partial and complete malfunction during operation: Partial malfunction lead the system into reduced capacity mode, and a complete malfunction resulting in system failure. The research employs the technique of supplementary variable and transforms of Laplace to establish and solve the governing differential equations corresponding to schematic system's diagram. Performance models for the system such as profit, MTTF, availability, sensitivity of MTTF and reliability are numerically validated and presented through tables and graphs. These findings are highly valuable for evaluating performance, identifying ideal system designs, and developing workable maintenance plans. The research contributes to enhancing system performance, increasing production output, and improving revenue mobilization in various application domains. تفاصيل المقالة