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A system-theoretic method, referred to as overlapping decomposition, is presented to evaluate the performance of a complex manufacturing system with assembly, parallel, rework, feedforward, and scrap operations. The idea of the method is to decompose the complex system into a set of serial production lines, with the first or last machines of each serial line overlapped with another line, and to modify the parameters of overlapping machines to accommodate the effects of machines and buffers in other lines. Iterative procedures are introduced to estimate the system production rate. The convergence of the procedures and the uniqueness of the solutions are proved analytically and the accuracy of the estimates is evaluated numerically. Note to practitioners - Many large volume manufacturing systems consist of complex operations, for instance, assembly, disassembly, rework loop, parallel lines, feedforward lines, scrap, etc. Development of a performance evaluation method to provide fast and accurate analysis of system throughput is important for design and continuous improvements. This paper introduces a system-theoretic method, referred to as, overlapping decomposition, to analyze the performance of such complex manufacturing systems. The complex system is decomposed into overlapped serial production lines and modifications are introduced to accommodate the coupling effects among all these lines. From the theoretical point of view, this paper presents the proofs of the convergence of recursive procedures and the uniqueness of solution. From the application point of view, the method has obtained good results in solving practical problems on the factory floor.