In this paper, a split production system which has a single station in the first stage followed by two parallel stations in the second stage with an initial buffer of finite capacity is analyzed in connection with the production rate of the system. A mathematical model is developed using semi-regenerative phenomena to study the system. System of convolution integral equations satisfied by various stale probabilities corresponding to different initial conditions is obtained. An iterative numerical method is used to solve the system of convolution integral equations obtained.
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