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Market conditions fluctuate abruptly in today's competitive environment and leads to imprecise demand information. In particular, market demand data for freshly launched products is highly uncertain. Further, most of the products are generally manufactured through complex multi-stage production systems that may produce defective items once they enter the out-of-control state. Production management of a multi-stage production system in these circumstances requires robust production model to reduce system costs. In this context, this paper introduces an imperfect multi-stage production model with the consideration of defective proportion in the production process and uncertain product demand. Fuzzy theory is applied to handle the uncertainty in demand information and the center of gravity approach is utilized to defuzzify the objective function. This defuzzified cost objective is solved through the analytical optimization technique and closed form solution of optimal lot size and minimum cost function are obtained. Model analysis verifies that it has successfully achieved global optimal results. Numerical experiment comprising of three examples is conducted and optimal results are analyzed through sensitivity analysis. Results demonstrate that larger lot sizes are profitable as the system moves towards a higher number of stages. Sensitivity analysis indicates that the processing cost is the most influencing factor on the system cost function. [ABSTRACT FROM AUTHOR]