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In most manufacturing processes, each product may contain a variety of quality characteristics which are of the interest to be optimized simultaneously through determination of the optimum setting of controllable factors. Although, classic experimental design presents some solutions for this regard, in a fuzzy environment, and in cases where the response data follow non-normal distributions, the available methods do not apply any more. In this paper, a general framework is introduced in which NORTA inverse transformation technique and fuzzy goal programming are used to deal with non-normality distribution of the response data and the fuzziness of response targets respectively. Moreover, the presented framework uses a simulation approach to investigate the effectiveness of the determined setting of controllable factors obtained from statistical analysis, for optimization of sink mark index, deflection rate and volumetric shrinkage in plastic molding manufacturing processes. The accuracy of the proposed method is verified through a real case study.