This paper presents two approaches for testing quality to make a decision based on the extended process capability indices. Common methods in measuring quality of the manufactured product have widely focused on the precise specification limits, but in this study the lower and upper specification limits are considered as non-precise/fuzzy sets. Based on a general statistical approach using an extended process capability index, the purpose of this study is estimating a critical value to determine whether the process meets the customer requirements. Moreover, a simulation approach to analyze the manufacturing process capability has been suggested for testing quality based on fuzzy specifications by normal data. Meanwhile, this paper discusses how well the Monte Carlo simulation approach can be used for non-normal data. Finally, the real application of the proposed methods is investigated in a real case study.

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