In capability analysis, the researcher considers and tests the fuzzy hypothesis “the capability index is low” against the fuzzy hypothesis “the capability index is high”. But, two fuzzy concepts low and high are usually formulated by two crisp hypotheses in traditional quality tests. In this paper, we formulate these two fuzzy concepts by considering two compliment fuzzy sets. Then, a new p-value-based approach is considered for testing the mentioned fuzzy hypotheses which is constructed on the basis of capability index Cp. To clarify the potential of the proposed approach in the process of capability analyses, an applied example is given based on a real-world data set.

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