In testing the capability of industrial processes, the researcher considers and tests the vague hypothesis “the capability index is low” against the vague 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 complement fuzzy sets. Afterwords, a new p-value-based approach is considered for testing the mentioned fuzzy hypotheses which is constructed on the basis of two capability indices Cp and Cpm. This new approach has several advantages over the common p-value methods for testing fuzzy hypotheses. The main one is depending the result of this new approach on both null and alternative fuzzy hypotheses, while the common p-value-based methods are according to only the null fuzzy hypothesis. To clarify the potential of the proposed approach in the process of capability analyses, two applied examples are given based on two real-world data set.

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