The purpose of this paper is to construct a statistical hypotheses test for process capability indices and compare the pairs of them with a fixed sample size. Since the sampling distribution of the estimators of pairs of two process capability indices (PCIs) is very complex, an exact statistical hypothesis test for them cannot be constructed. Therefore, the authors have proposed a bootstrap method to construct the hypothesis test for them on the basis of p-value. The authors have shown that by increasing n, the bootstrap method has better output relative to other methods and it can be easily implemented. The authors have also demonstrated that sometimes an exact hypotheses test cannot be constructed and need some assumptions. In the present paper, several methods to test of hypotheses about the difference between two process capability indices have been compared.

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