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This paper investigates repetitive acceptance sampling inspection plans of lots based on type I censoring when the lifetime has a Tsallis q-exponential distribution. A repetitive acceptance sampling inspection plan is introduced, and its components, along with the optimal average sample number and the operating characteristic value of the plan, are calculated under the specified values for the parameter of distribution and consumer's and producer's risks using a nonlinear programming optimization problem. Comparing the results of the proposed repetitive acceptance sampling plan with the optimal single sampling inspection plan demonstrates the efficiency of the repetitive acceptance sampling plan over the single sampling plan. Moreover, repetitive sampling plans with a limited linear combination of risks are introduced and compared with the existing plan. Results of the introduced plan in tables and figures show that this plan has a lower ASN and, therefore, more efficiency than the existing design. A practical example in the textile industry is used to apply the proposed schemes.

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This paper addresses the limitations of classical correlation measures when data are imprecise, inherently vague, or affected by measurement uncertainty. We develop a new method for computing the correlation coefficient and conducting the corresponding hypothesis test for intuitionistic fuzzy data. Using the  $(alpha, beta)$-cut approach and formulating an associated nonlinear programming problem, we derive the intuitionistic fuzzy correlation coefficient and generalize the related test statistic. We demonstrate the effectiveness of the method through two numerical examples and an extensive simulation study across three uncertainty levels and various sample sizes. Simulation results indicate that under high uncertainty, the proposed method substantially reduces the Type I error rate and achieves higher power than the approach based on conventional fuzzy sets. Furthermore, by enabling separate modeling of membership and non-membership degrees, the proposed method allows for evaluating the distinct influence of each component on the final outcomes, leading to more realistic analyses in imprecise environments.