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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.