A process-incapability–based optimization framework for product quality inspection using variable repetitive group sampling

Conventional variable single sampling (VSS) plans are commonly employed due to their straightforward implementation; however, the large sample sizes required result in substantial inspection costs and reduced quality control efficiency. To address the challenge of ensuring reliable quality assurance while minimizing inspection effort, this study proposes a novel acceptance sampling plan that integrates the process incapability index (Cpp) with a variable repetitive group sampling (VRGS) scheme. The objective is to minimize the average sample number (ASN) while satisfying specified producer’s and consumer’s risk requirements and quality standards. A nonlinear optimization model was developed under four scenarios to determine the optimal sampling parameters, with ASN minimization as the primary objective. The proposed Cpp-VRGS plan was evaluated through sensitivity analysis and comparative analysis against an existing Cpp-based VSS plan. The results demonstrate that the proposed Cpp-VRGS plan consistently achieves lower ASN values while maintaining the required risk protection levels. Different scenarios exhibit superior performance under different quality conditions, providing greater flexibility in selecting an appropriate inspection strategy. Sensitivity and comparative analyses further confirm the robustness and efficiency of the proposed approach. A case study involving monocrystalline silicon wafers validates its practical applicability in a real manufacturing environment. This study contributes to the acceptance sampling literature by integrating process incapability assessment with VRGS within an optimization-based framework. To support practical implementation, a user-friendly graphical user interface was developed to assist quality engineers in determining plan parameters and making inspection decisions efficiently. The proposed methodology offers a flexible, reliable, and cost-effective solution for industrial quality control.