Innovative Quality Determination by Integrating Process Incapability Index into Variable Sampling Plan Design

This study presents an innovative acceptance sampling plan for variables that integrates the process incapability index with a resubmitted sampling scheme (Cpp-RSP) to enhance them efficiency of lot sentencing. While conventional single-sampling plans (SSP) are attractive for their simplicity, they often require large fixed sample sizes, which generate substantial inspection costs for both producers and customers. To overcome this constraint, the proposed sampling plan leverages the statistical properties of Cpp to construct a nonlinear optimization model that determines the optimal plan parameters subject to prescribed quality standards and risks for producers and consumers. This parametric framework yields closed-form operating characteristic (OC) and average sample number (ASN) functions, leading to practical design tables for different quality and risk settings. Numerical investigations demonstrate that across a broad range of quality levels and risk combinations, the Cpp-RSP reduces the per-stage sample size required by roughly 25–50% compared with the corresponding SSP. These results indicate that incorporating capability indices and resubmission mechanisms into acceptance sampling can substantially reduce routine inspection effort while maintaining rigorous control of decision risks, offering a promising direction for more adaptive and economical quality control systems.