Analytical modeling of an acceptance sampling plan with the functional process capability index for circular profiles

This paper meticulously examines a flexible resampling policy that incorporates an analysis of past records to assess the quality of submissions based on the process capability index. Lot sentencing is crucial in buyer-seller contracts for deliveries, and maintaining continuous partnerships helps preserve valuable, historically traceable results. Hence, the proposed sampling strategy aims to optimize the procedure by limiting total sampling times, adapting to varying quality levels, leveraging past inspection results, and incorporating the widely-used process capability index C_pk. This approach reduces the average sample number (ASN) for lot sentencing, particularly for products where roundness is a critical quality characteristic, characterized by a circular profile. This innovative plan introduces the first-ever tailored sampling approach for circular profiles and leverages a functional process capability index that evaluates the process capability across the entire range of the explanatory variables (e.g., different locations in a part) within circular profiles. The parameters of the proposed sampling plan are derived by solving a nonlinear optimization model that accounts for producer and consumer risk constraints. The analysis demonstrates the proposed plan performs well, as evidenced by satisfactory values of ASN and operating characteristic (OC) curve performance. The practicality of the proposed plan is further validated through a real case study.