A modified sampling scheme for lot sentencing based on the third-generation capability index

The multiple sampling plan (MSP) is an extended model and has been shown to be more efficient with some cost savings associated with its usage than the single and double sam- pling plans. However, the variables MSP’s operating characteristic (OC) function is complex and difficult to obtain because the judgment at the current sampling should take the preced- ing sample information into consideration. Therefore, this study proposes the development of a modified MSP for variables inspection by considering independence between stages and integrating with the third-generation capability index. A mathematical model with two constraints is established for obtaining triple plan parameters, which satisfy the specified risk-and-quality conditions and minimize the average sample number (ASN). Additionally, we employed two generally-used performance indicators, ASN and OC curve, to evaluate the performance of the proposed model. The results show that the proposed model provides higher efficiency than the existing plan under the same settings and offers desired protection to both stakeholders. We applied the proposed model to the monocrystalline silicon wafers industry coupled with a designed graphical user interface to validate its practicability.