Developing a stage-independent multiple sampling plan with loss-based capability index for lot disposition

Multiple sampling plan (MSP) is a generalization of single and double sampling plans that enhances the efficiency by reducing the number of sample items needed for inspection. However, the operating characteristic function of MSP is relatively complicated to derive because the inspection at each stage is dependent on others, i.e., the lot judgment on the current lot not only depends on its inspected result but also considers the results of the previous stages. Therefore, in this study, we propose a stage-independent MSP (SIMSP) and integrate it with a loss-based capability index. SIMSP can be regarded as a relaxed form of the traditional MSP, assuming independence in inspections at each stage. SIMSP's parameters are solved for a cost-efficient purpose under an optimization model that aims to minimize the average sample number (ASN), adhering to constraints aligned with predefined quality and acceptable risk levels. The results indicate that SIMSP can not only perform better discriminatory power but also require fewer ASN for making lot disposition. Besides, SIMSP's performance is evaluated, analyzed, and contrasted with the traditional sampling plan under various settings. In addition, an example is presented using the developed graphical user interface to illustrate the real-world application of SIMSP.