Constructing a Sample‐Size Adaptable Sampling System Based on a Third‐Generation Process Capability Index

ABSTRACT Acceptance sampling plans (ASP) help practitioners economically and efficiently verify product quality, serving as a widely applied statistical quality control method. Among ASPs, the simplest form is the single sampling plan (SSP). Recently, acceptance sampling systems incorporating two SSPs as decision rules for lot disposition have gained significant attention due to their superior performance. Depending on the switching mechanism for decision rules, acceptance sampling systems can be categorized into quick switching systems and two‐plan sampling systems (TSS), where TSS exhibits greater flexibility and adaptability in its rule‐switching mechanism. In this study, we construct a TSS with a sample size adjustment mechanism and integrate it with a third‐generation process capability index. Detailed investigation and analysis reveal that the proposed method provides more substantial incentives for suppliers, as its properties penalize suppliers who submit poor‐quality lots through increased sample size while rewarding suppliers who submit high‐quality lots by requiring smaller sample sizes. Finally, we demonstrate the application of the proposed method through a practical case study.