Development of a cost-effective inspection scheme with adaptive lot-disposition mechanisms and a third-generation capability index

Acceptance sampling plans are regularly used for sampling inspections because they provide clear decision rules, enabling practitioners to sentence lots economically and efficiently. The multiple dependent-state sampling plan (MDSP) and repetitive group sampling plan (RGSP) have been developed using advanced sampling techniques. The former incorporates historical lot quality records into decision-making for lot disposition, and the latter employs a repetitive sampling mechanism. Researchers have combined these approaches into a more advanced inspection scheme, the modified RGSP (MRGSP). However, a detailed investigation and analysis identified three critical drawbacks of the MRGSP. These drawbacks include diminishing cost-effectiveness as a) more historical lot quality records are considered, b) lots with inferior historical quality records are repetitively sampled, and c) the number of repetitive samplings is not limited. This paper proposes an adaptive inspection scheme to address these deficiencies based on the third-generation process capability index, Cpmk, the combined adaptive multiple-dependent-state and repetitive group sampling plan (AMRSP). A detailed investigation revealed that the proposed AMRSP resolves the drawbacks of the MRGSP, is more cost-effective, and provides reliable protection for buyers and sellers. A case study demonstrates the practical applicability of the AMRSP, revealing that it can reduce the sample size by 25 %–56 % compared to the MRGSP, RGSP, and MDSP. It significantly enhances the efficiency of sampling inspections, which could be a motivation for promoting further industrial development.