Acceptance sampling plan is widely used for the inspections of incoming or outgoing products to provide the producer and the consumer a general benchmark for lot sentencing. To reduce the inspection cost, the multiple‐dependent‐state (MDS) plan that takes account of the preceding lots' quality history into the current lot disposition has been proposed. However, recent studies overlook the fact that the MDS plan's performance needed to reach target compliance decreases with an increase in the number of preceding lots considered. This unawareness makes the MDS plan fall into a conflictive situation. To overcome the drawback of the MDS plan, in this paper, we introduce a modified MDS plan to accommodate an adjustable mechanism, called adjustable MDS (AMDS) sampling plans. The presented AMDS plans are designed on the basis of the advanced process capability index, which is cognizant of both the process yield and the process loss. This established process‐capability‐qualified AMDS plan efficiently solves the conflictive situation of the MDS plan when encompassing more preceding lots in the lot‐disposition decision. Notably, its efficacy has been shown on high improvements in terms of the required sample size for the inspection, the discriminatory power, and the average run length for lot sentencing.

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Supplier-buyer relationships have been the focus of considerable supply chain management and marketing research for decades. To validate the process capability of a supplier, practitioners usually operate the acceptance sampling plan (ASP). The most basic ASP is a single sampling plan (SSP) due to its straightforward lot-disposition mechanism. However, since the lot-disposition mechanism of SSP cannot accommodate the historical lot-quality levels information, it requires a large sample size for inspection to validate the submitted lot's process capability. To obtain these benefits from historical information, multiple-lot dependent state (MDS) sampling plans have been proposed. The MDS plans have manufacturing traceability of historical lot-quality levels information to sentence the submitted lot. However, the MDS plan's manufacturing traceability has a drawback that cost-efficiency decreases as more historical lot-quality levels information are considered, which contradicts its initial development goal. To overturn this contradictory situation, we proposed the adaptive MDS (AMDS) plans based on the process loss restricted consideration with combinatorial mathematical treatment that can correct the MDS plans manufacturing traceability of historical lot-quality levels information that help practitioners to adopt more historical information into lot-disposition freely without bearing the reduction of cost-efficiency. Meanwhile, their performances are superior to existing MDS plans in terms of cost-effectiveness and discriminatory power. Moreover, we further developed a web-based app for our proposed plans to improve the convenience of applying them in practice. By operating the web-based app, practitioners can quickly obtain the optimal plan criteria without bearing the burdens of table-checking or mathematical model solving. These improvements can genuinely help buyers distinguish reliable suppliers efficiently and build up a strong partnership with them. Finally, the applicability of the proposed plan is demonstrated in a realworld case study.INDEX TERMS Lot tracing, process loss restricted, lot-dependent sampling plans, supplier-buyer relationships, historical lot-quality levels information.