Variables adjustable multiple dependent state sampling plans with a loss-based capability index

Acceptance sampling plans are a cross-functional quality control instrument for benchmarking compliant standards of incoming as well as outgoing lots. The multiple dependent state (MDS) plan has been proposed and proven to advantage the conventional single sampling plan (SSP). However, the MDS plan presents a contradictory situation: Its performance depreciates as the number of previously considered lots increases. This outcome implies that the greater the number of cumulative lot-sentencing results one intends to include is, the greater the sample size is required for inspection, where a loosened criterion for quality acceptance levels, unfavorably, is introduced as well. Therefore, we proposed a modified MDS plan that depends on the loss-based capability index to accommodate an adjustable mechanism, namely, the adjustable multiple dependent state (AMDS) sampling plan. The AMDS plan allows encompassing not only a greater number of preceding lots in the lot disposition decision but also reducing the sample size required for the inspection and raising the lot-sentencing quality standards to stimulate the supplier attaining with persistently reliable submissions for a long-term supplier-consumer relationship. In comparison to the plans’ performance, our proposed AMDS plans demonstrate superior cost-effectiveness, discriminatory powers, and average run lengths than those of the SSP and MDS sampling plans. Furthermore, we tabulated the plan parameters under numerous conditions and delivered a real industry case to demonstrate its applicability.