Adjustable variables multiple-dependent-state sampling plans based on a process capability index

Acceptance sampling plans are practical and economical methods of statistical quality control. In modern manufacturing processes, supplier’s products are produced from continuous-flow manufacturing processes; consequently, the quality of successive lots is expected to be homogeneous and dependent. The multiple dependent state (MDS) sampling plan considers the cumulative lot-sentencing results to prevent the primary disadvantage of past-lot exclusion from the single sampling plan (SSP). Unfortunately, the sampling efficiency of MDS plans declines as additional preceding-lot results are included. In this paper, an adjustable MDS (AMDS) sampling plan based on the most popular process capability index with bilateral specifications is developed. The proposed AMDS plans not only increase sampling performance as additional preceding lots are considered in the lot-sentencing decision but also garner economic gains from reducing the required sample size. After comparing the performance of different plans, our proposed AMDS plans demonstrate superior cost-effectiveness and discriminatory powers to that of the SSP and MDS plans; moreover, with adjustable mechanisms, they can be progressively implemented for developing a solid supplier-buyer partnership. Finally, the industrial applicability of the AMDS plans is illustrated in a case study.