Stage-independent multiple sampling plan by variables inspection for lot determination based on the process capability index Cpk

Multiple sampling plan (MSP) has been proved that the sample units required for inspection at each stage are usually smaller than the conventional single or double sampling. However, it is more complex to administer and difficult to derive the corresponding operating characteristic function since the judgment on the submitted lot under the MSP is not only dependent on the result of current sampling but also on previous sampling results. Thus, this paper attempts to provide a relaxed type of conventional MSP by assuming the sampling inspection at each stage is independent which is called variables stage-independent multiple sampling plan and integrated with the most widely-used process capability index Cpk. For the cost-efficient purpose, the plan parameters are solved under an optimisation model that minimises the average sample number by satisfying the required quality levels and tolerated risks. Finally, the applicability of the proposed plan is illustrated in a case study.