Developing a variables multiple dependent state sampling plan with simultaneous consideration of process yield and quality loss

Abstract

Acceptance sampling plans have been utilised predominantly for the inspection of outgoing and incoming lots; these plans provide effective rules to vendors and buyers for making decisions on product acceptance or rejection. Multiple dependent state (MDS) sampling plans have been developed for lot sentencing and are shown to be more efficient than traditional single sampling plans. The decision criteria of MDS sampling plans are based on sample information not only from the current lot but also from preceding lots. In this study, we develop a variables MDS sampling plan for lot sentencing based on the advanced process capability index, which was developed by combining the merits of the yield-based index and loss-based index. The operating characteristic function of the developed plan is derived based on the exact sampling distribution. The determination of plan parameters is formulated as an optimisation model with non-linear constraints, where the objective is to minimise the sample size required for inspection and the constraints are set by the vendor and the buyer to satisfy the desired quality levels and allowable risks. The performance of the developed plan is examined and compared with traditional sampling plans. A step-by-step procedure is provided, and the parameters of the plan under various conditions are tabulated for practical applications.