Designs of Attribute Sampling Plan Based on Single Point on Operating Characteristic Curve

The development of a single sampling plan indexed with Maximum Allowable Proportion Defective (MAPD) and Probability of Allowable Risk (PAR) represents a novel approach to acceptance sampling plans. Previous sampling plans typically relied on two points on the Operating Characteristic (OC) curve or one point on the OC curve along with an outgoing quality or constraint. In this new plan, emphasis is placed on a single point, specifically the point of inflection of the OC curve. The MAPD corresponds to the p-axis of this point, while PAR is represented on the Pa(p) axis, ensuring that all lots inspected with a specified incoming quality MAPD will be accepted if Pa(p)
PAR. The primary aim of this research is to establish a sampling plan based on a single point on the OC curve. A significant quality MAPD, paired with the corresponding probability Pa(p*), leads to a decreasing operating ratio that defines a unique sampling plan. Furthermore, the complement probability to PAR (PRR) and the ratio PAR/PRR are introduced to identify sampling plans and the discriminant angle
. The most discriminating operating ratio among all is given by PAR/PRR. A switching rule for sampling plans within a feasible interval of sample size, which can be inspected by manufacturers without affecting the Acceptable Quality Level (AQL), has been devised. OC curves illustrating PAR, PRR, the angle of discrimination, and the optimum sampling plan have been constructed. Additionally, tables with examples have been provided to aid in understanding. A conversion table for identifying other quality indices has also been included.