Sampling inspection plan with screening by variables for assuring average outgoing surplus quality loss limit

The quality of a lot has sometimes been evaluated based on attribute properties such as the percentage of nonconforming items or the number of nonconforming items in the lot. On the other hand, Taguchi has proposed the concept of "quality loss" as the evaluation measure of quality of items based on variable properties. Concretely, Taguchi's loss function has been defined as a quadratic function based on the departure from the target value of an item. Recently, from the viewpoint of assuring the quality loss based on Taguchi's loss function, a single sampling inspection plan based on operating characteristics has been proposed. This sampling procedure has been designed for the purpose of assuring both the specified producer's risk for the lot with an acceptable quality loss limit and the consumer's risk for the lot with a rejectable quality loss limit. However, the disposition of the rejected lot isn't specifically declared in the sampling inspection plan mentioned above. While, there is a sampling inspection plan with screening by attribute in which the rejected lot in the sampling inspection is thoroughly inspected and nonconforming items are exchanged for conforming items or repaired. In this sampling procedure, the sampling plans have been designed for the purpose of assuring the percentage of nonconforming items in every lot and the upper limit of the average outgoing quality level as the average outgoing percentage of nonconforming items. In this article, the quality evaluation based on Taguchi's loss function is adopted instead of the quality evaluation based on the percentage of nonconforming items as lot quality. Then, we propose a single sampling inspection plan with screening by variable indexed by Taguchi's loss function for the purpose of assuring the upper limit of the maximum expected surplus loss.