Variable sampling inspection with screening for assuring the upper limit of maximum expected surplus loss when lot quality follows mixed normal distribution consisting of two normal distributions

Taguchi has presented the concept of quality loss as an evaluation measure of the quality of items based on variable properties. Recently, Takemoto and Arizono, and Morita et al. have proposed variable sampling inspection with screening for the purpose of assuring the upper limit of maximum expected surplus loss after inspection. In this inspection scheme, it is assumed that the product lot consists of only items manufactured through a single production line and the lot quality characteristics follow a normal distribution. In previous literature regarding inspection schemes, it has been commonly assumed that lot quality characteristics obey the single normal distribution under the assumption that all the items are manufactured under the same conditions. On the other hand, the production line should be designed in order that the workload of respective processes becomes uniform on the basis of the concept of line balancing. Therefore, the bottleneck process for the workload is generally composed of more than one parallel workshop. The lot quality characteristics from such a production line with the process consisting of some parallel workshops might not strictly follow single normal distribution. Therefore, in this article, we expand an applicable scope of the above-mentioned variable sampling inspection with screening. Specifically, we consider variable sampling inspection with screening for the purpose of assuring the upper limit of maximum expected surplus quality loss in the production lots when the lot quality follows mixed normal distribution consisting of two normal distributions, as a basic study into quality assurance for mixed normal distributions. Then, the applicability and effectiveness of the sampling inspection are verified.