THE APPLICATION OF THE MULTINOMIAL CONTROL CHARTS UNDER INSPECTION ERROR - Chen, Long-Hui; Chang, Fengming M.; Chen, Yueh-Li (International Journal of Industrial Engineering: Theory, Applications and Practice, 2011)
Control charts have become one of the most commonly used tools for monitoring process variations in today’s manufacturing environment. The p chart plays the important role in controlling the fraction of nonconforming article produced. Instead of simply classifying qualities into conforming and non-conforming, products are classified into several classes of quality in this study. It is named as multinomial control charts. Classic multinomial control charts are built without taking into account the inspection error. However, the inspection through instruments or human observers will ever make mistakes such that the results of control charts are not valid. Therefore, how to examine the influence of inspection error on the multinomial control charts is concerned in this study. In this article, the inspection error influence on the multinomial control charts is examined. Two modified models using statistical approach are proposed to build the corresponding control charts when inspection error exists. In addition, two evaluation indexes including type I error and out-of-control ARL are performed to compare the performance of classic multinomial control charts and two modified models. When type I error is fixed, the out-of-control ARL results show that Model I (adjust true probability distribution) works better than Model II (adjust statistical values). Such approaches can provide more realistic modeling to monitor and identify the production process variations.