⊿^2 Chart for Small Number of Subgroups : Process Control Based on Categorical Data Distributed as Compound Distribution (Part 2)

Abstract

This paper discusses how to control the process from which categorical data obtained by inspection distributed as multivariate beta multinomial distribution. In order to control the process, the ⊿^2 Chart is proposed by Takahashi. However many charts are applied as soon as possible in practical process. Then the level of significance of the charts consisted small subgroups must be considered. First of all we discuss the level of significance of the ⊿^2 Chart in case of small number of subgroups and clarify some problems. Next we propose a method to solve the problems. Finally we clarify the level of significance of the ⊿^2 Chart based of proposed method to show this method is useful.