A transformation technique in designing multi-attribute C control charts

In a production process, when the quality of a product depends on more than one characteristic, multivariate quality control techniques are used. Although multivariate statistical process control is receiving increased attention in the literature, little work has been done to deal with multi-attribute processes. In this paper, a new methodology has been developed to monitor multi-attribute processes, in which the defect counts are important and different types of defect are dependent random variables. In order to do this, based on the symmetric square root transformation concept, first, multi-attribute data is transformed, such that the correlation between variables either vanishes or becomes very small. Then, by a simulation and bisection method, the symmetric control limits are found and a symmetric rectangular region is formed for control. In simulation studies, some numerical examples are presented to illustrate the proposed method and to evaluate and compare its performance to the ones of the existing method.