Multivariate Statistical Process Control In Two-dimensional Plane

Modern manufacturing industry required company to measure and control more and more quality characteristics during the process, thus to satisfy customer’s needs in product’s quality. Therefore the Multivariate Statistical Process Control(MSPC) techniques were introduced to monitor the manufacturing process. In this article, we proposed a new MSPC schema based on the two-dimensional Fused LASSO for quality control problem in which the mean shifts have some natural ordering in two-dimensional plane. Because the two-dimensional Fused LASSO penalties the difference between successive variables, it is a desirable tool to identify the natural ordering among variables. The numeric simulation study shows that the two-dimensional Fused LASSO based control chart can detect mean shift of such structure more quickly and efficiently, especially in the case which the shift value is large. An application to the engine flatness data shows that the two-dimensional Fused LASSO control chart is applicable and useful. However, not all the quality characteristics are measured in a continual scale. When the quality data are discrete, the normality assumption of two-dimensional Fused LASSO based control chart is violated. To compensate this, we proposed a control chart for multivariate count data based on the multivariate Poisson Log-normal distribution. This control chart can handle with multivariate over-dispersed count data with either positive or negative correlations. The parameters estimation is achieved by Markov Chain Monte Carol method. The numeric simulation study shows that the performance of some existing multi-attribute control charts are serious impact by the data over-dispersion. Furthermore, the newly proposed multi-attribute control chart performs well in the presence of over-dispersion. Finally, an application of the new multi-attribute control chart to the wafer defect data is shown.