On the Charting Procedures: Chart and DD-Diagram

Multivariate analysis is increasingly used to include all dimensions of quality concept, in light of rapid development of customer requirements. With the recent advances in information technology and in recording, large amounts of multivariate data are now needed to be analyzed. Many charting procedures are based on Mahalanobis distance, but their applicability relies heavily on the requirement of normality and their performance is related to the choice of a type I error rate. An alternative charting scheme based on data depth is pursued and its performance is assessed through a real example. This performance and that of a chart for individual observations are discussed. Using the centre-outward ranking, this new method named DD-diagram is used to detect any multivariate quality datum that one of its components exceeds its limiting variation interval. For a given error-free sample, the DD-diagram can be used to signal out any point of another observed sample taken from a multivariate quality process. This new scheme based on data depth uses a properly chosen limiting variation line or in order to evaluate the outlyingness of every point in the observed sample in all directions of the considered -variates of quality process. 1. Introduction Control charts are standard tools that are used to monitor quality process to identify instability within the manufacturing process. In practice, the quality of a product is determined by the interaction of multiple characteristics that are correlated, it is a multivariate phenomenon by nature. So adequate techniques need to be used to monitor the multivariate quality process. Multivariate Shewhart control chart was first introduced in 1947. It was based on the test statistic and known as Hotelling’s chart. Then, a number of multivariate control charts were designed to suit different situations such as multivariate CUSUM and multivariate EWMA charts. These classical monitoring charts have been developed under a number of assumptions quoted by [1]. The performance of the multivariate control charts relies heavily on the hypothesis that the underlying distribution of the quality process is multivariate normal. It is well known that in practice this hypothesis rarely holds. Alternative procedures are needed to overcome this limit. Based on a data depth notion, [2] refined a visual procedure named DD-diagram which uses data depth plot to monitor any multivariate quality data and does not require any assumptions about the underlying distribution of the process. This graphical method provides a visualization of a change in