The Control Chart of Data Depth Based on Influence Function of Variance Vector

Abstract

The concept of data depth has been used for multivariate control charts. One of the advantages of data depth is that statistics constructed independent of the distribution of quality characteristics or is known as free distributions. One of them is depth based on Mahalanobis distance. Individual Mahalanobis distance is essentially formed by the ratio of generalized variance (GV) calculated by not involving the individual to be calculated distances to the mean by GV calculated from the complete data. The Control charts constructed with Mahalanobis Depth can be visualized (exploration) is plot depth over depth, so it is known DD-diagram and create control limits as control chart Shewhart. The main disadvantage of Mahalobis distance lies in GV, the value of GV depends on the sample size and the number of quality characteristics, in addition two different covariance matrices can give the same GV value. Departing from the weakness of GV, this research will be focused on the formation of vector data depth control diagrams (VV), because VV can resolve the GV weaknesses. Based on the simulation study, it shows that both DD-GV and DD-VV control charts give the same pattern in ongoing process of in-control that is forming a straight line through point (0,0) and (1,1), for correlation between weak variables, but for correlation between variables are very strong, the DD-GV control does not expressly state the in control process. The application process control of data in both diagram medical product, indicate that there is a symptom of mean vector or covariance matrix.