An Adaptive Distribution-Free Multivariate EWMA Control Chart

The importance of statistical process control (SPC) techniques in quality improvement iswell recognized in industry. Control chart is the most important method and tool of SPCtechnology. Many industrial quality control process involves a series of features which is notsingle, but two or more, in other words, it is diverse. MSPC research works are mostly based onthe fundamental assumption that either the process data hava multinormal distributions or the ICdistributionF0(evenF1) is known. However, it is well recognized that in many applications, theunderlying process distribution is unknown and not multinormal. Therefore, the control chartunder the assumption of data independence and normal distribution will be highly affected,which could reduce the efficiency of the control chart. In addition, if the actual shifts are beyondthe monitoring rang of setted parameters, control chart will have badly performance, which maylead to a false judgement on the state.Based on the above consideration, we propose an adaptive multivariate distribution-free testwith EWMA sheme---ADFEWMA Control Chart. It combines multivariate EWMA which isbased on Wilcoxon rank-sum test with adaptive method in order to monitor a series of processshift. Its difference with the traditional control chart is mainly characterized by the following twoaspects：first of all, the probability control limits are determined based on the observation insteadof decided before monitoring. The second, it is able to deliver satisfactory in-control run-lengthperformance for any distribution with any dimension. Moreover, we use score function onchoosing parameters, reducing the effects of the artificial setting parameters. Finally, it is alsevery efficient in detecting multivariate process shifts when the process distribution isheavy-tailed or skewed.Comparing the performance of the ADFEWMA DFEWMA, SREWMA, SSEWMA,MSEWMA and MEWMA control chart, the simulation results show the effectiveness,robustness and sensitivity of ADFEWMA control chart：(i) it can always achieve the desired ICrun-length regardless the data distributions.(ii) under the non-normal distribution, ADFEWMAcontrol chart are sensitive to the small and moderate shifts.(iii) the change of the smoothparameter have less effect on the effectiveness and robustness of ADFEWMA control chart.