Nonparametric Control Chart Based On Data Depth

Statistical process control is an important element of product quality control. Andcontrol charts is an effective and widely used tool. In case of the increasinglycomplexity product, we often need to detect more than one quality characteristicssimultaneously. Traditional Shewhart control chart is based on the assumption that datadistribution is a normal distribution. But in fact it is hard to meet this assumption. Andthe multivariate nonparametric control charts can be a good solution of multiple qualitycharacteristics which can hardly be normal distribution. Because of people’sincreasingly requirements quality, we needs the chart to be more sensitive to small shiftsof the process, while the cumulative sum (CUSUM) control charts and exponentiallyweighted moving average (EWMA) control charts are good choices.In order to improve the detect of the small shifts of the process in which themultiple quality characters are non-normal or unknown, the theory of data depth, theCUSUM scheme and EWMA scheme are applied to construct the new control chart.Because data depth doesn’t rely on the distribution, and CUSUM, EWMA control chartare sensitive to small shifts. This paper proposes CUSUM charts and EWMA chartsbased on Mahalanobis depth (MhD) and simplicial depth (SD), denoted by MhD-CUSUM, SD-CUSUM, MhD-EWMA and SD-EWMA, respectively. The Matlabsimulation selects bivariate normal distribution and bivariate banana distribution. Theresult of new charts will compare to the traditional MCUSUM chart, MEWMA chartand the rEWMA charts that Messaoud made by the theory of rank.The results of simulation show that: The established SD-EWMA control chart andMhD-EWMA control chart were better than Messaoud’s SD-rEWMA control chartsand MhD-rEWMA control chart; in bivariate normal distribution simulation, thetraditional MEWMA control chart is superior to SD-EWMA control chart and MhD-EWMA control chart; in the bivariate banana distributed simulation, the establishedSD-EWMA control chart is better than the others, and Messaoud the SD-rMEWMAcontrol chart followed.