A New Distribution-free Multivariate Control Chart Based On Change-point Model

The importance of statistical process control (SPC) techniques in quality improvement iswell recognized in industry. With the rapid development of society, The demand of monitoringthe multiple properties of the product simultaneously (MSPC) become larger and larger. And thecorresponding multivariate control chart has been researched extensively. But most of thesemultivariate control charts are based on the fundamental assumption that either the quality indexof the tested products have multivariate normal distribution or some of the parameters of processdata is known. However, it is recognized that in most of the manufacturing process, theunderlying process distribution is unknown and not multinorrmal. Especially for ahigh-dimensional process, it is difficult to assume that the process data is multivariate normalvector. Thus, casual distribution’s assumption of the process data will lead to two seriousadverse consequences. One is that the run length of control charts in control will gravely deviatefrom the value which we want to achieve. And it enables us to judge whether the control chart isin control or not. The second one is that the test statistic assumed is not necessarily sensitivity tothe drift of the current process. So when the process is out of control, it’s often difficult to alarmquickly. Therefore, multivariate nonparametric or robust control chart is very necessary. Andmore and more attentions are given by scholars in the field of statistical quality control.In recent years, the reference methods of multivariate nonparametric control chart mainlyinclude the data depth, the rank method within vector and recently developed method based onspatial symbol and rank, but all of them have their own shortcomings. For example, thenon-robustness of high-dimensional, the correlation of each component and the in-controlsample is in small size, etc.For the above shortcomings, Chen Nan, Zou Changliang have proposed a multivariatenonparametric control chart (DFEWMA). They constructed a series of conditional distribution-free test statistics and used the online dynamic control line to test, obtaining good results.However, the EWMA control chart is more sensitive to small drift when is small; the EWMAcontrol chart is more sensitive to big drift when is big. So, this paper proposes a control chartbased on the change-point model (DFCP), and comparing with the DFEWMA control chart. Interms of DFEWMA control chart, the proposed DFCP control chart have good detectioncapability on a range of possible drift. In other way, the DFCP model has better robustness.