A New Distribution-free Multivariate Control Chart

Due to the development of science and technology, the modern industrial production hastaken more advancement. On one hand, it is able to produce the products quickly to meet theneeds of people. On the other hand, the large-scale automation production would produceunqualified products inevitably which affect the quality of the products and make the enterprisesuffer. The21st century is the century of quality which as the first priority. Most qualityassurance you need are depend on the (statistical process control). SPC not only can helpenterprises to reduce the loss by finding the solutions for the problems quickly which exist in theproduction, but also has a good ability to predict the future with the process of monitoring data.The more develop of the science and technology, the more combinations about the SPC andvarious fields. With the addition of computer, nature of high-dimensional data has become afocus topic.Through them, the technology which combined computer to detect the monitoring of qualityproblem online has a high practical application value. It requires measuring more qualitycharacteristics, meanwhile finding the unqualified products quickly. To ensure the efficiency endavoid the unnecessary waste. So the problem of multivariate nonparametric is the key of theresearch.The traditional control chart needs to assume the distribution of the sample. In fact it isdifficult to estimate the sample model which result in the deviation from the fact. And most ofthe existing nonparametric methods neither are based on some assumption, or using a lot ofhistorical data to estimate or distribution which are not the distribution free. So finding a newdistribution free control chart to solve the problem of high-dimensional nonparametric is theimportant of this article.Combine with the rank statistics and Wilcoxon theoretical which are nonparametricmethods to find a statistics which has nothing to do with the sample date. It really has nothing todo with the distribution. In order to solve the problem with the sample size is unknown to usingthe change point detection model. Use the exponentially weighted moving average control chartto design a new distribution free control chart. Make sure this kind of control chart, during the incontrol condition (IC) never before achieve the theory run length, and during the out of controlcondition (OC) to sound an alarm quickly when find the sample out of control to reduce theloss. Simulation results show that the new nonparametric control chart compared with theprevious nonparametric control chart can be more widely applicable to all kinds of distribution,particular in high dimension and with the less historical observations. It has very goodmonitoring effect even compared with the previous parameter control chart. The newnonparametric control chart has a good monitoring for small and medium-sized drift in highdimension multivariate distribution. Especially with less historical observation is difficult toestimate the distribution.