Online Monitoring Methods For Correlated High-Dimensional Data Streams

In recent years,the problem of the high dimensional data streams gradually is becoming hot,and how to improve product quality and reduce resources waste in process combining with the study of statistical control charts has become one of the important topics of current research.For the online data streams,when the probability of type?error is fixed,we try to decrease false alarm rate,increase the robust and reduce the ARL1,that becomes the research difficulty now.Because of complexity and actuality of the high-dimensional data,how to select the appropriate control chart of correlated high-dimensional data streams to monitor data,which makes the control chart stop as soon as possible,that is one of the great difficulties in statistical process control research.Majority of scholars consider the assumption that the date streams are independent to achieve the purpose of dimension reduction,then they establish the control chart with the methods of the cumulative sum or exponentially weighted moving average to monitor smaller mean shift detection in order to achieve the ideal effect by adjusting the control line,however they are related in fact.In this article,mainly according to the predecessors of the existing work,we combined with the methods applied in high-dimensional data streams which are independent of each other and then used in related ones which are given the correlation coefficient matrix.After that,we used the improved cumulative sum statistics based on the likelihood ratio to replace the original observations and linked with change point problem through the heterogeneous mixture test.From the same detectable range,we applied the method to improved the formula of goodness-of-fit test statistic.Finally,we can obtain one-side statistics about the sum and max of CUSUM statistic,higher criticism statistic and GOF statistic,choose appropriate control limit and like the average run length out of control as the standard to compare the merits of the four methods.After stimulation,it shows that goodness-of-fit statistics is the best in general.The main content of this paper is as follows:Firstly,it introduces the background and significance of studying CUSUM control chart,and the great contribution for the development of industry,lists some important researches about CUSUM control chart method in domestic and abroad.The problem we need to solve in this paper is putting forward in this paper definitely.Secondly,some needed basic knowledge was elaborated in this article,including the applied theory of the CUSUM control chart and the heterogeneous mixture test;determination and formula of the detectable range of higher criticism statistic;the practical theory of goodness-of-fit test and one-side statistic formula of the improved goodness-of-fit test;themethod of giving the alarm time.Thirdly,given the correlation matrix,we can find the appropriate limit from simulation,to find the right line,and compare the alarm times and whose variances of the different drifts out of control.In other words,the alarm time is the smaller in same drift size and same dimensions,the control chart is more sensitive and the variance is smaller,the control chart is more robust.Finally,it concludes that goodness-of-fit test is best of the overall optimal method.