Robust Monitoring Of High-dimensional Data Streams

In recent years,statistical approaches to continual surveillance of multiple data streams are greatly needed in today’s industrial,clinical,and epidemiological environment with the process of the society,the innovation of science and technology,the use of all kinds of mobile tools and the rapid development of internet technology.at the same time,which produces the large-scale date streams brings new challenge to the statistical process control(SPC).As a new form of data,the data streams have attracted more and more attention,we can see it everywhere around us,for example,information from sensors,real-time satellite imagery from meteorological satellites,the user communication records,stock information,and multi-stage monitoring of automotive body assembly.Therefore,we highly need the statistical methods for monitor the high-dimensional data streams.The quality control chart,as one of the most effective and important method of SPC.We must suggest the new chart to adapt the industrial production.The model of high-dimensional data streams we studied is also based on the change-point problem.In the monitoring process,we are interested in detecting an change-point as soon as possible,but we don’t know position of the change-point and which subset of data streams is affected by the change.One naive approach is to monitor each local data stream individually.For each local data stream,many efficient local monitoring schemes are available in the literature,and a partial list includes Shewhart’s control chart;moving average charts;or CUSUM,procedure.Unfortunately,the local monitoring approach does not take advantage of global information,and may lead to large detection delays if several data streams provide information about the occurring event.More importantly,even if the local false alarm rate is well controlled at each data stream,the global false alarm rate can be severe when the number of data streams is large,leading to obvious costs and the classic boy who cried wolf phenomenon.So more and more SPC workers promote the global online monitoring but local monitoring.May(2010)and Tartakovsky(2006)put forward respectively the global online monitoring system of high dimensional data stream based on the CUSUM control chart.In this paper,we will use the special properties of EWMAto construct the new control chart.