Spatial Distribution Pattern Based CUSUM Control Chart And Its Applications

In recent years,more and more scholars pay attention to the spatial distribu-tion pattern which changes over time under different scenarios.Monitoring spatial distribution pattern that changes over time can help us detect changes of geographic patterns quickly,an-alyze the causes of such changes early,and adopt appropriate strategies in a timely manner.However,the data involved in spatial distribution pattern contain not only the information of attribute,but also the information of geographical location.At present,there are few researches on the monitoring of spatial distribution pattern.In view of these situations,some researchers had proposed effective cumulative sum（CUSUM for short）control charts to monitor the data based on different spatial statistics describing spatial distribution pattern.In fact,among spatial statistics,Global Moran’s I、Local Moran’s I and Geary’s C Index can well describe spatial distribution pattern,and they are widely used in epidemiology,ecology,economics and other fields.However,their monitoring of spatial pattern changes has not been thoroughly studied.Based on this background,this paper has done the following two aspects of work:（1）In this paper,CUSUM control charts of global autocorrelation are proposed to monitor the changes of spatial distribution pattern.On the one hand,in the case that there is only one data of the spatial unit in the study area,making use of the Geary’s C Index,we propose a CUSUM control chart of Geary’s C Index.And then the simulated monitoring is carried out.On the other hand,in the case of more than one data of the spatial unit in the study area,in this paper,firstly,the CUSUM control chart of the Improved Global Moran’s I is presented by using the Improved Global Moran’s I.And then the proposed control chart is compared with the CUSUM control chart of Traditional Global Moran’s I.Finally,the proposed CUSUM control chart of the Improved Global Moran’s I is applied to monitor the actual_2.5data set.Through practice,we find that the monitoring scheme proposed in this paper has a good detection effect.（2）Considering the diversity of data,this paper proposes a multivariate cumulative sum（MCUSUM for short）control chart of local autocorrelation to monitor the changes of spatial distribution pattern.Because there is a Local Moran’s I in every spatial unit of the study area,we use these Local Moran’s Is to integrate them into a multivariate random vector,and then propose the MCUSUM control chart of the Local Moran’s Is.Finally,the proposed MCUSUM control chart of the Local Moran’s Is is applied to monitor the actual GDP data set and₂data set.We have proved the feasibility of the proposed monitoring scheme through practice.