Research On The Afdr-based Multivariate EWMA Chart

With the rapid development of sensing metrology and computing technology,statistical process monitoring methods dealing with high-dimensional observations become increasingly important,and have many important applications.Conventional statistical process control approaches commonly used in industry,such as theHotelling'sT~2 chart,Multivariate EWMA and CUSUM charts etc,show obvious drawback when dealing with high-dimensional process shift simultaneously.By assuming that not all variables in high-dimensional process will shift simultaneously,we introduce the AFDR-MEWMA chart which combines MEWMA chart and the AFDR control method.The AFDR-MEWMA chart first locates potentially out-of control variable via variable selection and then check those selected variables,which is helpful to narrow down the set of variable with suspected mean shift.To improve manufacturing process and product quality,fault detection and root cause identification are both important tasks in Multivariate Statistical Process Control.Most traditional control chart,includingHotelling'sT~2 chart,Multivariate EWMA chart,separate the two tasks into independent and successive procedure by signaling the existence of process faults followed by auxiliary methods to locate root causes.In this paper,we propose the AFDR-MEWMA chart which integrates these two tasks by using the dimensionality reduction techniques.Compared with the false discovery rate,the adaptive control of false discovery rate(AFDR)achieves more efficient fault detection and guarantees identification accuracy in a fairly high level.In this thesis,we bring the AFDR to MWMA.Numerical simulation results demonstrate that the AFDR-MWMA has the capability to detect process fault quickly and the ability to locate shifted variables accurately.When a signal is given,the algorithm also identifies the suspected variables for further root cause diagnosis.Compared with existing methods,the AFDR-MEWMA chart shows advantage in root cause identification as well.The dissertation consists of five chapters that are organized as follows.In Chapter 1,we first describe the backgrounds of statistical process control and then make an introduction to the method used in this paper.In Chapter 2,the theory of statistical process control is discussed at the beginning of this Chapter.Next,we make a brief introduction to the control chart and the average run length(ARL).In Chapter 3,a brief introduction to three different control charts,Shewhart,CUSUM and EWMA,are presented.In Chapter 4,the AFDR-MEWMA chart is proposed.Compared to MEWMA and VS-MEWMA,the numerical simulations are presented to illustrate the performance of the chart.In Chapter 5,compared to VS-MEWMA,a real example is presented to illustrate the performance of AFDR-MEWMA.