基于最新差异信息的重启EWMA控制图
A Restarting EWMA Control Chart Based on the Latest-Difference-Information of Sample
摘要: 在统计过程控制中，随机性会延迟对过程失控的诊断，所以挖掘与失控相关的非随机信息，尽早检测出失控信号是控制图设计亟待解决的关键问题。本文通过在样本数据中设计重启机制以消除反向信息的影响，以及在图统计量中加入样本最新差异信息以量化过程最新变化的影响，设计了改进型EWMA均值控制图(ReMEWMA)，实现了过程均值单侧漂移的检测。实验表明，与现有的MEWMA、EWMA和IEWMA控制图相比，ReMEWMA均值检测控制图在仿真数据和真实过程数据实验中均具有更小的失控平均运行长度(ARL1)。
Abstract: In statistical process control, randomness would delay the identification of out-of-control(OC) sig-nals, therefore, mining the OC-related non-random information to discover OC signals earlier is the key issue when designing a control chart. In this paper, an improved EWMA Mean control chart (ReMEWMA) is designed, in which a restart mechanism is set to the sample data to eliminate the in-fluence of reverse information, and the latest difference-information of the sample is weighted-ly-introduced into the graph statistics to quantify the influence of the latest changes of the process, and at last the detection of the potential one-sided-drifting on process mean is accomplished. Nu-merical experiments show that compared with the existing MEWMA, EWMA and IEWMA methods, the ReMEWMA mean-detection-control-chart presents a smaller average run length of out-of-control (ARL1) on both simulated and real process data.
文章引用：直雪瑶, 宋学力, 王凯明, 张亚洁. 基于最新差异信息的重启EWMA控制图[J]. 应用数学进展, 2023, 12(11): 4733-4742. https://doi.org/10.12677/AAM.2023.1211466

参考文献

[1] Qiu, P. (2013) Introduction to Statistical Process Control. CRC Press: Taylor and Francis Group, New York, 11-15. [Google Scholar] [CrossRef] 
[2] Montgomery, D.C. (2013) Introduction to Statistical Quality Control. 7th Edi-tion, Wiley, New York.
[3] Roberts, S.W. (1959) Control Chart Test Based on Geometric Moving Averages. Techno-metrics, 1, 239-250. [Google Scholar] [CrossRef] 
[4] Lucas, J.M. and Saccucci, M.S. (1990) Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements. Technometrics, 32, 1-12. [Google Scholar] [CrossRef] 
[5] Shewhart, W.A. (1925) The Application of Statistics as an Aid in Maintaining Quality of a Manufactured Product. Journal of the American Statistical Association, 20, 546-548. [Google Scholar] [CrossRef] 
[6] Patel, A.K. and Divecha, J. (2011) Modified Exponentially Weighted Moving Average Control Chart for an Analytical Process Data. Journal of Chemical Engineering and Materi-als Science, 2, 12-20.
[7] Khan, N., Aslam, M. and Jun, C.H. (2016) Design of a Control Chart Using a Modified EWMA Statistic. Quality and Reliability Engineering International, 33, 1095-1104. [Google Scholar] [CrossRef] 
[8] Alevizakos, V., Chatterjee, K. and Kouvinos, C. (2021) Modified EWMA and DEWMA Control Charts for Process Monitoring. Communications in Statistics Theory and Methods, 51, 7390-7412. [Google Scholar] [CrossRef] 
[9] William, H.W. and Mahmoud, M.A. (2005) The Inertial Properties of Quality Control Charts. Technometrics, 47, 425-436. [Google Scholar] [CrossRef] 
[10] Hamilton, M.D. and Crowder, S.V. (1992) Average Run Lengths of EWMA Controls for Monitoring a Process Standard Deviation. Journal of Quality Technology, 24, 44-50. [Google Scholar] [CrossRef] 
[11] Shu, L., Jiang, W. and Wu, S.A. (2007) One-Sided EWMA Control Chart for Monitoring Process Mean. Communication in Statistics-Simulation and Computation, 36, 901-920. [Google Scholar] [CrossRef] 
[12] 宋明顺, 张俊亮, 方兴华, 等. 基于蒙特卡罗方法的模型质量控制图[J]. 系统科学与数学, 2015, 35(11): 1291-1303.
[13] Robinson, P.B. and Ho, T.Y. (1978) Average Run Lengths of Geometric Moving Charts by Numerical Methods. Technometrics, 20, 85-93. [Google Scholar] [CrossRef] 
[14] Crowder, S.V. (1987) A Simple Method for Studying Run Length Distribution of Exponentially Weighted Moving Average Charts. Technometrics, 29, 401-407. [Google Scholar] [CrossRef] 
[15] Saccucci, M.S. and Lucas, J.M. (1990) Average Run Lengths for Exponentially Weighted Moving Average Control Schemes Using the Markov Chain Approach. Journal of Quality Technology, 22, 154-162. [Google Scholar] [CrossRef] 
[16] 王兆军, 巩震, 邹长亮. ARL计算综述[J]. 数理统计与管理, 2011, 30(3): 467-497.

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