Cusum Charts for Monitoring an Autocorrelated Process
Cusum Charts for Monitoring an Autocorrelated Process
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DOI：
10.1080/00224065.2001.11980082
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发表时间：
2001-07
影响因子：
2.5
通讯作者：
Chao-Wen Lu;M. R. Reynolds
中科院分区：
文献类型：
--
作者：
Chao-Wen Lu;M. R. Reynolds
传统上，过程监控控制图的设计和评估都是在假设过程输出在不同时间的观测是独立的情况下进行的。然而，自相关可能存在于许多过程中，并且可能对控制图的属性产生强烈影响。本文研究了在过程观测值可以建模为AR（1）过程加上一个附加随机误差的情况下，用于监控过程均值的ARUM控制图。基于绘制模型预测的残差或绘制原始观测值的图，被认为是最佳的。基于原始观测值的XUUM图的性能与残差的XUUM图一样好，但自相关水平较高且过程均值偏移较大的情况除外。给出了在自相关情况下观测值的最优图的设计方法。根据残差或原始观测值，将EWMA图与Shewhart图和EWMA图进行比较。CUSUM和EWMA图表在检测过程均值变化的能力方面表现相似。
Control charts for process monitoring have traditionally been designed and evaluated under the assumption that observations on the process output at different times are independent. However, autocorrelation may be present in many processes, and may have a strong impact on the properties of control charts. This paper investigates CUSUM control charts for monitoring the process mean for the situation in which observations from the process can be modeled as an AR(1) process plus an additional random error. CUSUM charts based on plotting the residuals from model forecasts, or on plotting the original observations, are considered. CUSUM charts based on the original observations perform as well as CUSUM charts of residuals, except in the case in which the level of autocorrelation is high and the shift in the process mean is large. A method for designing the CUSUM chart of the observations in the presence of autocorrelation is given. The CUSUM charts are compared to Shewhart and EWMA charts based on the residuals or on the original observations. The CUSUM and EWMA charts perform similarly in terms of the ability to detect shifts in the process mean.