Bootstrap Control Charts for Monitoring the Variance of Autocorrelated Processes

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  • 工程に自己相関がある場合の分散モニタリング管理図 －ブートストラップ法を用いて
  • コウテイ ニ ジコ ソウカン ガ アル バアイ ノ ブンサン モニタリング カンリズ ブートストラップホウ オ モチイテ

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In statistical process control charts, it is usually assumed that the observations taken from the process of interest are independent, but in practice the observations in many continuous processes, such as the chemical and maceutical process are actually autocorrelated. This autocorrelation has a large impact on the control charts developed under the independence assumption. A typical effect of autocorrelation is to increase the type I error ratio, when the process is positively autocorrelated. Almost all previous work on monitoring autocorrelated processes has focused on the process mean. The objective of this paper is to investigate control charts for monitoring the process variance when the process is auto correlated. Lu and Reynolds consider an EWMA charts based on the logs of the squared residuals for monitoring the variance of autocorrelated processes. The control limits in the Lu and Rynoles chart are set to be Average Run Length (ARL)=370.4 when the process is in control, and it does not correspond to the type I error ratio α=0.0027 because EWMA statistic is correlated statistic. Thus a method for determining the control limits using Bootstrap is proposed. The Bootstrap is a statistical technique that substitutes computing-power for traditional parametric assumptions. We also investigate Moving R control charts and apply Model Based Bootstrap to construct its control limits. The simulation studies are conducted to show the validity of the Bootstrap control limits. In most situations, the type I error ratios of the Bootstrap control limits are nearer to the desired value than those of conventional control limits.

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