A CUSUM scheme with variable sample sizes and sampling intervals for monitoring the process mean and variance
A CUSUM scheme with variable sample sizes and sampling intervals for monitoring the process mean and variance
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DOI：
10.1002/qre.782
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发表时间：
2007-03
影响因子：
2.3
通讯作者：
Zhang Wu;Shenmin Zhang;Penghui Wang
中科院分区：
文献类型：
--
作者：
Zhang Wu;Shenmin Zhang;Penghui Wang
自适应控制功能和自适应图是两种监测方案，比传统的静态休哈特图更有效地检测过程的均值和方差的变化。然而，自适应图的设计和分析在数学上是棘手的，操作是非常费力的。本文提出了一种VSSI WLC方案，这是一种使用可变样本大小和采样间隔（VSSI）的基于加权损失函数的加权和（WLC）方案。该方案基于单个统计量WL（加权损失函数）检测双侧均值偏移$\delta_{\mu}$和增加的标准差偏移$\delta_{\sigma}$。最重要的是，VSSI WLC方案比VSSI CCC方案更容易操作和设计，VSSI CCC方案包括三个单独的MANUUM图（其中两个监测增加和减少的均值偏移，一个监测增加的方差偏移）。总体而言，VSSI WLC方案比静态$\bar{X}$&S图（72.36%），VSSI $\bar {X}$&S图（30.97%）和静态WLC方案（50.94%）更有效。在大多数情况下，它甚至比复杂的VSSI CCC方案更有效。版权所有© 2006约翰威利父子有限公司。
The adaptive control feature and CUSUM chart are two monitoring schemes that are much more effective than the traditional static Shewhart chart in detecting process shifts in mean and variance. However, the designs and analyses of the adaptive CUSUM chart are mathematically intractable and the operation is very laborious. This article proposes a VSSI WLC scheme, which is a weighted‐loss‐function‐based CUSUM (WLC) scheme using variable sample sizes and sampling intervals (VSSI). This scheme detects the two‐sided mean shift $\delta_{\mu}$ and increasing standard deviation shift $\delta_{\sigma}$ based on a single statistic WL (the weighted loss function). Most importantly, the VSSI WLC scheme is much easier to operate and design than a VSSI CCC scheme which comprises three individual CUSUM charts (two of them monitoring the increasing and decreasing mean shifts and one monitoring the increasing variance shift). Overall, the VSSI WLC scheme is much more effective than the static $\bar{X}$&S charts (by 72.36%), the VSSI $\bar {X}$&S charts (by 30.97%) and the static WLC scheme (by 50.94%) for detection. It is even more effective than the complicated VSSI CCC scheme for most cases. Copyright © 2006 John Wiley & Sons, Ltd.