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A trinomial chart for monitoring the process variance
Computers & Industrial Engineering ( IF 7.9 ) Pub Date : 2021-04-17 , DOI: 10.1016/j.cie.2021.107332
Antonio Fernando Branco Costa

In this article we propose an attribute chart to control the process variability. A multiple-step gauge is used to classify the sample items in three excluding categories; that is, items in categories 1, 3, and 2, are, respectively, items with the X dimension in one of the two tails, in the central part, and in between the tails and the central part of the X distribution. After determining (n1, n2) – the number of items in the first and in the second categories, the monitoring statistic of the Trinomial chart, calculated as an1 + bn2, is compared with a control limit CLT; If an1 + bn2 > CLT, then the chart signals an increase in the process variance. The coefficients a and b are the weights assigned to the items according to their categories; for instance, if a = 2 and b = 1, then an item in the first category has the weight of two items in the second category. The Trinomial chart signals variance increases faster than the Range chart. The Trinomial chart is also more sensitive than its competitor even when the X distribution is no longer normally distributed. In comparison with the S2 chart, if the sample is small (n = 3 or 4), then the Trinomial chart signals faster, if the sample is large (n > 5), then the Trinomial chart requires samples of size (n + 1) to defeat its competitor; it is worthy to note that the use of larger samples is highly compensated by the fact that the Trinomial chart is an attribute chart, free of measurements and calculations to obtain the sample variances.



中文翻译:

用于监控过程差异的三项式图表

在本文中,我们提出了一个属性图来控制过程的可变性。多步骤量规用于将样本项目划分为三个排除类别。也就是说,类别1、3和2中的项目分别是X维度位于两个X分布的尾部之一,在中心部分以及在X分布的尾部和中心部分之间的项目。确定(后Ñ 1Ñ 2) -项目的数量在第一和第二类,三叉图表的监控统计,计算为一个1  +  BN 2,与控制极限进行比较CL Ť ; 如果一个1  +  bn 2  >  CL T,则该图表示过程方差增加。系数ab是根据项目类别分配给项目的权重;例如,如果a  = 2且b  = 1,则第一类中的一项的权重为第二类中两项的权重。Trinomial图表信号方差的增加快于Range图表。即使X分布不再是正态分布,三项图也比其竞争对手更敏感。与S 2图表相比,如果样本较小(n = 3或4),则Trinomial图表会发出更快的信号,如果样本很大(n  > 5),则Trinomial图表需要大小(n  +1)的样本才能击败竞争对手。值得注意的是,三项式图是一个属性图,无需进行任何测量和计算即可获得样本方差,因此对较大样本的使用得到了高度补偿。

更新日期:2021-04-27
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