Abstract In this article, we propose the Trinomial - ATTRIVAR (T-ATTRIVAR) control chart where attribute and variable sample data are used to control the process mean. Firstly, two discriminating limits sort the sample items into three excluding categories; that is, items in categories A, B, or AB, are, respectively, items with X dimensions smaller than the lower discriminating limit, larger than the upper discriminating limit, or neither smaller than the lower discriminating limit nor larger than the upper discriminating limit. Depending on the number of sample items in each category, one of three decisions is made: the process is declared in-control, the process is declared out-of-control, or all sample items are also measured. In this last case, the sample mean of X is used to decide the state of the process. Aslam et al. (2015) worked with the particular case where the sample items are classified as defective (items in category - A plus items in category - B) or not-defective (items in category - AB). The strategy of splitting defectives into two excluding categories (A and B) enhances the performance of the ATTRIVAR chart. It is worth to emphasize that the previous attribute classification truncates the X distribution. Consequently, the mathematical development to obtain the ARLs is complex – the Average Run length (ARL) is the average number of samples the control chart requires to signal. With the density function of the sum of truncated X distributions, we obtained the exact ARLs. The exact minimum ARLs are lower than the minimum ARLs Ho and Aparisi (2016) obtained with the Genetic Algorithm.

中文翻译：

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三项式 ATTRIVAR 控制图

摘要 在本文中，我们提出了三项式 - ATTRIVAR (T-ATTRIVAR) 控制图，其中使用属性和可变样本数据来控制过程均值。首先，两个判别界限将样本项目分为三个排除类别；即A类、B类、AB类中的物品分别是X维小于判别下限、大于判别上限或既不小于判别下限也不大于判别上限的项目. 根据每个类别中样本项目的数量，做出以下三个决定之一：宣布过程处于受控状态，过程宣布处于失控状态，或同时测量所有样本项目。在最后一种情况下，X 的样本均值用于决定过程的状态。阿斯拉姆等人。(2015) 处理样本项目被归类为有缺陷（类别中的项目 - A 中的项目加上类别 - B 中的项目）或无缺陷（类别中的项目 - AB）的特殊情况。将缺陷品分为两个排除类别（A 和 B）的策略增强了 ATTRIVAR 图表的性能。值得强调的是，前面的属性分类截断了X分布。因此，获得 ARL 的数学发展是复杂的——平均运行长度 (ARL) 是控制图需要发出信号的平均样本数。使用截断的 X 分布之和的密度函数，我们获得了准确的 ARL。确切的最小 ARL 低于使用遗传算法获得的最小 ARL Ho 和 Aparisi (2016)。