The progressive mean (PM) statistic is based on a simple idea of accumulating information of each subgroup by calculating the average progressively. Its weighting structure is based on a subgroup number that changes arithmetically, which makes the PM chart unique and efficient compared with the existing classical memory control charts. In a recent article (see reference 1), it was claimed that the PM chart is a special case of the exponentially weighted moving average (EMWA) chart. In this article, it is shown that even though the PM statistic can be written in the form of an EWMA statistic, the variance of the PM statistic is different from that of the EWMA statistic. Consequently, the limits of the PM chart are different from that of the EWMA chart. Therefore, it is found that the PM chart is not a special case of the EWMA chart; hence, the claim in reference 1 is incorrect. Furthermore, it is pointed out in this paper that no adaptive property in the weighting parameter of the PM statistic exists, further contradicting the claim in reference 1.

中文翻译：

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渐进平均控制图不是指数加权移动平均控制图的特例

渐进平均 (PM) 统计量基于通过渐进计算平均值来累积每个子组的信息的简单想法。它的权重结构基于一个在算术上变化的子组数，这使得 PM 图与现有的经典记忆控制图相比具有独特性和高效性。在最近的一篇文章（参见参考资料 1）中，声称 PM 图是指数加权移动平均 (EMWA) 图的一个特例。在本文中，表明即使 PM 统计量可以写成 EWMA 统计量的形式，但 PM 统计量的方差与 EWMA 统计量的方差不同。因此，PM 图表的限制与 EWMA 图表的限制不同。因此，发现PM图并不是EWMA图的特例；因此，参考文献 1 中的主张是不正确的。此外，本文还指出 PM 统计量的加权参数不存在自适应特性，这进一步与参考文献 1 中的主张相矛盾。