An auxiliary information-based (AIB) maximum exponentially weighted moving average (MaxEWMA) chart has been proposed to simultaneously monitor both increases and decreases in the process mean and/or variability, called the AIB-MaxEWMA chart, which is superior to the existing MaxEWMA chart. In this paper, we propose the AIB maximum generally weighted moving average chart, called the AIB-MaxGWMA chart, to further enhance the sensitivity of the AIB-MaxEWMA chart. Numerical simulation studies indicate that the AIB-MaxGWMA chart is sensitive to small shifts in the process mean and/or variability. The performance of the AIB-MaxGWMA chart based on average run lengths (ARLs) also outperforms than its counterparts including AIB-MaxEWMA, MaxGWMA and MaxEWMA charts. An example is used to illustrate the efficiency of the proposed AIB-MaxGWMA chart in detecting small process shifts.

中文翻译：

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用于同时监测过程均值和变异性的基于辅助信息的最大一般加权移动平均图

已经提出了一种基于辅助信息 (AIB) 的最大指数加权移动平均 (MaxEWMA) 图来同时监测过程均值和/或变异性的增加和减少，称为 AIB-MaxEWMA 图，它优于现有的 MaxEWMA图表。在本文中，我们提出了 AIB 最大值一般加权移动平均图，称为 AIB-MaxGWMA 图，以进一步增强 AIB-MaxEWMA 图的敏感性。数值模拟研究表明，AIB-MaxGWMA 图对过程均值和/或变异性的微小变化很敏感。基于平均运行长度 (ARL) 的 AIB-MaxGWMA 图表的性能也优于其对应图表，包括 AIB-MaxEWMA、MaxGWMA 和 MaxEWMA 图表。