The CUSUM (C) charts are well recognized as a potentially advanced process monitoring tools because of their sensitivity against small and moderate shifts. In this paper, we first improve the sensitivity of the Brownian motion–based C (BC) chart with an appropriate transformation, named new BC (NBC) chart, for monitoring moderate and large shifts in the mean of a normal process. Then, using the control charting structure of the Crosier C (CC) chart, we propose the NBCC (NBC with CC structure) chart. In addition, for efficiently detecting a mean shift within an interval, dual version of these control charts are also proposed, named the dual NBC (DNBC) and dual NBCC (DNBCC) charts. Moreover, the fast initial response feature is also incorporated into the proposed charts. Using the Monte Carlo simulation, the run length properties of the proposed charts are computed. The run length performances of the existing and proposed charts are compared using the extra quadratic loss and integral relative average run length as performance criterion. It turns out that the NBC and NBCC (DNBC and DNBCC) charts are uniformly more sensitive than the C, CC, and NBC (dual C and dual CC) charts when detecting the mean shifts in small, moderate, and large intervals, where the DNBCC chart outperforms all considered charts. The proposed charts are also applied on real data sets to support the proposed theory.

中文翻译：

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新的CUSUM和双重CUSUM均值图表

CUSUM（C）图表由于对中小班次的敏感度而被公认为是潜在的高级过程监视工具。在本文中，我们首先通过名为New BC（NBC）图表的适当转换来提高基于布朗运动的C（BC）图表的敏感性，以监视正常过程中的中等和较大变化。然后，使用Crosier C（CC）图表的控制图表结构，提出NBCC（具有CC结构的NBC）图表。另外，为了有效地检测间隔内的平均偏移，还提出了这些控制图的双重版本，称为双重NBC（DNBC）和双重NBCC（DNBCC）图。此外，快速初始响应功能也已合并到建议的图表中。使用蒙特卡洛模拟，计算建议图表的游程长度属性。使用额外的二次损失和积分相对平均游程长度作为性能标准，比较了现有图表和拟议图表的游程长度性能。事实证明，在检测小，中和大间隔的均值漂移时，NBC和NBCC（DNBC和DNBCC）图比C，CC和NBC（双C和双CC）图更加一致地敏感。 DNBCC图表的表现优于所有考虑的图表。拟议的图表还适用于实际数据集以支持拟议的理论。事实证明，在检测小，中和大间隔的均值漂移时，NBC和NBCC（DNBC和DNBCC）图比C，CC和NBC（双C和双CC）图更加一致地敏感。 DNBCC图表的表现优于所有考虑的图表。拟议的图表还适用于实际数据集以支持拟议的理论。事实证明，在检测小，中和大间隔的均值漂移时，NBC和NBCC（DNBC和DNBCC）图比C，CC和NBC（双C和双CC）图更加一致地敏感。 DNBCC图表的表现优于所有考虑的图表。拟议的图表还适用于实际数据集以支持拟议的理论。