The precision of process monitoring often encounters challenges in determining the exact shift size. Therefore, combined control charts have gained considerable attention because of their excellent speed to detect simultaneously small-to-moderate and large-size shifts. The effectiveness of the applied quality control methods strongly depends on the performance of the measurement system. Measurement error presence contributes significantly negatively toward the performance of the usual control charting schemes. This article proposes novel two-sided combined Shewhart-Cumulative EWMA-sum (Shewhart-CUESUM) control charts designed to efficiently monitor the mean of normally distributed processes. In addition, to address measurement errors, the M-Shewhart-CUESUM chart is proposed, incorporating an additive measurement error model. Evaluation of the charts through Monte-Carlo simulations, considering metrics such as average run length (ARL), extra quadratic loss, relative ARL, and performance comparison index. It is found that the combined Shewhart-CUESUM outperforms than CUESUM chart. The results show that the presence of measurement errors can significantly diminish the charts’ performance, which can be mitigated by utilizing a multiple measurements scheme. Among the different well-established combined charts examined, the M-Shewhart-CUESUM chart shows considerably more sensitive to detecting simultaneously detect small and large size shifts. To employ simulated datasets to illustrate the impact of measurement errors and demonstrate the implications of the proposed charts on process mean shifts.

中文翻译：

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新颖的组合 Shewhart-CUmulative EWMA-SUM 平均值图表，无测量误差和有测量误差

过程监控的精度在确定准确的班次大小时经常遇到挑战。因此，组合控制图因其同时检测小到中和大尺寸变化的出色速度而受到广泛关注。所应用的质量控制方法的有效性很大程度上取决于测量系统的性能。测量误差的存在对通常的控制图方案的性能产生显着的负面影响。本文提出了新颖的两侧组合 Shewhart-Cumulative EWMA-sum (Shewhart-CUESUM) 控制图，旨在有效监控正态分布过程的平均值。此外，为了解决测量误差，提出了 M-Shewhart-CUESUM 图，其中结合了附加测量误差模型。通过蒙特卡罗模拟评估图表，考虑平均游程长度 (ARL)、额外二次损失、相对 ARL 和性能比较指数等指标。结果发现，组合的 Shewhart-CUESUM 优于 CUESUM 图。结果表明，测量误差的存在会显着降低图表的性能，这可以通过利用多重测量方案来缓解。在所检查的不同成熟组合图表中，M-Shewhart-CUESUM 图显示出对同时检测小尺寸和大尺寸变化更加敏感。使用模拟数据集来说明测量误差的影响，并演示所提出的图表对过程均值漂移的影响。