Beta-distributed process outputs are common in manufacturing industry because they range from 0 to 1 based on inputs like yield. Under the normality assumption, Shewarts control charts and Hotelling's control charts based on the deviance residual have been applied to monitor the process mean of the beta-distributed process outputs. The normality assumption can be violated according to the shape of the beta distribution. Therefore, without the normality assumption, we propose antirank control charts, exponentially weighted moving average (EWMA) control charts and cumulative sum (CUSUM) control charts. The proposed control charts outperform the existing control charts in the experimental results. The previous research has been focused on monitoring the process mean only. For the first time, in order to monitor the process variance of the beta-distributed process outputs, we propose the multivariate exponentially weighted mean squared deviation (MEWMS) chart, the first norm distance of the MEWMS deviation from its expected value (MEWMSL₁) chart, the chart based on MEWMS deviation with the approximated distribution of trace (MEWMS_AT), the multivariate trace sum squared deviation (MTSSD) chart and the multivariate matrix sum squared deviation (MMSSD) chart based on the deviance residual. The proposed control charts are compared and recommended in terms of the experimental results. This research can be a guideline for practitioners who monitor the deviance residual.

中文翻译：

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用于监控 Beta 分布过程的基于偏差残差的控制图

Beta 分布的过程输出在制造业中很常见，因为它们基于产量等输入的范围从 0 到 1。在正态性假设下，基于偏差残差的 Shewarts 控制图和 Hotelling 控制图已被应用于监控 Beta 分布过程输出的过程均值。根据 β 分布的形状，可以违反正态性假设。因此，在没有正态性假设的情况下，我们提出了反秩控制图、指数加权移动平均 (EWMA) 控制图和累积总和 (CUSUM) 控制图。所提出的控制图在实验结果中优于现有的控制图。以前的研究只关注监控过程均值。首次，₁）图表，基于MEWMS偏差的图表和近似轨迹分布（MEWMS _AT），多元轨迹和平方偏差（MTSSD）图表和基于偏差残差的多元矩阵和平方偏差（MMSSD）图表。根据实验结果对所提出的控制图进行比较和推荐。这项研究可为监测偏差残差的从业者提供指导。