ABSTRACT In this paper, we propose maximum weighted adaptive Crosier CUSUM (MaxWACCUSUM) charts with three different unbiased estimators of the process mean and variance shifts for joint monitoring of the mean and variance of a normal process. The MaxWACCUSUM charts provide an overall good performance for detecting a range of joint mean and dispersion shift sizes. The run length characteristics of the proposed charts are computed using the Monte Carlo simulation method. A detailed comparative study is conducted to compare the run length performances of the proposed and existing charts. It is found that the MaxWACCUSUM charts are more sensitive than the maximum EWMA, double EWMA and CUSUM charts when detecting a range of joint shift sizes. Real datasets are considered to support the theory.

中文翻译：

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用于同时监控过程均值和方差的最大加权自适应 CUSUM 图

摘要 在本文中，我们提出了最大加权自适应 Crosier CUSUM (MaxWACCUSUM) 图，其中包含三个不同的过程均值和方差偏移的无偏估计量，用于联合监测正常过程的均值和方差。MaxWACCUSUM 图表为检测一系列联合均值和离散偏移大小提供了整体良好的性能。建议图表的运行长度特征是使用蒙特卡罗模拟方法计算的。进行了详细的比较研究，以比较提议的和现有图表的运行长度性能。发现 MaxWACCUSUM 图在检测关节位移大小范围时比最大 EWMA、双 EWMA 和 CUSUM 图更敏感。真实数据集被认为支持该理论。