In this study, we propose a design for a control chart for the normal distribution using a modified double sampling scheme. The probability of in control, out of control, the average run length (ARL), and the standard deviation of run length (SDRL) of the proposed control chart is derived. The proposed control chart using the modified double sampling scheme is found to be more efficient in detecting small shifts of a process in comparison with existing, single, and double sampling control charts. The efficiency of the proposed control chart is investigated in terms of ARL and SDRL via simulation and application to a real data set.

中文翻译：

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改进的双重抽样方案及其措施和应用

在这项研究中，我们提出了一种使用改进的双采样方案的正态分布控制图设计。得出了所提出的控制图的处于控制状态，失控状态，平均行程长度（ARL）和行程长度标准偏差（SDRL）的概率。与现有的，单采样和双采样控制图相比，发现使用改进的双采样方案的拟议控制图在检测过程的微小偏移方面更有效。通过仿真并将其应用于实际数据集，以ARL和SDRL的形式研究了建议控制图的效率。