Abstract

Control charts based on the sample mean X¯¯¯$\overline{X}$$\overline{X}$ are used for monitoring shifts in the process mean under the assumption that the process standard deviation is stable or well estimated. However, in many applications, this assumption is violated. In this case, t control charts are preferred as they are robust to changes in the process standard deviation. In this article, a generally weighted moving average chart based on the t statistic (referred as GWMA t chart) is proposed for monitoring shifts in the process mean. Its performance is studied using Monte Carlo simulation. It is shown that the proposed chart is more effective than the Shewhart t and EWMA t charts. Moreover, it is found more robust than the GWMA X¯¯¯$\overline{X}$$\overline{X}$ chart to changes in the process standard deviation. Finally, two illustrative examples are given to display the application of the proposed chart.

摘要

基于样本均值的控制图X￣￣￣$\stackrel{￣}{X}$$\overline{X}$用于在过程标准差稳定或良好估计的假设下监控过程均值的变化。然而，在许多应用中，这个假设被违反了。在这种情况下，首选t控制图，因为它们对过程标准偏差的变化具有鲁棒性。在本文中，提出了一种基于t统计量的通用加权移动平均图（称为 GWMA t图），用于监控过程均值的变化。使用蒙特卡罗模拟研究其性能。结果表明，所提出的图比 Shewhart t和 EWMA t图更有效。此外，它比 GWMA 更稳健X￣￣￣$\stackrel{￣}{X}$$\overline{X}$图表显示过程标准偏差的变化。最后，给出了两个说明性示例来展示所提出的图表的应用。