Abstract

The EWMA-t chart is used to monitor the process mean as it is robust against errors in estimating the process standard deviation or changing standard deviation. In this paper, we propose a double EWMA-t (DEWMA-t) chart for monitoring the process mean, which is a natural extension of the EWMA-t chart. The idea is to first construct the t chart using the EWMA statistic, and then put it into another EWMA statistic to devise the DEWMA-t chart. The DEWMA-t chart encompasses the EWMA-t chart. The Monte Carlo simulation method is used to compute the run length properties of the DEWMA-t chart. Based on detailed run length comparisons, it turns out that, with some reasonable assumptions, the DEWMA-t chart performs uniformly and substantially better than the EWMA-t chart when detecting different kinds of shift in the process mean. A similar trend is observed when these control charts are compared with their counterparts based on the variable sampling interval feature. In addition, real datasets are also used to support the theory.

摘要

EWMA- t图用于监控过程均值，因为它在估计过程标准偏差或改变标准偏差时对错误具有鲁棒性。在本文中，我们提出了一种用于监控过程均值的双 EWMA- t (DEWMA- t ) 图，它是 EWMA-t 图的自然扩展。这个想法是首先使用 EWMA 统计量构建t图，然后将其放入另一个 EWMA 统计量以设计 DEWMA- t图。DEWMA- t图包含 EWMA- t图。蒙特卡罗模拟方法用于计算 DEWMA- t的运行长度属性图表。基于详细的运行长度比较，事实证明，在一些合理的假设下，DEWMA - t图在检测过程均值中不同类型的偏移时，其性能均匀且明显优于 EWMA- t图。当这些控制图与基于可变采样间隔特征的对应图进行比较时，会观察到类似的趋势。此外，还使用真实数据集来支持该理论。