ABSTRACT

The homogeneously weighted moving average (HWMA) control chart is a new memory-type chart that allocates a specific weight to the current sample and the remaining weight is distributed equally to the previous samples. In this paper, the HWMA control chart is proposed for monitoring count data. This chart is based on the Conway–Maxwell (COM) distribution, which can be used to model under-spread and over-spread count data. The performance of the proposed chart is evaluated in terms of the average run-length (ARL), standard deviation of the run-length (SDRL), median run-length (MRL) as well as the expected ARL, SDRL and MRL values for both location and dispersion shifts in the process. The sensitivity of the new control chart is compared with those of some existing well-known COM-Poisson memory-type control charts in terms of the out-of-control ARL. The results of this study reveal that the proposed control chart performs competitively well with the existing charts in detecting shifts in the location and dispersion parameters in many situations. Numerical examples are given to demonstrate the application of the proposed chart.

摘要

均匀加权移动平均（HWMA）控制图是一种新的内存型图表，它为当前样本分配特定的权重，剩余的权重平均分配给之前的样本。在本文中，提出了 HWMA 控制图来监控计数数据。此图表基于康威-麦克斯韦 (COM) 分布，可用于对欠展和超展计数数据进行建模。建议图表的性能根据平均运行长度 (ARL)、运行长度的标准偏差 (SDRL)、运行长度中值 (MRL) 以及预期的 ARL、SDRL 和 MRL 值进行评估在这个过程中，位置和分散都发生了变化。在失控 ARL 方面，将新控制图的灵敏度与一些现有的著名 COM-Poisson 记忆型控制图的灵敏度进行了比较。这项研究的结果表明，在许多情况下，所提出的控制图在检测位置和分散参数的变化方面与现有的控制图相比表现良好。给出了数值例子来演示所提出的图表的应用。