Adeoti Olatunde Adebayo, Malela-Majika Jean-Claude, Shongwe Sandile Charles, Aslam Muhammad
Department of Statistics, Federal University of Technology Akure, Akure, Nigeria.
Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria, South Africa.
J Appl Stat. 2021 Jun 15;49(12):3090-3119. doi: 10.1080/02664763.2021.1937582. eCollection 2022.
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.
均匀加权移动平均（HWMA）控制图是一种新的记忆型控制图，它为当前样本分配特定权重，其余权重则平均分配给先前的样本。本文提出了用于监控计数数据的HWMA控制图。该控制图基于康威-麦克斯韦（COM）分布，可用于对欠分散和过分散计数数据进行建模。通过平均运行长度（ARL）、运行长度的标准差（SDRL）、中位数运行长度（MRL）以及过程中位置和离散度偏移的预期ARL、SDRL和MRL值来评估所提出控制图的性能。在失控ARL方面，将新控制图的灵敏度与一些现有的著名COM-泊松记忆型控制图的灵敏度进行了比较。研究结果表明，在许多情况下，所提出的控制图在检测位置和离散度参数的偏移方面与现有控制图相比具有良好的竞争力。给出了数值示例以说明所提出控制图的应用。
