Alevizakos Vasileios, Chatterjee Kashinath, Koukouvinos Christos
Department of Mathematics, National Technical University of Athens, Zografou, Athens, Greece.
Department of Population Health Sciences, Division of Biostatistics and Data Science, Augusta University, Augusta, GA, USA.
J Appl Stat. 2023 Mar 15;51(6):1171-1190. doi: 10.1080/02664763.2023.2189771. eCollection 2024.
Distribution-free or nonparametric control charts are used for monitoring the process parameters when there is a lack of knowledge about the underlying distribution. In this paper, we investigate a single distribution-free triple exponentially weighted moving average control chart based on the Lepage statistic (referred as TL chart) for simultaneously monitoring shifts in the unknown location and scale parameters of a univariate continuous distribution. The design and implementation of the proposed chart are discussed using time-varying and steady-state control limits for the zero-state case. The run-length distribution of the TL chart is evaluated by performing Monte Carlo simulations. The performance of the proposed chart is compared to those of the existing EWMA-Lepage (EL) and DEWMA-Lepage (DL) charts. It is observed that the TL chart with a time-varying control limit is superior to its competitors, especially for small to moderate shifts in the process parameters. We also provide a real example from a manufacturing process to illustrate the application of the proposed chart.
当对基础分布缺乏了解时，无分布或非参数控制图用于监控过程参数。在本文中，我们研究了一种基于勒佩奇统计量的单无分布三重指数加权移动平均控制图（称为TL图），用于同时监控单变量连续分布中未知位置和尺度参数的变化。使用零状态情况的时变和稳态控制限来讨论所提出控制图的设计和实施。通过进行蒙特卡罗模拟来评估TL图的运行长度分布。将所提出控制图的性能与现有的EWMA - 勒佩奇（EL）图和DEWMA - 勒佩奇（DL）图的性能进行比较。可以观察到，具有时变控制限的TL图优于其竞争对手，特别是对于过程参数中小到中等程度的变化。我们还提供了一个制造过程的实际例子来说明所提出控制图的应用。
