Nawaz Muhammad Shujaat, Azam Muhammad, Aslam Muhammad
Department of Statistics, National College of Business Administration and Economics, Lahore, Pakistan.
Department of Statistics and Computer Science, University of Veterinary and Animal Sciences, Lahore, Pakistan.
J Appl Stat. 2020 Jan 4;48(1):4-40. doi: 10.1080/02664763.2019.1709809. eCollection 2021.
In this paper, we present a repetitive sampling method to construct control charts using exponentially weighted moving averages (EWMA) and double exponentially weighted moving averages (DEWMA) to monitor shift in the process. For non-normal processes, -distribution with various degrees of freedom (i.e. ) is used as symmetric distribution, gamma distribution with unit scale parameter and various shape parameters (i.e. ) is used as positively skewed distribution and Weibull distribution with unit scale parameter and various shape parameters (i.e. 10 and 20) is used as negatively skewed distribution. We use Monte Carlo simulations to check whether the process is out of control. We use average run length as a tool to find the ability of proposed control charts to identify a shift earlier in a process, as compared to other control charts currently used to monitor the same type of process. The proposed control charts are applied to two real datasets.
在本文中，我们提出了一种重复抽样方法，用于构建使用指数加权移动平均（EWMA）和双指数加权移动平均（DEWMA）的控制图，以监测过程中的偏移。对于非正态过程，具有不同自由度（即 ）的 -分布用作对称分布，具有单位尺度参数和不同形状参数（即 ）的伽马分布用作正偏态分布，具有单位尺度参数和不同形状参数（即10和20）的威布尔分布用作负偏态分布。我们使用蒙特卡罗模拟来检查过程是否失控。与当前用于监测同一类型过程的其他控制图相比，我们使用平均运行长度作为一种工具，来发现所提出的控制图在过程中更早识别偏移的能力。所提出的控制图应用于两个真实数据集。
