Zaka et al provided a new distribution called the Weighted Power function distribution (WPFD), which has application in reliability engineering and survival analysis. They used different estimation methods to estimate the unknown parameters of WPFD and proved that modified maximum likelihood estimator (MMLE) is best to consider for the estimation of parameters. We have constructed the memoryless and memory-based control charts based on the assumption that the distribution of the underlying process does not follow the normal distribution. In this paper, we provide modified control charts using MMLE of the shape parameter for WPFD. We develop control charts to keep the process in control when the distribution of errors of underlying process follows WPFD. We propose the modified memoryless control chart, that is, Shewhart control chart and modified memory-based control chart, that is, Exponentially weighted moving average (EWMA) and Hybrid exponentially weighted moving average (HEWMA) control charts. We have made the comparison of the proposed control charts using Monte Carlo simulation and the real-life application for both and the memoryless control charts and memory-based control charts. We see that HEWMA based on MMLE performs better as compared to other proposed control charts.

中文翻译：

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经典估计下加权幂函数分布形状参数监测的改进控制图

Zaka 等人提供了一种称为加权幂函数分布 (WPFD) 的新分布，它在可靠性工程和生存分析中有应用。他们使用不同的估计方法来估计 WPFD 的未知参数，并证明了改进的最大似然估计器 (MMLE) 最适合用于参数估计。我们基于底层过程的分布不遵循正态分布的假设构建了无记忆和基于记忆的控制图。在本文中，我们使用 WPFD 形状参数的 MMLE 提供了修改后的控制图。当基础流程的错误分布遵循 WPFD 时，我们开发控制图以保持流程处于受控状态。我们提出修改后的无记忆控制图，即 休哈特控制图和改进的基于记忆的控制图，即指数加权移动平均 (EWMA) 和混合指数加权移动平均 (HEWMA) 控制图。我们已经使用蒙特卡罗模拟和现实生活中的应用程序对建议的控制图进行了比较，无记忆控制图和基于记忆的控制图。我们看到，与其他提议的控制图相比，基于 MMLE 的 HEWMA 表现更好。