The reflected power function distribution (RPFD) has applications in the fields of reliability engineering and survival analysis. To identify and remove the variation in different reliability processes and also to monitor the reliability of machines where the number of errors follows RPFD, we develop control charts to keep the process in control. A memory less control chart like a Shewhart control chart, and two memory-based control charts like an exponentially weighted moving average (EWMA) control chart and a hybrid exponentially weighted moving average (HEWMA) control chart are discussed and compared with each other. Proposal of these control charts is based on two different estimators, the percentile estimator (PE) and the modified maximum likelihood estimator (MMLE). This study shows that an HEWMA control chart based on PE performs better than PE-based Shewhart and EWMA control charts, as well as MMLE-based Shewhart, EWMA, and HEWMA control charts.

中文翻译：

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经典估计下反射功率函数分布形状参数的控制图

反射功率函数分布（RPFD）在可靠性工程和生存分析领域有应用。为了识别和消除不同可靠性过程中的变化，并监控错误数量遵循 RPFD 的机器的可靠性，我们开发了控制图来控制过程。讨论并比较了像 Shewhart 控制图这样的无记忆控制图，以及像指数加权移动平均 (EWMA) 控制图和混合指数加权移动平均 (HEWMA) 控制图这样的两个基于记忆的控制图。这些控制图的提议基于两个不同的估计量，即百分位数估计量 (PE) 和修正的最大似然估计量 (MMLE)。