Abstract

In the case of contamination for skewed distributions, the modified Shewhart, modified weighted variance, and modified skewness correction methods are newly introduced by Karagöz (Hacet J Math Stat 47(1):223–242, 2018). In this study, we propose to modify these methods by considering simple random sampling (SRS), ranked set sampling (RSS) and median ranked set sampling (MRSS) designs under the contaminated type I Marshall–Olkin bivariate Weibull and lognormal distributions. These bivariate distributions are chosen since they can represent a wide variety of shapes from nearly symmetric to highly skewed. We evaluate the performance of proposed modified methods based on different ranked set sampling designs by using Monte Carlo Simulation. The type I risks of \({\bar{X}}\) charts for existing and newly proposed modified methods by using SRS, RSS and MRSS designs in the case of contamination for these distributions are obtained via simulation study. The proposed modified methods using RSS and MRSS designs for the \({\bar{X}}\) chart can be a favorable substitute in process monitoring when the distribution is highly skewed and contaminated.

中文翻译：

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基于中位数排序集抽样设计的漂亮均值图方法

摘要

在偏态分布受到污染的情况下，Karogöz新引入了修正的Shewhart，修正的加权方差和修正的偏度校正方法（Hacet J Math Stat 47（1）：223–242，2018）。在这项研究中，我们建议在污染的I型Marshall-Olkin双变量Weibull和对数正态分布下考虑简单随机抽样（SRS），排序集抽样（RSS）和中位数排序集抽样（MRSS）设计来修改这些方法。选择这些双变量分布是因为它们可以代表从几乎对称到高度偏斜的各种形状。我们使用蒙特卡洛模拟评估基于不同排名集抽样设计的改进方法的性能。我有\（{\ bar {X}} \）类型的风险通过模拟研究获得了针对这些分布的污染情况下使用SRS，RSS和MRSS设计的现有和新提议的修改方法的图表。当分布高度偏斜和受污染时，针对\（{\ bar {X}} \）图表使用RSS和MRSS设计的拟议修改方法可以是过程监视的理想替代方法。