Robust design is one of the main tools employed by engineers for the facilitation of the design of high-quality processes. However, most real-world processes invariably contend with external uncontrollable factors, often denoted as outliers or contaminated data, which exert a substantial distorting effect upon the computed sample mean. In pursuit of mitigating the inherent bias entailed by outliers within the dataset, the concept of weight adjustment emerges as a prudent recourse, to make the sample more representative of the statistical population. In this sense, the intricate challenge lies in the judicious application of these diverse weights toward the estimation of an alternative to the robust location estimator. Different from the previous studies, this study proposes two categories of new weighted Hodges-Lehmann (WHL) estimators that incorporate weight factors in the location parameter estimation. To evaluate their robust performances in estimating the location parameter, this study constructs a set of comprehensive simulations to compare various location estimators including mean, weighted mean, weighted median, Hodges-Lehmann estimator, and the proposed WHL estimators. The findings unequivocally manifest that the proposed WHL estimators clearly outperform the traditional methods in terms of their breakdown points, biases, and relative efficiencies.

翻译：稳健设计是工程师促进高质量过程设计的主要工具之一。然而，大多数实际过程不可避免地会受到外部不可控因素（常称为异常值或污染数据）的影响，这些因素会对计算出的样本均值产生显著的扭曲效应。为减轻数据集中异常值所固有的偏差，权重调整的概念成为一种明智的选择，旨在使样本更能代表统计总体。在此意义上，如何审慎地运用这些不同的权重来估计稳健位置参数的替代方案，成为一项复杂的挑战。与以往研究不同，本研究提出了两类新的加权Hodges-Lehmann（WHL）估计量，它们在位置参数估计中引入了权重因子。为了评估这些估计量在位置参数估计中的稳健性能，本研究构建了一系列综合模拟，比较了多种位置估计量，包括均值、加权均值、加权中位数、Hodges-Lehmann估计量以及所提出的WHL估计量。研究结果明确表明，所提出的WHL估计量在崩溃点、偏差和相对效率方面均明显优于传统方法。