  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.
