An Interval-Based Robust Response Surface Design Using the W24 Estimator for Asymmetric and Contaminated Data

Robust parameter design plays a crucial role in quality optimization when process data deviate from normality due to skewness or contamination. Dual response surface methodology (DRSM) is widely used to model process mean and variability simultaneously; however, conventional implementations typically rely on normality-based estimators that are sensitive to outliers. This study proposes an interval-based robust parameter design framework that integrates the W24 robust M-estimator into the DRSM structure for dispersion modeling. The method combines confidence interval-based location modeling with robust dispersion estimation to improve stability under non-normal and asymmetric data conditions. The proposed approach is first illustrated using a real-world printing process example under nominal-the-best and larger-the-better objectives, where it demonstrates performance comparable to existing interval-based robust methods. To further investigate its behavior, a comprehensive simulation study is conducted under varying degrees of data contamination, skewness, and outlier severity. The simulation results indicate that the relative performance of robust estimators depends strongly on the underlying contamination structure. While benchmark methods may exhibit similar or occasionally better performance under mild contamination, the W24-based approach demonstrates increased stability and competitive performance, particularly under moderate-to-severe contamination. These findings underscore the importance of selecting appropriate robust estimators in interval-based quality optimization and suggest that the proposed framework provides a flexible and effective alternative for response surface optimization under asymmetric and contaminated data conditions.