Robust Rank Regression for Weibull Parameter Estimation Using M‐Estimation and Fast MCD

ABSTRACT This paper develops a robust rank‐based estimation framework for the parameters of the Weibull distribution in the presence of contaminated lifetime data. Classical estimation procedures, including maximum likelihood estimation and ordinary rank regression, are known to be sensitive to outliers and leverage points that frequently occur in reliability and survival datasets. To address this limitation, we propose a robust regression approach that integrates rank‐based Weibull linearization with bounded‐influence M‐estimation and high‐breakdown covariance estimation via the Fast Minimum Covariance Determinant (FMCD) algorithm. The proposed framework provides simultaneous protection against vertical outliers and leverage points in the transformed regression space while preserving the structural interpretability of Weibull parameters. The finite‐sample performance of the estimators is evaluated through extensive Monte Carlo simulations under controlled contamination scenarios and different parameter regimes. Results indicate that the proposed robust estimators substantially reduce estimation error relative to classical methods, particularly for the shape parameter, which is highly sensitive to extreme observations. The methodology is further illustrated using an industrial lifetime dataset of battery failure times. Both simulation and empirical results demonstrate that the proposed robust rank‐based estimators provide stable and accurate parameter estimation for Weibull models under contaminated sampling conditions.