Method of medians for lifetime data with Weibull models

Area of Science:

• Statistics
• Reliability Engineering
• Survival Analysis

Background:

• The Weibull distribution is widely applied in failure time analysis.
• Maximum likelihood estimation (MLE) for Weibull models is sensitive to outliers and requires complex adjustments for censored data.

Purpose of the Study:

• To introduce and evaluate the method of medians estimator for the two-parameter Weibull model.
• To provide a robust and computationally simpler alternative to MLE, especially for contaminated or censored datasets.
• To develop a criterion for selecting between MLE and the method of medians to optimize finite-sample efficiency.

Main Methods:

• The study focuses on the method of medians, an M-estimator with a bounded influence function, for the two-parameter Weibull distribution.
• The method of medians requires solving a single equation, making it computationally efficient.
• The research includes a simulation study to assess the performance of the proposed estimator and its confidence intervals under various contamination scenarios.

Main Results:

• The method of medians demonstrates high robustness against outliers and handles censored observations without requiring specific adjustments.
• Approximately 16% of upper and 34% of lower censored observations can be accommodated without impacting calculations.
• The proposed estimator and confidence intervals performed well in simulations with contaminated Weibull models.

Conclusions:

• The method of medians provides a robust, efficient, and computationally feasible approach for Weibull failure time analysis, particularly with outlier-prone or censored data.
• The developed criterion aids in choosing the most appropriate estimator (MLE or method of medians) for enhanced finite-sample efficiency.
• The findings are validated through practical examples using lifetime data sets.