Robust Fitting of a Weibull Model with Optional Censoring.

Area of Science:

• Statistics
• Reliability Engineering

Background:

• The Weibull distribution is a standard for modeling lifetime and failure data.
• Classical maximum likelihood estimation (MLE) for Weibull parameters lacks robustness against data contamination.
• Existing Weibull models are limited to positive data and monotone failure rates.

Purpose of the Study:

• Introduce a robust procedure for fitting Weibull models using L2 distance.
• Develop an augmented Weibull model with a weight parameter to handle contaminated data effectively.
• Compare the performance of the new L2 estimator against the traditional MLE for contaminated and right-censored data.

Main Methods:

• Utilized L2 distance (integrated square distance) of the Weibull probability density function for parameter estimation.
• Augmented the standard Weibull model with a weight parameter to enhance robustness.
• Employed both simulated and real-world datasets, including right-censored data, for comparative analysis.

Main Results:

• The proposed L2 parametric estimation method demonstrates superior robustness compared to MLE when dealing with contaminated data.
• The new L2 estimation approach provides a better fit for the augmented Weibull model under data contamination.
• The preference for the L2 distance criterion and the new Weibull model extends to scenarios involving right-censored data with contamination.

Conclusions:

• The L2 distance-based estimation offers a more robust alternative to MLE for Weibull modeling, particularly in the presence of data contamination.
• The augmented Weibull model with a weight parameter effectively addresses limitations of classical methods.
• The findings are applicable to both complete and right-censored lifetime data, enhancing reliability analysis in various fields.