Uncertainty Evaluation of Weibull Estimators through Monte Carlo Simulation: Applications for Crack Initiation...

Area of Science:

• Materials Science
• Mechanical Engineering
• Reliability Engineering

Background:

• Stress corrosion cracking initiation testing typically uses interval-censored reliability tests.
• The Weibull distribution is a standard model for crack initiation, estimated via maximum likelihood estimation (MLE) or median rank regression (MRR).
• Determining optimal specimen numbers and censoring intervals for accurate Weibull parameter estimation remains challenging.

Purpose of the Study:

• To compare the accuracy of MLE and MRR for Weibull parameter estimation in stress corrosion cracking.
• To investigate the impact of experimental variables (specimen count, test duration, censoring intervals, shape parameters) on estimator uncertainty.
• To provide guidance on suitable experimental conditions for probabilistic crack initiation modeling.

Main Methods:

• Monte Carlo simulation was employed to systematically evaluate MLE and MRR.
• The study analyzed the influence of key factors including total specimens, test duration, censoring interval, and true Weibull shape parameters.
• Quantitative uncertainties of both estimators were assessed against true Weibull parameters.

Main Results:

• The study quantifies the uncertainties associated with MLE and MRR under various experimental conditions.
• It identifies the sensitivity of Weibull estimator accuracy to the number of specimens, test duration, and censoring strategy.
• The research provides a comparative analysis of the performance of MLE versus MRR in the context of crack initiation testing.

Conclusions:

• The findings offer data-driven recommendations for designing effective crack initiation tests.
• Optimal experimental parameters are suggested to achieve reliable probabilistic crack initiation models.
• This research contributes to improving the accuracy and efficiency of stress corrosion cracking reliability testing.