Bayesian inference of the Weibull model based on interval-censored survival data

Area of Science:

• Statistics
• Reliability Engineering
• Survival Analysis

Background:

• Interval-censored data presents unique challenges in failure time analysis.
• Estimating Weibull parameters is crucial for reliability and risk assessment.
• Limited literature exists on Bayesian methods for Weibull parameter estimation with interval-censored data.

Purpose of the Study:

• To review and compare classical maximum likelihood and Bayesian approaches for Weibull parameter estimation using interval-censored data.
• To address the gap in literature regarding Bayesian estimation for this data type.
• To evaluate the performance of different Bayesian loss functions.

Main Methods:

• Review of the maximum likelihood estimation (MLE) method for Weibull parameters.
• Application of Bayesian inference with three distinct loss functions for Weibull parameter estimation.
• Comparative performance analysis through a simulation study.
• Illustration with a real-world data application.

Main Results:

• The Bayesian estimator showed better performance compared to the classical maximum likelihood estimator.
• Both scale and shape parameters were more accurately estimated using the Bayesian approach.
• Simulation results validated the preference for Bayesian methods.

Conclusions:

• The Bayesian approach is recommended for estimating Weibull parameters with interval-censored data.
• The study provides valuable insights for reliability engineers and statisticians.
• Further research could explore other Bayesian methodologies for complex survival data.