A 3-component mixture of Rayleigh distributions: properties and estimation in Bayesian framework

Area of Science:

• Engineering
• Statistics
• Reliability Theory

Background:

• Engineering processes often exhibit complex lifetime behaviors.
• Mixture models are suitable for modeling the heterogeneity in process lifetimes.
• Censored sampling is common in reliability and survival analysis.

Purpose of the Study:

• To develop and analyze a Bayesian 3-component mixture model for Rayleigh lifetime distributions.
• To derive Bayes estimators and posterior risks under censored sampling.
• To provide guidance on hyperparameter elicitation when prior information is limited.

Main Methods:

• Bayesian inference for a 3-component Rayleigh mixture model.
• Derivation of Bayes estimators and posterior risks.
• Numerical simulations to evaluate estimator performance under different priors, loss functions, sample sizes, and test termination times.
• Application to a real-life engineering dataset.

Main Results:

• The study derives expressions for Bayes estimators and posterior risks for the 3-component Rayleigh mixture model.
• Numerical simulations demonstrate the performance of these estimators with informative and non-informative priors.
• The practical utility of the model is illustrated with a real-world engineering data example.

Conclusions:

• The proposed Bayesian mixture model effectively analyzes engineering process lifetimes, especially under censored conditions.
• The study provides a robust framework for estimating parameters and assessing uncertainty.
• The findings offer valuable insights for reliability and survival analysis in engineering applications.