Bayesian Estimation of Multicomponent Stress-Strength Model Using Progressively Censored Data from the Inverse...

Area of Science:

• Engineering
• Statistics
• Reliability Theory

Background:

• Reliability estimation is crucial for system performance.
• Progressively censored data is common in reliability studies.
• The inverse Rayleigh distribution is suitable for modeling failure times.

Purpose of the Study:

• To estimate multicomponent stress-strength reliability.
• To compare classical and Bayesian estimation methods.
• To investigate the impact of different loss functions and priors in Bayesian inference.

Main Methods:

• Maximum Likelihood Estimation (MLE).
• Bayesian estimation under various loss functions (squared error, linear exponential, general entropy) with gamma priors.
• Lindley and Markov Chain Monte Carlo (MCMC) approximation methods for Bayesian calculations.
• Asymptotic confidence intervals and Bayesian credible intervals.

Main Results:

• Bayesian estimators demonstrated superior performance compared to MLE.
• The choice of loss function and prior distribution significantly influences Bayesian estimates.
• MCMC methods provide reliable Bayesian credible intervals.

Conclusions:

• The proposed Bayesian methods offer a robust approach for reliability estimation.
• The study highlights the practical applicability of these methods through a real-life example.
• Bayesian inference is recommended for multicomponent stress-strength reliability analysis with censored data.