AI Summary & Key Takeaways
AI InsightFinally, the practical applicability of the methodology is demonstrated with a real-world dataset on steel specimens.
📌 3 Key Takeaways
Abstract
This study develops both classical and Bayesian estimation procedures for the stress--strength reliability parameter under a joint Type-II censoring scheme applied to $k$ independent strength samples from non-identical Weibull populations and a single Weibull stress population. Each strength population is assumed to follow the Weibull distribution with a common shape parameter $\beta$ but distinct scale parameters $\theta_i \ (i=1,2,\dots,k)$, while the stress population follows the Weibull distribution with the same shape parameter $\beta$ and scale parameter $\theta_{k+1}$. Maximum likelihood estimation are derived, and their existence and uniqueness are established. The asymptotic 95% confidence intervals are then constructed using the observed Fisher information matrix. In the Bayesian framework, independent gamma priors are specified, and estimation is carried out under the squared error loss function. Posterior computations are performed using Gibbs sampling combined with a Metropolis--Hastings step, and highest posterior density credible intervals are provided. The performance of the estimators is evaluated through extensive simulation studies, and in the special case $\beta=1$, closed form maximum likelihood estimations are derived for exponential populations. Finally, the practical applicability of the methodology is demonstrated with a real-world dataset on steel specimens.