Journal Article

Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling

Al-Nefaie, Abdullah H., Almongy, Hisham M., Yousef, Manal M., Almetwally, Ehab M., Hassan, Amal S.

2022

Overview

The current work focuses on ranked set sampling and a simple random sample as sampling approaches for determining stress–strength reliability from the inverted Topp–Leone distribution. Asymptotic confidence intervals are established, along with a maximum likelihood estimator of the parameters and stress–strength reliability. The reliability of such a system is assessed using the Bayesian approach under symmetric and asymmetric loss functions. The highest posterior density credible interval is constructed successively. The results are extracted using Monte Carlo simulation to compare the proposed estimators performance with different sample sizes. Finally, by looking at waiting time data and failure times of insulating fluid, the usefulness of the suggested technique is demonstrated.

• Publisher: MDPI AG
• Subject: Analysis / Bayesian analysis / Bayesian inference / Bayesian statistical decision theory / Confidence intervals / Estimation theory / Failure times / Food science / Fuzzy sets / Insulation / inverted Topp Leone distribution / Markov processes / Maximum likelihood estimators / Methods / Monte Carlo method / Monte Carlo simulation / Numerical analysis / Random variables / ranked set sampling method / Ranking and selection (Statistics) / Reliability (Engineering) / Reliability analysis / Sampling / Set theory / stress–strength reliability / System design / System reliability / Systems analysis