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One- and Two-Sample Predictions Based on Progressively Type-II Censored Carbon Fibres Data Utilizing a Probability
Mahmoud El-Morshedy1,2, Rashad M El-Sagheer3, Samah H El-Essawy4
1Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia.
Computational Intelligence and Neuroscience
|May 23, 2022
Summary
This study introduces predictive intervals for the new Weibull-Pareto distribution under progressive censoring. It applies Bayesian and maximum likelihood methods for reliability engineering and material science applications.
Area of Science:
- Statistics
- Reliability Engineering
- Materials Science
Background:
- The new Weibull-Pareto distribution is crucial for analyzing lifetimes and material properties.
- Progressive type-II censoring is a common data collection method in reliability studies.
Purpose of the Study:
- To develop predictive intervals for unobserved units from a new Weibull-Pareto distribution.
- To compare Bayesian and maximum likelihood estimation approaches for these predictions.
Main Methods:
- Utilized progressive type-II censored samples from the new Weibull-Pareto distribution.
- Implemented Bayesian inference using Markov chain Monte Carlo (MCMC) via Metropolis-Hastings and Gibbs sampling.
- Applied maximum likelihood estimation (MLE) for parameter estimation and prediction.
Main Results:
- Constructed one-sample and two-sample predictive intervals for unobserved data.
- Provided methods for predicting future upper-order statistics.
- Demonstrated the methodology with simulated and real-world carbon fiber data.
Conclusions:
- The proposed Bayesian and MLE methods effectively provide predictive intervals for the new Weibull-Pareto distribution under progressive censoring.
- The findings are applicable to reliability engineering and the analysis of materials like polymers and carbon fibers.
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