Reliability Analysis and Applications of Generalized Type-II Progressively Hybrid Maxwell–Boltzmann Censored Data

Today, the reliability or quality practitioner always aims to shorten testing duration and reduce testing costs without neglecting efficient statistical inference. So, a generalized progressively Type-II hybrid censored mechanism has been developed in which the experimenter prepays for usage of the...

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Bibliographic Details
Published in:Axioms Vol. 12; no. 7; p. 618
Main Authors: Elshahhat, Ahmed, Abo-Kasem, Osama E., Mohammed, Heba S.
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.07.2023
Subjects:
Approximation
Bayes inference
Boltzmann distribution
Censored data (mathematics)
Confidence intervals
Data collection
Datasets
Estimation
Experiments
Failure
Failure times
Gases
generalized Type-II progressive hybrid censoring
Markov chains
Mathematical models
Mathematical research
maximum likelihood
Maximum likelihood estimators
Maxwell–Boltzmann model
Mean
Monte-Carlo Markov-chain algorithms
Parameters
Quantum statistics
Random variables
Reliability analysis
Statistical analysis
Statistical inference
Test facilities
Wind speed
Windshields
Egypt
ISSN:2075-1680, 2075-1680
Online Access:Get full text
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Summary:Today, the reliability or quality practitioner always aims to shorten testing duration and reduce testing costs without neglecting efficient statistical inference. So, a generalized progressively Type-II hybrid censored mechanism has been developed in which the experimenter prepays for usage of the testing facility for T units of time. This paper investigates the issue of estimating the model parameter, reliability, and hazard rate functions of the Maxwell–Boltzmann distribution in the presence of generalized progressive Type-II hybrid censored data by making use of the likelihood and Bayesian inferential methods. Using an inverse gamma prior distribution, the Bayes estimators of the same unknown parameters with respect to the most commonly squared-error loss are derived. Since the joint likelihood function is produced in complex form, following the Monte-Carlo Markov-chain idea, the Bayes’ point estimators as well as the Bayes credible and highest posterior density intervals cannot be derived analytically, but they may be examined numerically. Via the normal approximation of the acquired maximum likelihood and log-maximum-likelihood estimators, the approximate confidence interval bounds of the unknown quantities are derived. Via comprehensive numerical comparisons, with regard to simulated root mean squared-error, mean relative absolute bias, average confidence length, and coverage probability, the actual behavior of the proposed estimation methodologies is examined. To illustrate how the offered methodologies may be used in real circumstances, two different applications, representing the failure time points of aircraft windscreens as well as the daily average wind speed in Cairo during 2009, are explored. Numerical evaluations recommend utilizing a Bayes model via the Metropolis-Hastings technique to produce samples from the posterior distribution to estimate any parameter of the Maxwell–Boltzmann distribution when collecting data from a generalized progressively Type-II hybrid censored mechanism.
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ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12070618