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Symmetry
Volume 15
Issue 9
10.3390/sym15091698
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Article

Modeling of System Availability and Bayesian Analysis of Bivariate Distribution

by
Muhammad Farooq
1,
Ahtasham Gul
2,
Huda M. Alshanbari
3,* and
Saima K. Khosa
4
1
Department of Statistics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
2
Pakistan Bureau of Statistics, Islamabad 44000, Pakistan
3
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
4
Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, SK S7N 5A2, Canada
*
Author to whom correspondence should be addressed.
Symmetry 2023, 15(9), 1698; https://doi.org/10.3390/sym15091698
Submission received: 21 July 2023 / Revised: 23 August 2023 / Accepted: 24 August 2023 / Published: 4 September 2023
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines III)
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Abstract

To meet the desired standard, it is important to monitor and analyze different engineering processes to obtain the desired output. The bivariate distributions have received a significant amount of attention in recent years due to their ability to describe randomness of natural as well as artificial mechanisms. In this article, a bivariate model is constructed by compounding two independent asymmetric univariate distributions and by using the nesting approach to study the effect of each component on reliability for better understanding. Furthermore, the Bayes analysis of system availability is studied by considering prior parametric variations in the failure time and repair time distributions. Basic statistical characteristics of marginal distribution like mean median and quantile function are discussed. We used inverse Gamma prior to study its frequentist properties by conducting a Monte Carlo Markov Chain (MCMC) sampling scheme.
Keywords: reliability; system availability; Weibull Inverse Lomax; Monte Carlo Markov Chain; Bayesian; maximum likelihood estimation reliability; system availability; Weibull Inverse Lomax; Monte Carlo Markov Chain; Bayesian; maximum likelihood estimation

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MDPI and ACS Style

Farooq, M.; Gul, A.; Alshanbari, H.M.; Khosa, S.K. Modeling of System Availability and Bayesian Analysis of Bivariate Distribution. Symmetry 2023, 15, 1698. https://doi.org/10.3390/sym15091698

AMA Style

Farooq M, Gul A, Alshanbari HM, Khosa SK. Modeling of System Availability and Bayesian Analysis of Bivariate Distribution. Symmetry. 2023; 15(9):1698. https://doi.org/10.3390/sym15091698

Chicago/Turabian Style

Farooq, Muhammad, Ahtasham Gul, Huda M. Alshanbari, and Saima K. Khosa. 2023. "Modeling of System Availability and Bayesian Analysis of Bivariate Distribution" Symmetry 15, no. 9: 1698. https://doi.org/10.3390/sym15091698

APA Style

Farooq, M., Gul, A., Alshanbari, H. M., & Khosa, S. K. (2023). Modeling of System Availability and Bayesian Analysis of Bivariate Distribution. Symmetry, 15(9), 1698. https://doi.org/10.3390/sym15091698

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