Multi Stress-Strength Reliability Based on Progressive First Failure for Kumaraswamy Model: Bayesian and Non-Bayesian Estimation

It is highly common in many real-life settings for systems to fail to perform in their harsh operating environments. When systems reach their lower, upper, or both extreme operating conditions, they frequently fail to perform their intended duties, which receives little attention from researchers. T...

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Autores principales:	Manal M. Yousef, Ehab M. Almetwally
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	multi stress-strength progressive first failure censoring balanced loss functions Lindley’s approximation Markov Chain Monte Carlo symmetric and asymmetric loss functions Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/e84ae449d6444a7cae26bc64294ce2a0
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spelling	oai:doaj.org-article:e84ae449d6444a7cae26bc64294ce2a02021-11-25T19:06:56ZMulti Stress-Strength Reliability Based on Progressive First Failure for Kumaraswamy Model: Bayesian and Non-Bayesian Estimation10.3390/sym131121202073-8994https://doaj.org/article/e84ae449d6444a7cae26bc64294ce2a02021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2120https://doaj.org/toc/2073-8994It is highly common in many real-life settings for systems to fail to perform in their harsh operating environments. When systems reach their lower, upper, or both extreme operating conditions, they frequently fail to perform their intended duties, which receives little attention from researchers. The purpose of this article is to derive inference for multi reliability where stress-strength variables follow unit Kumaraswamy distributions based on the progressive first failure. Therefore, this article deals with the problem of estimating the stress-strength function, <i>R</i> when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>X</mi><mo>,</mo><mi>Y</mi></mrow></semantics></math></inline-formula>, and <i>Z</i> come from three independent Kumaraswamy distributions. The classical methods namely maximum likelihood for point estimation and asymptotic, boot-p and boot-t methods are also discussed for interval estimation and Bayes methods are proposed based on progressive first-failure censored data. Lindly’s approximation form and MCMC technique are used to compute the Bayes estimate of <i>R</i> under symmetric and asymmetric loss functions. We derive standard Bayes estimators of reliability for multi stress–strength Kumaraswamy distribution based on progressive first-failure censored samples by using balanced and unbalanced loss functions. Different confidence intervals are obtained. The performance of the different proposed estimators is evaluated and compared by Monte Carlo simulations and application examples of real data.Manal M. YousefEhab M. AlmetwallyMDPI AGarticlemulti stress-strengthprogressive first failure censoringbalanced loss functionsLindley’s approximationMarkov Chain Monte Carlosymmetric and asymmetric loss functionsMathematicsQA1-939ENSymmetry, Vol 13, Iss 2120, p 2120 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	multi stress-strength progressive first failure censoring balanced loss functions Lindley’s approximation Markov Chain Monte Carlo symmetric and asymmetric loss functions Mathematics QA1-939
spellingShingle	multi stress-strength progressive first failure censoring balanced loss functions Lindley’s approximation Markov Chain Monte Carlo symmetric and asymmetric loss functions Mathematics QA1-939 Manal M. Yousef Ehab M. Almetwally Multi Stress-Strength Reliability Based on Progressive First Failure for Kumaraswamy Model: Bayesian and Non-Bayesian Estimation
description	It is highly common in many real-life settings for systems to fail to perform in their harsh operating environments. When systems reach their lower, upper, or both extreme operating conditions, they frequently fail to perform their intended duties, which receives little attention from researchers. The purpose of this article is to derive inference for multi reliability where stress-strength variables follow unit Kumaraswamy distributions based on the progressive first failure. Therefore, this article deals with the problem of estimating the stress-strength function, <i>R</i> when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>X</mi><mo>,</mo><mi>Y</mi></mrow></semantics></math></inline-formula>, and <i>Z</i> come from three independent Kumaraswamy distributions. The classical methods namely maximum likelihood for point estimation and asymptotic, boot-p and boot-t methods are also discussed for interval estimation and Bayes methods are proposed based on progressive first-failure censored data. Lindly’s approximation form and MCMC technique are used to compute the Bayes estimate of <i>R</i> under symmetric and asymmetric loss functions. We derive standard Bayes estimators of reliability for multi stress–strength Kumaraswamy distribution based on progressive first-failure censored samples by using balanced and unbalanced loss functions. Different confidence intervals are obtained. The performance of the different proposed estimators is evaluated and compared by Monte Carlo simulations and application examples of real data.
format	article
author	Manal M. Yousef Ehab M. Almetwally
author_facet	Manal M. Yousef Ehab M. Almetwally
author_sort	Manal M. Yousef
title	Multi Stress-Strength Reliability Based on Progressive First Failure for Kumaraswamy Model: Bayesian and Non-Bayesian Estimation
title_short	Multi Stress-Strength Reliability Based on Progressive First Failure for Kumaraswamy Model: Bayesian and Non-Bayesian Estimation
title_full	Multi Stress-Strength Reliability Based on Progressive First Failure for Kumaraswamy Model: Bayesian and Non-Bayesian Estimation
title_fullStr	Multi Stress-Strength Reliability Based on Progressive First Failure for Kumaraswamy Model: Bayesian and Non-Bayesian Estimation
title_full_unstemmed	Multi Stress-Strength Reliability Based on Progressive First Failure for Kumaraswamy Model: Bayesian and Non-Bayesian Estimation
title_sort	multi stress-strength reliability based on progressive first failure for kumaraswamy model: bayesian and non-bayesian estimation
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/e84ae449d6444a7cae26bc64294ce2a0
work_keys_str_mv	AT manalmyousef multistressstrengthreliabilitybasedonprogressivefirstfailureforkumaraswamymodelbayesianandnonbayesianestimation AT ehabmalmetwally multistressstrengthreliabilitybasedonprogressivefirstfailureforkumaraswamymodelbayesianandnonbayesianestimation
_version_	1718410312846147584

Multi Stress-Strength Reliability Based on Progressive First Failure for Kumaraswamy Model: Bayesian and Non-Bayesian Estimation

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