Stress–Strength Reliability Analysis for Different Distributions Using Progressive Type-II Censoring with Binomial Removal

In the statistical literature, one of the most important subjects that is commonly used is stress–strength reliability, which is defined as δ=PW<V, where V and W are the strength and stress random variables, respectively, and δ is reliability parameter. Type-II progressive censoring with binomial...

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Published inAxioms Vol. 12; no. 11; p. 1054
Main Authors Elbatal, Ibrahim, Hassan, Amal S., Diab, L. S., Ben Ghorbal, Anis, Elgarhy, Mohammed, El-Saeed, Ahmed R.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.11.2023
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ISSN2075-1680
2075-1680
DOI10.3390/axioms12111054

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Abstract In the statistical literature, one of the most important subjects that is commonly used is stress–strength reliability, which is defined as δ=PW<V, where V and W are the strength and stress random variables, respectively, and δ is reliability parameter. Type-II progressive censoring with binomial removal is used in this study to examine the inference of δ=PW<V for a component with strength V and being subjected to stress W. We suppose that V and W are independent random variables taken from the Burr XII distribution and the Burr III distribution, respectively, with a common shape parameter. The maximum likelihood estimator of δ is derived. The Bayes estimator of δ under the assumption of independent gamma priors is derived. To determine the Bayes estimates for squared error and linear exponential loss functions in the lack of explicit forms, the Metropolis–Hastings method was provided. Utilizing comprehensive simulations and two metrics (average of estimates and root mean squared errors), we compare these estimators. Further, an analysis is performed on two actual data sets based on breakdown times for insulating fluid between electrodes recorded under varying voltages.
AbstractList In the statistical literature, one of the most important subjects that is commonly used is stress–strength reliability, which is defined as δ=P[W<V], where V and W are the strength and stress random variables, respectively, and δ is reliability parameter. Type-II progressive censoring with binomial removal is used in this study to examine the inference of δ=P[W<V] for a component with strength V and being subjected to stress W. We suppose that V and W are independent random variables taken from the Burr XII distribution and the Burr III distribution, respectively, with a common shape parameter. The maximum likelihood estimator of δ is derived. The Bayes estimator of δ under the assumption of independent gamma priors is derived. To determine the Bayes estimates for squared error and linear exponential loss functions in the lack of explicit forms, the Metropolis–Hastings method was provided. Utilizing comprehensive simulations and two metrics (average of estimates and root mean squared errors), we compare these estimators. Further, an analysis is performed on two actual data sets based on breakdown times for insulating fluid between electrodes recorded under varying voltages.
In the statistical literature, one of the most important subjects that is commonly used is stress–strength reliability, which is defined as δ=PW<V, where V and W are the strength and stress random variables, respectively, and δ is reliability parameter. Type-II progressive censoring with binomial removal is used in this study to examine the inference of δ=PW<V for a component with strength V and being subjected to stress W. We suppose that V and W are independent random variables taken from the Burr XII distribution and the Burr III distribution, respectively, with a common shape parameter. The maximum likelihood estimator of δ is derived. The Bayes estimator of δ under the assumption of independent gamma priors is derived. To determine the Bayes estimates for squared error and linear exponential loss functions in the lack of explicit forms, the Metropolis–Hastings method was provided. Utilizing comprehensive simulations and two metrics (average of estimates and root mean squared errors), we compare these estimators. Further, an analysis is performed on two actual data sets based on breakdown times for insulating fluid between electrodes recorded under varying voltages.
Audience Academic
Author Elbatal, Ibrahim
El-Saeed, Ahmed R.
Ben Ghorbal, Anis
Elgarhy, Mohammed
Diab, L. S.
Hassan, Amal S.
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CitedBy_id crossref_primary_10_1016_j_jrras_2025_101340
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Snippet In the statistical literature, one of the most important subjects that is commonly used is stress–strength reliability, which is defined as δ=PW<V, where V and...
In the statistical literature, one of the most important subjects that is commonly used is stress–strength reliability, which is defined as δ=P[W<V], where V...
In the statistical literature, one of the most important subjects that is commonly used is stress–strength reliability, which is defined as δ=P W<V , where V...
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StartPage 1054
SubjectTerms Bayesian estimation
binomial distribution
Burr distributions
Censoring (Statistics)
Engineering
Estimates
Failure
Independent variables
Insulation
Life expectancy
Maximum likelihood estimators
Medicine
Metropolis–Hastings algorithm
Monte Carlo simulation
Parameters
Random variables
Reliability analysis
Strains and stresses
Strength of materials
Stress relaxation (Materials)
Stress relieving (Materials)
stress–strength model
Type-II progressive censoring
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Title Stress–Strength Reliability Analysis for Different Distributions Using Progressive Type-II Censoring with Binomial Removal
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