Estimation of reliability <i>P</i>(<i>X &gt; Y</i>) for distributions with power hazard function based on upper record values

Abravesh, Akbar; Ganji, Masoud; Mostafaiy, Behdad

doi:10.1080/08898480.2018.1493867

Cited by 4 publications

(2 citation statements)

References 24 publications

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“…Thereafter, the problem of estimating R has been discussed by a great number of researchers. Of the recent efforts pertaining to stress-strength models, to name a few, are Al-Mutairi, Ghitany, and Kundu (2013), Genc (2013), Singh, Singh, and Sharma (2014), Rezaei, Noughabi, and Nadarajah (2015), Akgül and Şenoglu (2017), Mahdizadeh and Zamanzade (2018), Abravesh, Ganji, and Mostafaiy (2019), Jose and Drisya (2020), Sadeghpour, Nezakati, and Salehi (2021) and Biswas, Chakraborty, and Mukherjee (2021).…”

Section: Introductionmentioning

confidence: 99%

Multicomponent Stress-strength Reliability with Exponentiated Teissier Distribution

Pasha-Zanoosi

Pourdarvish²,

Asgharzadeh

2022

AJS

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This article deals with the problem of reliability in a multicomponent stress-strength (MSS) model when both stress and strength variables are from exponentiated Teissier (ET) distributions. The reliability of the system is determined using both classical and Bayesian methods, based on two scenarios where the common scale parameter is unknown or known. In the first scenario, where the common scale parameter is unknown, the maximum likelihood estimation (MLE) and the approximate Bayes estimation are derived. In the second scenario, where the scale parameter is known, the MLE, the uniformly minimum variance unbiased estimator (UMVUE) and the exact Bayes estimation are obtained. In the both scenarios, the asymptotic confidence interval and the highest probability density credible interval are established. Furthermore, two other asymptotic confidence intervals are computed based on the Logit and Arcsin transformations. Monte Carlo simulations are implemented to compare the different proposed methods. Finally, one real example is presented in support of suggested procedures.

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Section: Introductionmentioning

confidence: 99%

Multicomponent Stress-strength Reliability with Exponentiated Teissier Distribution

Pasha-Zanoosi

Pourdarvish²,

Asgharzadeh

2022

AJS

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“…The component fails at the instant that the stress applied to it exceeds the strength in the past years; simple random sampling is used in estimation of R=Pfalse[Y<Xfalse] , where X and Y are random variables following the specified distribution that has been considered many times using both parametric and nonparametric models. Babayi et al (2014) discussed the inference of Pfalse[Y<Xfalse] for generalized logistic distribution; Ghitany et al (2015) estimated Pfalse[Y<Xfalse] for power Lindley distribution; Najarzadegan et al (2016) studied Pfalse[Y<Xfalse] for Levy distribution; Hassan (2017) studied the different estimators of Pfalse[Y<Xfalse] for two Lindley distribution; Hassan (2018a) introduced the maximum penalized likelihood estimator for Pfalse[Y<Xfalse]; Hassan (2018b) discussed the estimation of Kumaraswamy exponential–Weibull distribution; Hassan (2018c) studied Pfalse[Y<Xfalse] for beta Gompertz distribution; and Abravesh et al (2019) estimated Pfalse[Y<Xfalse] for power hazard function based on upper record values. In the recent years, the ranked set sampling is used ...…”

Section: Introductionmentioning

confidence: 99%

Ranked set sampling on estimation of P[Y<X] for inverse Weibull distribution and its applications

Hassan

2021

IJQRM

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PurposeDistribution. The purpose of this study is to obtain the modified maximum likelihood estimator of stress–strength model using the ranked set sampling, to obtain the asymptotic and bootstrap confidence interval of P[Y < X], to compare the performance of author’s estimates with the estimates under simple random sampling and to apply author’s estimates on head and neck cancer.Design/methodology/approachThe maximum likelihood estimator of R = P[Y < X], where X and Y are two independent inverse Weibull random variables common shape parameter that affect the shape of the distribution, and different scale parameters that have an effect on the distribution dispersion are given under ranked set sampling. Together with the asymptotic and bootstrap confidence interval, Monte Carlo simulation shows that this estimator performs better than the estimator under simple random sampling. Also, the asymptotic and bootstrap confidence interval under ranked set sampling is better than these interval estimators under simple random sampling. The application to head and neck cancer disease data shows that the estimator of R = P[Y < X] that shows the treatment with radiotherapy is more efficient than the treatment with a combined radiotherapy and chemotherapy under ranked set sampling that is better than these estimators under simple random sampling.FindingsThe ranked set sampling is more effective than the simple random sampling for the inference of stress-strength model based on inverse Weibull distribution.Originality/valueThis study sheds light on the author’s estimates on head and neck cancer.

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Reliability of stress–strength model for exponentiated Teissier distribution based on lower record values

Pasha-Zanoosi

2023

Jpn J Stat Data Sci

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Estimation of reliability P(X > Y) for distributions with power hazard function based on upper record values

Cited by 4 publications

References 24 publications

Multicomponent Stress-strength Reliability with Exponentiated Teissier Distribution

Multicomponent Stress-strength Reliability with Exponentiated Teissier Distribution

Ranked set sampling on estimation of P[Y<X] for inverse Weibull distribution and its applications

Reliability of stress–strength model for exponentiated Teissier distribution based on lower record values

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