Estimation of stress-strength probability in a multicomponent model based on geometric distribution

Jovanović, Miodrag; Milošević, Bojana; Obradović, M

doi:10.15672/hujms.681608

Cited by 6 publications

(5 citation statements)

References 21 publications

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“…Such a structure for data is observed in many studies. For more details, one can refer to [3,23,[37][38][39][40]. On the other hand, there are other studies that the basic data structure for random stress and strength samples in the above model is considered as a matrix.…”

Section: Real Data Set Imentioning

confidence: 99%

“…Thereafter, many authors have shown considerable interest in the MSS model. Some recent efforts regard to the issue, can be found in [3,4,14,[21][22][23][24][25][26][27][31][32][33]37] for the Topp-Leone, exponentiated Pareto distribution, Kumaraswamy, unit-Gompertz, unit generalized Rayleigh, Geometric, Chen, proportional reversed hazard rate family, bivariate Kumaraswamy, Weibull, the general class of inverted Exponentiated models, inverted exponentiated Rayleigh, Burr XII, and bathtub-shaped distributions, respectively.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multicomponent stress-strength reliability based on a right long-tailed distribution

PASHA-ZANOOSİ

Pourdarvish

2022

Hacettepe Journal of Mathematics and Statistics

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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 inverse Kumaraswamy distribution. The reliability of the system is estimated using classical and Bayesian approaches when the common second shape parameter is known or unknown. The maximum likelihood estimation and its asymptotic confidence interval for the reliability of the system are obtained. Furthermore, two other asymptotic confidence intervals are computed based on Logit and Arcsin transformations. The uniformly minimum variance unbiased estimator for the reliability of the MSS model is obtained when the common second shape parameter is known. The Bayes estimate is obtained exactly when the second shape parameter is known and it is approximated by using the Monte Carlo Markov Chain method when the second shape parameter is unknown. The highest probability density credible interval is established using the Gibbs sampling technique. Monte Carlo simulations are implemented to compare the different proposed methods. Finally, two real data sets are presented in support of the suggested procedures.

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Section: Real Data Set Imentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multicomponent stress-strength reliability based on a right long-tailed distribution

PASHA-ZANOOSİ

Pourdarvish

2022

Hacettepe Journal of Mathematics and Statistics

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“…Recently, the estimation the R is very popular in the literature and many authors have studied the problem of estimation R under various assumptions on X and Y for various distributions. For some references and more applications of the R, see [2,15,19,22,29]. On the other hand, some authors have investigated the estimation of R based on record data.…”

Section: Introductionmentioning

confidence: 99%

Estimation of $Pr(X<Y)$ for exponential power records

Tanış

Saraçoğlu

Asgharzadeh

et al. 2023

Hacettepe Journal of Mathematics and Statistics

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In this study, we tackle the problem of estimation of stress-strength reliability R = Pr(X < Y) based on upper record values for Exponential Power distribution. We use the maximum likelihood and Bayes methods to estimate R. The Tierney-Kadane approximation is used to compute the Bayes estimation of R since the Bayes estimator can not be obtained analytically. We also derive asymptotic confidence interval based on the asymptotic distribution of the maximum likelihood estimator of R. We consider a Monte Carlo simulation study in order to compare the performances of the maximum likelihood estimators and Bayes estimators according to mean square error criteria. Finally, a real data application is presented.

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“…Thereafter, many authors have shown considerable interests in the MSS model. Some recent efforts regard to the issue, to mention a few, can be found in Nadar and Kızılaslan (2015), Pak, Kumar Gupta, and Bagheri Khoolenjani (2018), Akgül (2019), Kohansal and Shoaee (2019), Maurya and Tripathi (2020), Kayal, Tripathi, Dey, andWu (2020), Mahto, Tripathi, andKızılaslan (2020) and Jovanović, Milošević, and Obradović (2020).…”

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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Estimation of stress-strength probability in a multicomponent model based on geometric distribution

Cited by 6 publications

References 21 publications

Multicomponent stress-strength reliability based on a right long-tailed distribution

Multicomponent stress-strength reliability based on a right long-tailed distribution

Estimation of $Pr(X<Y)$ for exponential power records

Multicomponent Stress-strength Reliability with Exponentiated Teissier Distribution

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