Estimation of reliability in a multicomponent stress–strength model based on a bivariate Kumaraswamy distribution

Kızılaslan, Fatih; Nadar, Mustafa

doi:10.1007/s00362-016-0765-8

Cited by 68 publications

(18 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the above-transformed data, one can refer to Kizilaslan and Nadar [11] for more details, whereas the complete monthly water capacity of the Shasta reservoir in California, USA between 1981 to 1985 is provided in Appendix G.…”

Section: Real Data Illustrationmentioning

confidence: 99%

“…The ls-out-of-k G system has raised much attention and the associated reliability estimation of the multicomponent system has been widely discussed by many researches. For instance, Dey et al [7], Kayal [8], Kizilaslan [9,10], Kizilaslan and Nadar [11], Nadar and Kizilaslan [12], and Rao et al [13], when the underlying distributions follow Kumaraswamy, Chen, a class of inverse exponentiated, proportional reversed hazard rate model, bivariate Kumaraswamy, bivariate Weibull, bathtub-shaped, and Burr XII, respectively.…”

Section: Introduction and Notationmentioning

confidence: 99%

“…which have the chi-square distributions with 2(n − 1) and 2n degrees of freedom respectively, where α (•) = α or α 1 under common and unequal parameter cases respectively, and X (11) , X (21) , . .…”

mentioning

confidence: 99%

See 2 more Smart Citations

Estimation of Stress-Strength Reliability for Multicomponent System with Rayleigh Data

et al. 2021

View full text Add to dashboard Cite

Inference is investigated for a multicomponent stress-strength reliability (MSR) under Type-II censoring when the latent failure times follow two-parameter Rayleigh distribution. With a context that the lifetimes of the strength and stress variables have common location parameters, maximum likelihood estimator of MSR along with the existence and uniqueness is established. The associated approximate confidence interval is provided via the asymptotic distribution theory and delta method. Meanwhile, alternative generalized pivotal quantities-based point and confidence interval estimators are also constructed for MSR. More generally, when the lifetimes of strength and stress variables follow Rayleigh distributions with unequal location parameters, likelihood and generalized pivotal-based estimators are provided for MSR as well. In addition, to compare the equivalence of different strength and stress parameters, a likelihood ratio test is provided. Finally, simulation studies and a real data example are presented for illustration.

show abstract

Section: Real Data Illustrationmentioning

confidence: 99%

Section: Introduction and Notationmentioning

confidence: 99%

See 1 more Smart Citation

Estimation of Stress-Strength Reliability for Multicomponent System with Rayleigh Data

et al. 2021

View full text Add to dashboard Cite

show abstract

“…An exhaustive bibliography on the estimation of R is available in [17]. Some recent papers on this topic include [22], [27], [14], [18], [7], [16], [28], [33] and [2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Inference on reliability of stress-strength model with Peng-Yan extended Weibull distributions

Jovanović

Milošević

Obradović

et al. 2021

Filomat

View full text Add to dashboard Cite

In this paper we estimate R = PfX < Yg when X and Y are independent random variables following the Peng-Yan extended Weibull distribution. We find maximum likelihood estimator of R and its asymptotic distribution. This asymptotic distribution is used to construct asymptotic confidence intervals. In the case of equal shape parameters, we derive the exact confidence intervals, too. A procedure for deriving bootstrap-p confidence intervals is presented. The UMVUE of R and the UMVUE of its variance are derived and also the Bayes point and interval estimator of R for conjugate priors are obtained. Finally, we perform a simulation study in order to compare these estimators and provide a real data example.

show abstract

“…The cases of Burr-XII, Weibull and two parameter exponentiated Weibull distribution were studied in [14,23,24], respectively. The Kumaraswamy distribution was considered in [5,15,16]. General classes of inverse exponentiated and exponentiated inverted exponential distributions were investigated in [7,13], respectively.…”

Section: Introductionmentioning

confidence: 99%

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

Jovanović

Milošević

Obradović

2020

Hacettepe Journal of Mathematics and Statistics

View full text Add to dashboard Cite

In this paper, the estimation of the stress-strength probability in a multicomponent model, in the case when all components follow the geometric distribution, is studied. This is the first time that multicomponent models with discrete probability distributions are considered. The MLE, UMVUE and Bayes point estimator, as well as asymptotic and bootstrap confidence intervals are presented. A simulation study is performed in order to compare the performance of various estimators. Finally, the methods are applied to real data examples from climatology and sport.

show abstract

Estimation of reliability in a multicomponent stress–strength model based on a bivariate Kumaraswamy distribution

Cited by 68 publications

References 32 publications

Estimation of Stress-Strength Reliability for Multicomponent System with Rayleigh Data

Estimation of Stress-Strength Reliability for Multicomponent System with Rayleigh Data

Inference on reliability of stress-strength model with Peng-Yan extended Weibull distributions

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

Contact Info

Product

Resources

About