Interval Estimation of Stress-Strength Reliability Based on Lower Record Values from Inverse Rayleigh Distribution

Tarvirdizade, Bahman; Garehchobogh, Hossein Kazemzadeh

doi:10.1155/2014/192072

Cited by 7 publications

(6 citation statements)

References 12 publications

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“…Birnbaum (1956), Gupta (2005, 2006), Razaei, Tahmasbi, andMahmoodi (2010), Hussian, (2013) studied the estimation of R for different distributions. The recorded values and more studies about R with different distributions and different methods of estimation found in Baklizi (2008Baklizi ( , 2014, Essam (2012), Tarvirdizade, and Kazemzadeh Garehchobogh (2014).…”

Section: Introductionmentioning

confidence: 96%

Estimation of R for geometric distribution under lower record values

Mohamed

2020

JART

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In this paper, the estimation of the stress-strength model R=P(Y<X), based on lower record values is derived when both X and Y are independent and identical random variables with geometric distribution. Estimating R with maximum likelihood estimator and Bayes estimator with non-informative prior information based on mean square errors and LINIX loss functions for geometric distribution are obtained. The confidence intervals of R are constructed by using exact, bootstrap and Bayesian methods. Finally, different methods have been used for illustrative purpose by using simulation. The main results are obtained and introduced through a set of tables and figures with discussions.

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Section: Introductionmentioning

confidence: 96%

Estimation of R for geometric distribution under lower record values

Mohamed

2020

JART

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“…The survival probability of stress-strength R = P(Y < X) based on record values is considered in Baklizi [6] for generalized exponential distribution. Subsequent papers extended this work assuming various lifetime distributions for stress-strength random variables, for instance, in Baklizi [7,8,9], for one and two parameter exponential distribution, Essam [10] for type I generalized logistic distribution, Baklizi [11] for two-parameter Weibull distribution, Tarvirdizade and Kazemzadeh Garehchobogh [12] for inverse Rayleigh distribution, Al-Gashgari and Shawky [13] for exponentiated Weibull distribution, Hassan et al [14] for exponentiated inverted Weibull distribution and Hassan et al [15] for generalized inverted exponential distribution.…”

Section: Introductionmentioning

confidence: 99%

Estimation of multicomponent stress-strength reliability following Weibull distribution based on upper record values

Hassan

Nagy

Muhammed

et al. 2020

Journal of Taibah University for Science

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Stress-strength models are of special importance in reliability literature and engineering applications. This paper deals with the estimation problem of a stress-strength model incorporating multi-component system. The system is regarded as alive only if at least S out of k (S < k) strength components exceed the stress. The reliability of such system is obtained when strength and stress variables have Weibull distributions. Maximum likelihood estimator of R S,k and asymptotic confidence intervals are obtained based on upper record values. Bayesian estimator under squared error and linear exponential loss functions using gamma prior distributions and the corresponding credible intervals are obtained. Due to the lack of explicit forms for the Bayes estimates, the Markov Chain Monte Carlo (MCMC) method is employed. A simulation study is implemented to assess the performance of estimates. A real-life example is presented to show how the proposed model may be utilized in breaking strength of jute fibre data.

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“…Also, authors found Bayesian analysis for record data Based on Generalized Inverted Exponential Model which considered in [3]. For finding interval estimation for Inverse Rayleigh Distribution based on lower record see [4]. For estimating the reliability for a family of life time distribution based on records see [5].…”

Section: Introductionmentioning

confidence: 99%

“…Figure 2: MSEs OF MLE AND BAYES ESTIMATORS WHEN R=0.75 Shows that the MSEs of MLE and BAYES estimators decrease as n and m are increase at R=0.75, also, MSEs of MLE is smallest than MSEs of BayesFor Real data figures[3,4] …”

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confidence: 99%

On estimation of stress-strength reliability using lower record values from odd generalized exponential: Exponential distribution

Mohamed¹,

Reda²

2021

J Appl Eng Science

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This research paper aims to find the estimated values closest to the true values of the reliability functionunder lower record values and to know how to obtain these estimated values using point estimation methodsor interval estimation methods. This helps researchers later in obtaining values of the reliability function intheory and then applying them to reality which makes it easier for the researcher to access the missing datafor long periods such as weather. We evaluated the stress–strength model of reliability based on point andinterval estimation for reliability under lower records by using Odd Generalize Exponential–Exponentialdistribution (OGEE) which has an important role in the lifetime of data. After that, we compared theestimated values of reliability with the real values of it. We analyzed the data obtained by the simulationmethod and the real data in order to reach certain results. The Numerical results for estimated values ofreliability supported with graphical illustrations. The results of both simulated data and real data gave us thesame coverage.

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Interval Estimation of Stress-Strength Reliability Based on Lower Record Values from Inverse Rayleigh Distribution

Cited by 7 publications

References 12 publications

Estimation of R for geometric distribution under lower record values

Estimation of R for geometric distribution under lower record values

Estimation of multicomponent stress-strength reliability following Weibull distribution based on upper record values

On estimation of stress-strength reliability using lower record values from odd generalized exponential: Exponential distribution

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