Interval estimation of the stress–strength reliability in the two-parameter exponential distribution based on records

Baklizi, Ayman

doi:10.1080/00949655.2013.816307

Cited by 39 publications

(23 citation statements)

References 15 publications

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“…The numerical study is designed through the following steps: and stress random variables (n, m) are chosen to be (10,10), (10,15), (15,10), (15,15), (15,20), (20,15) and (20,20). • The MLEs of λ 1 and λ 2 are obtained from (9), then the MLE of R S,k is obtained by substitutingλ 1 andλ 2 in (10).…”

Section: Numerical Studymentioning

confidence: 99%

“…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%

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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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Section: Numerical Studymentioning

confidence: 99%

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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“…From (5) the log-likelihood function of the observed data x and y is and likelihood equations of 1 and 2 are obtained as where (⋅) is the pdf and (⋅) is the cdf of standard normal distribution and ̂1 and ̂2 are the ML estimators of the parameters 1 and 2 which is obtained by solving nonlinear Eqs. (6) and (7).…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

“…Moreover, the estimation of the stress-strength reliability R = P(Y < X) was addressed by Iranmanesh et al [28] when X and Y were two independent inverted gamma distributions. Besides, the maximum likelihood (ML) and Bayesian estimates of stress-strength reliability were addressed by Baklizi [6,7] for two-parameter exponential distributions based on records. Further, the estimation of R based on the upper record values in two-parameter bathtub-shaped lifetime distribution was studied by Tarvirdizadeh and Ahmadpour [46].…”

Section: Introductionmentioning

confidence: 99%

Estimation of stress–strength reliability in the inverse Gaussian distribution under progressively type II censored data

Rostamian

Nematollahi

2019

Math Sci

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The stress-strength parameter R = P(Y < X) , as a reliability parameter, is considered in different statistical distributions. In the present paper, the stress-strength reliability is estimated based on progressively type II censored samples, in which X and Y are two independent random variables with inverse Gaussian distributions. The maximum likelihood estimate of R via expectation-maximization algorithm and the Bayes estimate of R are obtained. Furthermore, we obtain the bootstrap confidence intervals, HPD credible interval and confidence intervals based on generalized pivotal quantity for R. Additionally, the performance of point estimators and confidence intervals are evaluated by a simulation study. Finally, the proposed methods are conducted on a set of real data for illustrative purposes.

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“…The following the simulated record values are given by Baklizi (2013). The first record values which are generated from location-scale exponential distribution with θ 1 = 1 and η 1 = 3 are 3.…”

Section: An Examplementioning

confidence: 99%

Preliminary Test and ‎‎Shrinkage Estimations of Scale Parameters for Two Exponential Distributions based on Record Values

Zakerzadeh¹,

Jafari²,

Karimi³

2016

JSRI

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The exponential distribution is applied in a very wide variety of statistical procedures.Among the most prominent applications are those in the field of life testing and reliability theory. When there are two record samples available for estimating the scale parameter, a preliminary test is usually used to determine whether to pool the samples or use the individual sample. In this paper, the preliminary test estimator and shrinkage estimator are studied. The optimum level of significance for preliminary test estimation and the optimum values of shrinkage coefficient are obtained based on minimax regret criterion under the weighted square error loss function.

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Interval estimation of the stress–strength reliability in the two-parameter exponential distribution based on records

Cited by 39 publications

References 15 publications

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

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

Estimation of stress–strength reliability in the inverse Gaussian distribution under progressively type II censored data

Preliminary Test and ‎‎Shrinkage Estimations of Scale Parameters for Two Exponential Distributions based on Record Values

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