Estimation of Reliability in a Multicomponent Stress-Strength Model

Bhattacharyya, G. K.; Johnson, Richard A.

doi:10.2307/2286173

Cited by 59 publications

(53 citation statements)

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“…Let the random samples Y, X 1 , X 2 , · · · , X k be independent, G(y) be the continuous distribution function of Y and F (x) be the common continuous distribution function of X 1 , X 2 , · · · , X k . The reliability in a multicomponent stress-strength model developed by Bhattacharyya and Johnson [20] is…”

Section: Multicomponent Stress-strength Modelmentioning

confidence: 99%

“…We generate 3000 random samples of size 10, 15, 20, 25, 30 each from stress and strength populations for (β 1 , β 2 ) = (3.0, 1.5), (2.5, 1.5), (2.0, 1.5), (1.5, 1.5), (1.5, 2.0), (1.5, 2.5) and (1.5,3.0) as proposed by Bhattacharyya and Johnson [20]. The MLEs of β, α and δ, sayβ,α andδ are estimated by solutions of the nonlinear equation.…”

Section: Simulation Studymentioning

confidence: 99%

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Estimation of the Stress-Strength Reliability for the Dagum Distribution

Alzahrani¹,

Basloom²

2016

JAS

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The paper deals with the problem of estimating the reliability of a single and multicomponent stress-strength based on a three-parameter Dagum distribution. The maximum likelihood estimators and the Bayes estimators of R = P (Y < X) when X and Y are two independent random variables follow Dagum distribution and their asymptotic distributions are obtained. Also, the reliability of a multicomponent stress-strength model is estimated using the maximum likelihood. Consequently, the asymptotic confidence intervals of the reliability of a single and multicomponent stress-strength model are constructed. Gibbs and Metropolis sampling were used to provide sample-based estimates of the reliability and its associated credible intervals. Finally, Monte Carlo simulations are carried out for illustrative purposes.

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Section: Multicomponent Stress-strength Modelmentioning

confidence: 99%

Section: Simulation Studymentioning

confidence: 99%

Estimation of the Stress-Strength Reliability for the Dagum Distribution

Alzahrani¹,

Basloom²

2016

JAS

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“…3,000 random sample of size 10(5)35 each from stress population, strength population were generated for ( , )  = (3.0,1.0), (2.5,1.0), (2.0,1.0), (1.5,1.0), (1.0,1.0), (1.5,2.0),(1.5,2.5) and (1.5,3.0) on lines of Bhattacharyya and Johnson (1974). The ML estimators of and  were then substituted in  to obtain the reliability in a multicomponent stressstrength for (s, k) = (1, 3), (2,4).…”

Section: Simulation Study and Data Analysis Simulation Studymentioning

confidence: 99%

“…The probability in (3) is called reliability in a multicomponent stress-strength model (Bhattacharyya & Johnson, 1974). The survival probability of single component stress-strength versions have been considered by several authors assuming various lifetime distributions for the stress-strength random variates (Enis & Geisser, 1971;Downtown, 1973;Awad & Gharraf, 1986;McCool, 1991;Nandi & Aich, 1994;Surles & Padgett, 1998;Kundu & Gupta, 2005, 2006Raqab, et al, 2008;Kundu & Raqab, 2009).…”

Section: Introductionmentioning

confidence: 99%

“…The survival probability of single component stress-strength versions have been considered by several authors assuming various lifetime distributions for the stress-strength random variates (Enis & Geisser, 1971;Downtown, 1973;Awad & Gharraf, 1986;McCool, 1991;Nandi & Aich, 1994;Surles & Padgett, 1998;Kundu & Gupta, 2005, 2006Raqab, et al, 2008;Kundu & Raqab, 2009). Reliability in a multicomponent stress-strength was developed by Bhattacharyya and Johnson (1974) and Pandey and Borhan Uddin (1985) and the references therein cover the study of estimating () P Y X  in many standard distributions assigned to one or both of stress, strength variates. Recently Srinivasa Rao and Kantam (2010) 369 studied estimation of reliability in multicomponent stress-strength for log-logistic distribution.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of Reliability in Multicomponent Stress-Strength Based on Generalized Rayleigh Distribution

Rao

2014

J. Mod. App. Stat. Meth.

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A multicomponent system of k components having strengths following k-independently and identically distributed random variables x1, x2,…, xk and each component experiencing a random stress Y is considered. The system is regarded as alive only if at least s out of k (s < k) strengths exceed the stress. The reliability of such a system is obtained when strength and stress variates are given by a generalized Rayleigh distribution with different shape parameters. Reliability is estimated using the maximum likelihood (ML) method of estimation in samples drawn from strength and stress distributions; the reliability estimators are compared asymptotically. Monte-Carlo simulation is used to compare reliability estimates for the small samples and real data sets illustrate the procedure.

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