Estimation of Reliability in a Multicomponent Stress-Strength Model

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

doi:10.1080/01621459.1974.10480238

Cited by 196 publications

(49 citation statements)

References 4 publications

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“…The reliability in a multicomponent stress-strength model developed by Bhattacharyya and Johnson [22] is given by (1) In our case, we assume that is a random sample from a MOBW distribution with parameters , and is a random variable from a Weibull distribution with parameters . Therefore, for our case, is given by using (1).…”

Section: Ifmentioning

confidence: 99%

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Estimation of Reliability in a Multicomponent Stress-Strength Model Based on a Marshall-Olkin Bivariate Weibull Distribution

Nadar

Kızılaslan

2016

IEEE Trans. Rel.

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In this paper, we consider a system which has s-independent and identically distributed strength components, and each component is constructed by a pair of s-dependent elements. These elements follow a Marshall-Olkin bivariate Weibull distribution, and each element is exposed to a common random stress which follows a Weibull distribution. The system is regarded as operating only if at least out of strength variables exceed the random stress. The multicomponent reliability of the system is given by (at least of the exceed ) where , . We estimate by using frequentist and Bayesian approaches. The Bayes estimates of have been developed by using Lindley's approximation, and the Markov Chain Monte Carlo methods, due to the lack of explicit forms. The asymptotic confidence interval, and the highest probability density credible interval are constructed for . The reliability estimators are compared by using the estimated risks through Monte Carlo simulations. Index Terms-Marshall-Olkin bivariate Weibull distribution, stress-strength, stress-strength model. 0018-9529

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Section: Ifmentioning

confidence: 99%

“…This multicomponent stress-strength system functions when or more components simultaneously survive. It was first studied by Bhattacharyya and Johnson [22]. This type of system appears in both industrial and military applications.…”

mentioning

confidence: 99%

Estimation of Reliability in a Multicomponent Stress-Strength Model Based on a Marshall-Olkin Bivariate Weibull Distribution

Nadar

Kızılaslan

2016

IEEE Trans. Rel.

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“…Most of the engineering systems consist of several components and the components might have different statistical properties. Multicomponent stress-strength reliability in a static form has been studied in various papers including Bhattacharyya and Johnson [7], Chandra and Owen [8], Johnson [1], Pandey et al [9], Eryilmaz [10], and Eryilmaz [11]. Assume that a system consists of components and the deteriorating strength of the th component at time is denoted by the process , 1 2 .…”

Section: Multicomponent Setupmentioning

confidence: 99%

On Stress-Strength Reliability with a Time-Dependent Strength

Eryılmaz

2013

Journal of Quality and Reliability Engineering

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e study of stress-strength reliability in a time-dependent context needs to model at least one of the stress or strength quantities as dynamic. We study the stress-strength reliability for the case in which the strength of the system is decreasing in time and the stress remains �xed over time; that is, the strength of the system is modeled as a stochastic process and the stress is considered to be a usual random variable. We present stochastic ordering results among the lifetimes of the systems which have the same strength but are subjected to different stresses. Multicomponent form of the aforementioned stress-strength interference is also considered. We illustrate the results for the special case when the strength is modeled by a Weibull process.

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“…For T j following exponential ð j Þ distribution, for j ¼ 1, 2, 3, and S following exponential ðÞ distribution, (4) and (1) give For T j following exponential ð j Þ distribution, for j ¼ 1, 2, 3, and S following exponential ðÞ distribution, (4) and (1) give…”

Section: Reprintsmentioning

confidence: 99%