Availability theory for two-unit nonindependent series systems subject to shut-off rules

Osaki, Shunji; Yamada, Shigeru; Hishitani, Jun

doi:10.1016/0951-8320(89)90022-7

Cited by 13 publications

(2 citation statements)

References 3 publications

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“…7. Osaki et al [30] provided some results for availability measures of systems in which two units are in series, failure of unit 1 shuts off unit 2, but not vice versa, the lifetimes follow Marshall and Olkin's distribution, the units have arbitrary repair-time distributions, and two alternative assumptions are made about the repair discipline. 8.…”

Section: Bivariate Exponential Distributionmentioning

confidence: 99%

Marshall and Olkin’s Distributions

Nadarajah

2008

Acta Appl Math

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A review is provided of the continuous and discrete distributions introduced by the eminent Professors Marshall and Olkin. The topics reviewed include: bivariate geometric distribution, extreme value behavior, bivariate negative binomial distribution, bivariate exponential distribution, concomitants, reliability, distributions of sums and ratios, Ryu's bivariate exponential distribution, bivariate Pareto distribution and generalized exponential and Weibull distributions. Some hitherto unknown results about these distributions are also mentioned.Keywords Continuous distributions · Discrete distributions · Marshall and Olkin's distributions IntroductionThe contribution of Professors Marshall and Olkin to statistics has been and continues to be phenomenal. In this note, we review the continuous and discrete distributions-both univariate and bivariate-introduced by Professors Marshall and Olkin. We also derive some hitherto unknown results about Marshall and Olkin's distributions. Bivariate Geometric DistributionThe bivariate geometric distribution can be constructed in different ways. Marshall and Olkin [21] provided a construction based on the sequence of bivariate Bernoulli random variables. Consider a vector (U, V ) having Bernoulli marginals. This vector has only four This is a tribute to the work of Professors Marshall and Olkin.

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Section: Bivariate Exponential Distributionmentioning

confidence: 99%

Marshall and Olkin’s Distributions

Nadarajah

2008

Acta Appl Math

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“…It has received wide ranging applications in reliability, see [43,38,12,8,39,28,42]. The marginal pdfs of X and Y are exponential with parameters θ 1 + θ 3 and θ 2 + θ 3 , respectively; so, in particular,…”

Section: Marshall and Olkin's Bivariate Exponentialmentioning

confidence: 99%