System availability in a gamma alternating renewal process

Pham‐Gia, T.; Turkkan, N.

doi:10.1002/(sici)1520-6750(199910)46:7<822::aid-nav5>3.0.co;2-d

Cited by 30 publications

(13 citation statements)

References 34 publications

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“…The Gibbs sampler allows the generation of a sample from the following full conditional distributions g(oll data,6 Z,03) g(Oz ldata,°1,0 3 ) g(031data,O) ,Oz) (11) These conditional distributions are used in the iterative scheme to generate samples for each of the three marginal distributions and subsequently of A"" using (4) .…”

Section: Bayesian Inference Of A«>mentioning

confidence: 99%

“…Pointwise availability A(t) is, undoubtedly, the most important of these since it gives the probability that the system is functioning at time t (Klassen & Van Peppen, 1989) . Its limit value, when it exists, is called the steady-state or asymptotic availability (pham-Gia & Turkkan, 1999). Aoo is defined as the expected fraction of time that the system operates satisfactorily in the long run .…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Highest Posterior Density Intervals for the Availability of a System With a 'Rest-Period' for the Repair Facility

Yadavalli

Bekker

Mostert

et al. 2012

The South African Journal of Industrial Engineering

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In this paper Bayesian estimation for the steady state availability of a one-unit system with a rest-period for the repair facility is studied. The assumption is that the repair facility takes rest with probability p after each repair completion and the facility does not take the same with probability (l -p). The prior information is assumed to be vague and the Jeffreys' prior is used for the unknown parameters in the system. Gibbs sampling is used to derive the posterior distribution of the availability and subsequently the highest posterior density (HPD) intervals. A numerical example illustrates these results. OPSOMMINGIn .hierdie artikel word die Bayes-beraming van die ewewigstoestandsbeskikbaarheid van 'n steise1 wat afwisselend gebruik word, voorgestel.Daar word veronderstel dat die herstelfasiliteit na voltooiing van clke herstel Of 'n rustydperk binnegaan of nie. Die rustydperk sal geneem word met waarskynlikheid p en die waarskynlikheid dat daar nie 'n rustydperk genccm word nie, is (l -p). Jeffrey se a priori-verdeling word vir die onbekende parameters in die stelsel aanvaar. Gibbs-steekproefneming word gcbruik om die a posterioriverdeling van die beskikbaarheid en daarna die hoogste a posteriori-digtheidsintervalle (HPD) afte lei. 'n Numeriese voorbeeld illustreer hierdic resultate . 17http://sajie.journals.ac.za

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Section: Bayesian Inference Of A«>mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bayesian Highest Posterior Density Intervals for the Availability of a System With a 'Rest-Period' for the Repair Facility

Yadavalli

Bekker

Mostert

et al. 2012

The South African Journal of Industrial Engineering

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show abstract

“…That is some {α n } N n=1 can be equal while others can be distinct. In the statistical literature, other expressions for p Z (z) in terms of Humbert or Whittaker functions and zonal polynomials exist, see for example [10] and references therein. However the Moschopoulos p.d.f allows us to obtain a mathematically tractable outage probability solution.…”

Section: The Moschopoulos Pdf Representation Of the Sum Of Gamma Vamentioning

confidence: 99%

“…However the Moschopoulos p.d.f allows us to obtain a mathematically tractable outage probability solution. If all N scale parameters are equal to β, the p.d.f simplifies to [10]. Since we neglect the path loss effects in this paper, this condition means the shape parameters must also be the same.…”

Section: The Moschopoulos Pdf Representation Of the Sum Of Gamma Vamentioning

confidence: 99%

Outage probability of cooperative relay networks in Nakagami-m fading channels

2006

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Abstract-It is well known that the cooperation among nodes can improve the performance of a wireless network. In this letter we analyze the outage probability behaviour of a relay network in Nakagami-m fading channels. A closed-form solution for the outage probability is derived. When m = 1, the results are applicable for Rayleigh fading. Computer simulations confirm the presented mathematical analysis.Index Terms-Cooperative diversity, multihop transmission, outage probability, Nakagami-m channels.

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“…(5) for deterministic (i.e., data-independent) loop bounds AE since deriving the moments of È Ñ for stochastic AE is mathematically very complex [13]. The mean and variance of È Ñ are given by…”

Section: Empirical Approachmentioning

confidence: 99%

A statistical approach to branch modeling in static program performance prediction

Gautama

Gemund

Proceedings International Parallel and Distributed Processing Symposium

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Current static performance prediction methods have been less successful in statistically accounting for program workload distribution due to input data set variability, of which data-dependent branches are usually the most important contributors. While data-dependent basic block execution time is often characterized in terms of, e.g., mean and variance, branching conditions still are typically characterized by only one parameter, usually known as the truth probability. In this paper we propose and evaluate three statistical approaches to modeling branching behavior, to be used within a compositional method to predict program execution time distribution. The approaches are coined the Empirical, the Bernoulli, and the ARP (Alternating Renewal Processes) approach. While the Empirical approach is based on measuring branching behavior in terms of the surrounding loop construct, the other approaches aim at deriving a statistical model of the branch itself, which enables a higher level of compositionality. Our measurement results, based on synthetic as well as on real programs, show that the Empirical approach delivers the highest accuracy, whereas the alternative approaches trade accuracy for compositionality. For Markovian branches, the compositional approaches deliver high prediction accuracy. In contrast to intuition and our synthetic experiments, in real programs the two-parameter ARP approach does not always outperform the one-parameter Bernoulli approach.

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System availability in a gamma alternating renewal process

Cited by 30 publications

References 34 publications

Bayesian Highest Posterior Density Intervals for the Availability of a System With a 'Rest-Period' for the Repair Facility

Bayesian Highest Posterior Density Intervals for the Availability of a System With a 'Rest-Period' for the Repair Facility

Outage probability of cooperative relay networks in Nakagami-m fading channels

A statistical approach to branch modeling in static program performance prediction

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