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

Yadavalli, V.S.S. ; Bekker, A. ; Mostert, P.J. ; Botha, M. (2001)

The original publication is available at http://sajie.journals.ac.za/pub/

Journal Article

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.

In hierdie artikel word die Bayes-beraming van die ewewigstoestandsbeskikbaarheid van 'n stelsel wat afwisselend gebruik word, voorgestel. Daar word veronderstel dat die herstelfasiliteit na voltooiing van elke herstel of 'n rustydperk binnegaan of nie. Die rustydperk sal geneem word met waarskynlikheid p en die waarskynlikheid dat daar nie 'n rustydperk geneem word nie, is (l - p). Jeffrey se a priori-verdeling word vir die onbekende parameters in die stelsel aanvaar. Gibbs-steekproefneming word gebruik om die a posterioriverdeling van die beskikbaarheid en daarna die hoogste a posteriori-digtheidsintervalle (HPD) af te lei. 'n Numeriese voorbeeld illustreer hierdie resultate .

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