BAYESIAN HIGHEST POSTERIOR DENSITY INTERVALS FOR THE AVAILABILITY OF A SYSTEM WITH A 'REST-PERIOD' FOR THE REPAIR FACILITY

• V.S.S. Yadavalli Department of Statistics, University of South Africa
• A. Bekker Department of Statistics, University of South Africa
• P.J. Mostert Department of Statistics and Actuarial Science, Stellenbosch University
• M. Botha Department of Statistics, University of South Africa

DOI:

https://doi.org/10.7166/12-2-345

Abstract

ENGLISH ABSTRACT: 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.

AFRIKAANSE OPSOMMING: In .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 .