Bayesian highest posterior density intervals for the availability of a system with a 'rest-period' for the repair facility

Date
2001
Journal Title
Journal ISSN
Volume Title
Publisher
SAIIE
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.
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.
Description
CITATION: Yadavalli, V. S. S., et al. 2001. Bayesian highest posterior density intervals for the availability of a system with a 'rest-period' for the repair facility. South African Journal of Industrial Engineering, 12(2):17-24, doi:org/10.7166/12-2-345.
The original publication is available at http://sajie.journals.ac.za
Keywords
Bayesian statistical decision theory, One-unit systems, Jeffreys' prior, Gibbs sampling
Citation
Yadavalli, V. S. S., et al. 2001. Bayesian highest posterior density intervals for the availability of a system with a 'rest-period' for the repair facility. South African Journal of Industrial Engineering, 12(2):17-24, doi:org/10.7166/12-2-345