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

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. 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

A Complex Three-Unit Parallel System With Preparation Time for Repair

“…But this preparation time usually starts immediately after each repair completion, so that the facility becomes available at the earliest. In this paper a threeunit standby redundant system is studied in which the preparation time has been introduced (Sarma [9]; Yadavalli et al [13], [14]). Asymptotic confidence limits for the steady state availability are also obtained.…”