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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

Bayesian estimation is presented for the stationary rate of disappointments, D∞, for two models (with different specifications) of intermittently used systems. The random variables in the system are considered to be independently exponentially distributed. Jeffreys’ prior is assumed for the unknown parameters in the system. Inference about D∞ is being restrained in both models by the complex and non-linear definition of D∞. Monte Carlo simulation is used to derive the posterior distribution of D∞ and subsequently the highest posterior density (HPD) intervals. A numerical example where Bayes estimates and the HPD intervals are determined illustrates these results. This illustration is extended to determine the frequentistical properties of this Bayes procedure, by calculating covering proportions for each of these HPD intervals, assuming fixed values for the parameters.

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Based on a type II censored sample, Bayesian estimation for the scale parameter of the Rayleigh model is carried out under the assumption of the squared error loss function. A generalised hypergeometric distribution with its versatile shape of tails is introduced as a prior, and beta special cases are examined. A simulation study is carried out to investigate the sensitivity of four special cases of this beta prior family in terms of bias, frequentist coverage and mean square error and to determine their effect on robustness. Prediction bounds are derived for the lifetime of unused components using this beta prior family. A data set is used to illustrate and support some of the findings.