Original Research

Computation of posterior distribution in Bayesian analysis – application in an intermittently used reliability system

V. S.S. Yadavalli, P. J. Mostert, A. Bekker, M. Botha
Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie | Vol 21, No 3 | a231 | DOI: https://doi.org/10.4102/satnt.v21i3.231 | © 2002 V. S.S. Yadavalli, P. J. Mostert, A. Bekker, M. Botha | This work is licensed under CC Attribution 4.0
Submitted: 28 September 2002 | Published: 28 September 2002

About the author(s)

V. S.S. Yadavalli, Departement Bedryfsingenieurswese, Universiteit van Pretoria, South Africa
P. J. Mostert, Departement Statistiek en Aktuariële Wetenskap, Universiteit Stellenbosch, South Africa
A. Bekker, Departement Statistiek, Universiteit van Suid-Afrika, South Africa
M. Botha, Departement Statistiek, Universiteit van Suid-Afrika, South Africa

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Abstract

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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