Author(s)

J. Augutis, I. Zutautaite, R. Alzbutas & E. Uspuras

Abstract

In this paper the iterative estimation of reliability parameters using the Bayesian approach is considered. The conjugate pairs of the likelihood function and parameters prior distribution are applied in the estimation of reliability parameters. Using the developed method and a numerical example it was shown how to model and estimate the reliability parameters related to the ageing process. 1 Introduction One of the most complicated problems in reliability modelling, when the information (e.g. failure events observations) related to these parameters are available, is the estimation of time dependent random parameters (e.g. failure rates). The reliability models with time dependent parameters usually are related with an ageing process. In order to estimate such parameters the iterative process based on the Bayesian approach was used. Reliability estimates when new evidence becomes available could be updated by using Bayes theorem: ∫ ⋅ ⋅ = θ θ θ θ θ θ d E L p E L p E p ) | ( ) ( ) | ( ) ( ) | ( ; (1) where ) | ( E p θ – the posterior distribution of parameter θ in light of evidence E ; ) (θ p – the prior distribution of parameter θ ; ) | ( θ E L – the likelihood

Keywords