# An Extension Graphical Duration Models Integrating Conditional Sojourn Time Distributions
##### Volume 13, Number 2, March 2017 - Paper 6 - pp. 153-172
## J. FOUlliaron^{1}, L. Bouillaut^{1}, P. Aknin^{2}, and A. Barros^{3}
^{1}IFSTTAR - 14-20 Bd Newton 77420 Champs-sur-Marnes, France
^{2}IRT-SystemX - 8 Avenue de la Vauve, 91120 Palaiseau, France
^{3}Department of Production and Quality Engineering, 7491, Trondheim, Norway
(Received on November 10, 2016, Revised on February 18 and 28, 2017)
## Abstract:
System degradation modelling is a key problem when performing any type of reliability study. It is used to determine the quality of the computed reliability indicators and prognostic estimates. However, the mathematical models that are commonly used in reliability studies (Markov chains, gamma process. etc.) make certain assumptions that can lead to a loss of information regarding the degradation dynamics. Many studies have shown how Dynamic Bayesian Networks (DBNs) can be relevant in representing complex multicomponent systems and in performing reliability studies. In a previous paper [10], Donat et al. introduced a type of degradation model based on DBNs called a graphical duration model (GDM) for discrete-state systems to represent a wide range of duration models. This paper introduces a new type of degradation model based on the GDM approach that integrates the concept of conditional sojourn time distributions (CSTDs) to improve the degradation modelling. It introduces the possibility of considering many degradation dynamics simultaneously. It allows the degradation modelling to be adapted based on newly available observations of a system to account for changes in dynamics over time. A comparative study of the presented methodology and the GDM approach was conducted using simulated data to demonstrate the advantages of this new approach in performing prognostic computations. Only two coexisting dynamics are considered in the experiments for the sake of simplicity.
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