Reliability analysis has become an integral part of system design and operating. This is especially true for systems performing critical tasks such as mass transportation systems. This explains the numerous advances in the field of reliability modelling. More recently, some studies involving the use of Probabilistic Graphical Models (PGMs), a.k.a. Bayesian Networks (BNs), have been proved relevant to represent complex systems and perform reliability studies. This paper aims to describe a Dynamic PGM (DPGM) designed to model stochastic degradation processes, allowing any kind of state sojourn distributions along with an accurate context description. We meet these objectives using a specific DPGM, namely a Graphical Duration Model (GDM). In this article, we give qualitative and quantitative descriptions of the proposed model and describe how to compute the reliability of the underlying system and some of its classic related metrics. Finally, we illustrate our approach by applying a GDM in order to perform the survival analysis of railway track supposed to be subjected to one context variable.