Reliability analysis has become an integral part of system design and operating. This is especially true for systems performing critical tasks. Moreover, recent works in reliability involving the use of probabilistic graphical models, also known as Bayesian networks, have been proved relevant. This paper describes a specific dynamic graphical model, named graphical duration model (GDM), to represent complex stochastic degradation processes with any kind of state sojourn time distributions. We give qualitative and quantitative descriptions of the proposed model and detail a simple algorithm to estimate the system reliability. Finally, we illustrate our approach with a three-states system subjected to one context variable and non-exponential sojourn time distributions.