Risk analysis in dynamic systems: Petri networks - Principles

Despite its appeal, the Markov process analytical approach (see [SE 4 070] "Risk analysis of dynamic systems: a preliminary approach") quickly reaches its limits when the complexity of the industrial systems to be studied or the probabilistic parameters to be assessed increases.

A qualitative leap forward is required, forcing us to abandon the analytical approach in favor of the statistical approach known as Monte-Carlo simulation. This involves drawing numbers at random to animate a model representing the behavior of the system under study, whose simulated evolution over a large number of histories makes it possible to evaluate the probabilistic information – reliability, availability, production availability, etc. – sought.

Once the step of simulation has been taken, the next step is to select an effective behavior model on which to run the simulation. Since the behavior of industrial systems is very similar to that of finite-state automata – discrete and countable states – one of them stood out and was adopted and adapted for this purpose as early as the late 1970s: the Petri net (RdP).

It's the graphical representation of the Petri net that gives it its most interesting features: controlled construction of large, complex models from a very limited number of elements, synthetic visualization of the resulting model, step-by-step manual animation to check behavior, etc.

After laying the foundations of Monte-Carlo simulation, this dossier sets out to show how Petri nets are a formidable simulation tool for tackling virtually any probabilistic problem encountered in the industrial sector.

Following on from the analytical approaches (see [SE 4 070] and