The supply chain of spare parts is the intersection between the supply chain, the after-sales

and the maintenance services. Some authors have tried to define improvement paths in terms

of models to satisfy the performance criteria. In addition, other authors are directed towards

the integration of risk management in the demand forecasting and the stock management

(performance evaluation) through probabilistic models. Among these models, the probabilistic

graphical models are the most used, for example, Bayesian networks and petri nets.

Performance evaluation is done through performance indicators.

To measure the appreciation of the supply of the spare parts stock, this paper focuses on the

performance evaluation of the system by petri nets. This evaluation will be done through

an analytical study. The purpose of this study is to evaluate and analyze the performance of

the system by proposed indicators. First, we present a literature review on Petri nets which

is the essential tool in our modeling. Secondly, we present in the third section the analytical

study of the model based on bath deterministic and stochastic petri networks. Finally, we

present an analysis of the proposed model compared to the existing ones.