Title: About the reliability analysis of complex dynamical systems via fluidification: numerical approach

Authors: Hamid El-Moumen; Nabil El Akchioui; Mohammed Hassani Zerrouk

Addresses: Faculty of Sciences and Technology Al Hoceima, University Abdelmalek Essaadi, Tétouan and Tangier, Larache, Morocco ' Faculty of Sciences and Technology Al Hoceima, University Abdelmalek Essaadi, Tétouan and Tangier, Larache, Morocco ' Faculty of Sciences and Technology Al Hoceima, University Abdelmalek Essaadi, Tétouan and Tangier, Larache, Morocco

Abstract: The fluidification of stochastic discrete event models is a more interesting method to overcome the problem of combinatorial explosion of states. It allows to relax the conditions of stochastic Petri nets to continuous Petri nets, in order to accelerate the slow convergence of stochastic simulations. In our study, we will study an example of a large manufacturing workshop, in order to give limitations of the direct fluidification which does not always lead to the same behaviour between the two models. Secondly, we propose a numerical approach called adaptive that devotes to the adaptation of the maximum speeds of crossing the transitions that is considered as functions depending on the time. Consequently, this approach shows an excellent convergence of the continuous model to the stochastic one whatever the type of network and whatever the initial marking.

Keywords: reliability analysis; Markov model; stationary state; stochastic Petri nets; fluidification; continuous Petri nets; numerical approach.

DOI: 10.1504/IJRS.2023.132945

International Journal of Reliability and Safety, 2023 Vol.17 No.1, pp.1 - 20

Received: 01 Nov 2022
Accepted: 02 Feb 2023
Published online: 20 Aug 2023 *