**Plenary Lecture
Applications of Stochastic Processes in Reliability Theory and in Hydrology**

**Professor Mario Lefebvre**

Department of Mathematics and Industrial Engineering

École Polytechnique of Montréal

Canada

E-mail: mario.lefebvre@polymtl.ca

**Abstract: ** In this talk, we will first consider the problem of modeling the wear of a machine. Let X(t) denote the wear of the machine at time t. Because wear should increase with time, we propose a two-dimensional diffusion process (X(t), Y(t)), where Y(t) is the number of items produced by the machine per unit time, defined in such a way that X(t) is indeed an increasing function of t. Based on this model, we will compute the average useful lifetime of the machine. Next, using real data, we will show that a model based on queueing theory is appropriate for the flow of a river when it exceeds a certain threshold. The states will be defined so that the stochastic process is a particular birth-and-death process. Then, making use of this model, we could easily forecast what would happen if, because of climate change, the rate at which important hydrological events occur grows significantly and/or these events increase the river flow for a longer period of time.

**Brief Biography of the Speaker: ** Mario Lefebvre holds a B.Sc. and an M.Sc. in mathematics from the University of Montréal, Canada, and a Ph.D. in mathematics from the University of Cambridge, England. He is a full professor in the Department of Mathematics and Industrial Engineering of the École Polytechnique of Montréal. He has published 13 books, three of them with Springer, and numerous papers on applied probability, stochastic processes and optimal control in international mathematical and engineering journals. A list of his most important publications since 1994 can be found at the following address: http://www.polymtl.ca/recherche/rc/professeurs/details.php?NoProf=178&showtab=PUB