Résumé:
Many engineers and technicians rely on experimental designs to improve their products or
production processes based on experience. However, traditional strategies for conducting experiments
often prove to be expensive, inefficient, and yield limited exploitable results. To
address these challenges, the planning of experiments has become essential.
Experimental designs offer a structured approach to conducting tests in scientific research
and industrial studies. They find applications in various disciplines and industries when investigating
the relationship between a quantity of interest (y) and controllable variables (x
).
The objective is to establish mathematical models that relate these quantities of interest to the
variables.
This thesis introduces new digital experimental designs based on the theory of stochastic
processes, specifically area interaction point processes, also known as object processes. These
designs leverage both the distribution of points within the experimental region and specific
characteristics associated with those points. The designs are obtained using a Monte Carlo
Markov chain method (MCMC), and a thorough investigation of the Markov chain’s convergence
has been conducted. Furthermore, a comparative analysis between our approach and other
existing computer designs has been performed.
Keywords: Experimental Designs, Numerical Experimental Designs, Point Processes,
Area-Interaction Point Processes, Voronoi Tessellation, Markov Chain Monte Carlo (MCMC),
Metropolis-Hastings Algorithm.
