A New Approach For Generating Designs Of Computer Experiments From Area-Interaction Point Processes

Abstract

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.