Introduction à la planification d'expériences

The following courses will be dedicated to the presentation and use of several types of designs, developed to answer different types of problems.

> Introduction
─ Objectives, technical and economical interest, investigation methodology.

> Constitutive elements
─ The factors : discrete, continuous, ... ; main factors, noise factors,...
─ Treatments, experimental units, ...
─ Observations, special case : quality (reduction of the signal to noise ratio).
─ The expected model, additivity hypotheses of the contributions, state vector, free or constrained effects.

> Searching for an optimal design of experiments
─ The sampling variance/co-variance matrix of the effects.
─ The a priori analysis of an experimentation, optimality criteria.
─ Execution of a designed experimental set (randomisation, error estimation, ...).
─ Reminder on the significance of statistical tests, risks, comparison of variance estimations (Fisher-Snedecor test), of mean estimations (Student test, Tuckey test) ...

> Presentation/use of some types of designs
─ Discrete factor designs : complete blocking, incomplete, latin squares, ...
─ Full factorial designs, 2p designs with interactions.
─ Fractional designs, Taguchi designs, Box designs ..., notion of aliases, resolution ...
─ Response surface designs, quadratic designs : Doehlert, composite, Box-Behnken.
─ Mixture designs.
─ Simplex design for optimum search.

The goal of the design of experiments is to conceive, execute and analyze a set of ex-periments resulting if the best possible compromise between quality of the requested information (precision, independence, ...) and the experimental effort deployed, consi-dering the formulated hypotheses on the studied system’s behavior. Frequently used by the industrial sector for R&D and quality control, the method appears also more and more for research purposes.

─ Isolate / detect the influencing factors of a system or process;
─ Build an optimized experience plan;
─ Conduct an experience plan during the experiments;
─ Use the results of an experiment plan;
─ Interpret the results of an experiment plan;
─ Optimize a system or process from an experience plan.

Other concepts discussed and not deepened (not required): Evaluate the validity and the precision of the experiment plan used; Use Taguchi plans to optimize a system or process.