Experiment design, reliability, uncertainty

Presentation

• Linear covariance models, multiple interactions, mixed models.
• Principle of randomized experiments and classical experiments design
• Factorial, fractional designs
• Examples with the SAS or JMP software 
• Numerical design of experiments (quasi-Monte Carlo sequences, Latin Hypersquares)
• Response surfaces and metamodels (polynomials, kriging, links to statistical learning).
• Analysis of uncertainties for numerical simulations: propagation of uncertainties, reliability methods (FORM/SORM, order statistics ..) , sensitivity analysis
• Industrial applications: design with uncertainties, risk analysis.

Objectives

At the end of this module, the student will have understood and be able to explain:

• the main methods of experimental design,
• the analysis of uncertainties,
• the reliability methods,
• the probability estimation of  of rare events.

The student will be able to:

• plan an experiment in the framework of a linear model,
• built a response surface
• perform a sensitivity analysis for the treatment of uncertainties in numerical simulation.

Needed prerequisite

Elements of statistical modelling [I4MMMS71]
Softwares and methods of statistical exploratory data analysis [4MMSP81]

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...