Ensait - Design of Experiment

2008-04-30
duration 2h00

All documents are allowed

Some Guidelines

1. The first quality that is expected from an engineer is the ability to submit clearly her/his findings. All listings, computations, charts and other "printer outputs" can in no way replace a statement of conclusions, coined in an accurate and scientific language.
2. Doing cut and paste with scissors and glue is probably the fastest way to incorporate the right part of all your printer outputs at the right place of your work.
3. Check the printers at the beginning of the evaluation, and print each piece as soon as possible. At exactly the specified time, printers will be disconnected.
4. On any printed document, the FAMILY_NAME/Given_name of the student must appear (especially in the title of the figures).
5. Students are advised that the network traffic of their computer is likely to be recorded during the evaluation.

1 Encoding a Design

Download the files located at: http://www.douillet.info/~douillet/cours/planx_ds08/dat_planx_ds08_1.txt and http://www.douillet.info/~douillet/cours/planx_ds08/dat_planx_ds08_2.txt. Both files are describing a DOE dealing with two results and they differ only by their last column. The first file gives the result Y1 and the second file gives the result Y2. The remaining columns describe the settings (adjustments) of the parameters.

1. How many trials ($jx$) are occurring? How many factors ($ix$)? What is, for each factor, the number of levels? What is the size of $\Omega$? What is the size ($lx$) of the code suitable for an affine model without correlation ?
2. Read one of the files into Scilab and give the matrix $ma$ coding the design.
3. Give some Cartesian representations of the design under study. What can be observed? What do you think of this allocation?
4. Recall what is the measure typically used to determine the quality of a design of experiment. Get, by a random pick, an alternative design. How good is it? Compare with the design described by the given file.

2 Best Boolean Models Without Interaction

1. Use the least squares method and determine the affine model without interactions mx1 that provides the best fit with the experimental results b=Y1.
2. Assess the confidence that can be given to this model. Give the details of computations, draw and print any useful graphic.
3. Evaluate the (isolated) influence of each factor (plot, print and comment any useful graphic).
4. Treat the same questions with the second file and the results b=Y2.

3 Best choice

The former DOE was undertaken to determine what is to be done in order to obtain the greatest Y1 and, at the same time, the lowest Y2. Which conclusions can be drawn from the results ?

4 Asking for a better design

1. Recall the formulae giving the standard error of prevision $\epsilon_{i}$ when using, at point $F_{i}\in\Omega$, the model obtained from the chosen experiments $\omega=\left\{ F_{1}\cdots F_{j}\right\}$.
2. Obtain $F_{k}\in\omega$ realizing the minimal value of $\epsilon_{k}$.
3. Obtain $F_{i}\in\Omega\setminus\omega$ realizing the maximal value of $\epsilon_{i}$.
4. Describe how to combine these results and obtain a better design of the experimental campaign.
5. Launch the routine in planx.sce that tries to obtain a better design. Obtain mA and mS=mA'*mS. Compare the Cartesian maps of mA and ma.