Design of experiments

Contents

Design of experiments

Introduction

Design of experiments (DoE) defines a set of tools dedicated to produce a good set of experiments. These experiments (a set of tuning parameters of an engine for example) are then applied to a system and the output of the system is measured. The set of experiments + the measures are then used to build a statistical model of the system:

we can use a polynomial to modelize the inputs / output relationship
we can use neural networks
we can use Kriging and other technics

Design of experiments is a very widespread tool in the industrial field (in automotive industry, DoE are used to tune a diesel engine, to find the best size of a bar, etc ...).

GSOC 2012

During the GSOC 2012, Maria Christopoulou has chosen this project :

https://scilab.gitlab.io/legacy_wiki/Contributor-DoE-GSOC2012

This work has been mentored by Michael Baudin and Yann Collette.

We chose to update a former project of Yann Collette, adding new features, improved implementations, new unit tests and new help pages. The goal was to provide the same functions as in Matlab. The first version (0.1) of the "scidoe" project was released 6th of August 2012 on ATOMS, with 14 functions:

scidoe_fullfact: A full factorial design
scidoe_ff2n: A full factorial design with 2 factors
scidoe_bbdesign: Box-Behnken design
scidoe_simplelinreg : univariate linear regression
scidoe_multilinreg : multivariate linear regression
scidoe_regress : multiple linear regression
scidoe_regressprint : print regression summary
scidoe_yates: Yates Algorithm
scidoe_ryates: Inverse Yates Algorithm
scidoe_compare : The default comparison function used in the sort-merge.
scidoe_plotcube : Plots a d dimensions cube in [-1,1].
scidoe_sort : A flexible sorting function.
scidoe_sortdesign : Sort the experiments of a design of experiments
scidoe_string : Sort the experiments of a design of experiments

The second version of the "scidoe" toolbox (v0.2) was released 15th of February 2013, with 5 new functions:

scidoe_ccdesign — A Central Composite Design of Experiments
scidoe_fracfact — Fractional Factorial Design
scidoe_lhsdesign — Latin Hypercube Sampling
scidoe_star — Produces a star point design of experiments
scidoe_pdist — Pairwise point distances of a matrix

What do we need in 2013

A list of functions has been identified for a next project:

scidoe_pdist: A C-based implementation is required, see http://forge.scilab.org/index.php/p/scidoe/issues/879/

Optimal Designs

scidoe_optdesign: Optimal design (a-optimal)
scidoe_optdesign: Optimal Design based on a criterion.
mtlb_doptdesign: Matlab compatible D-optimal Design

Supersaturated Designs

scidoe_comp_ssd: Supersaturated Design ('a-optimal').
scidoe_comp_ssd: Supersaturated Design based on a criterion.

Model Building

scidoe_poly_model: Produces a polynomial model
scidoe_model_select: Produces a new polynomial model using forward or backward selection.
scidoe_plot_model: Plots regression line and residuals distribution
scidoe_build_regression_matrix: Regression matrix of a model
scidoe_var_regression_matrix: Regression matrix of the variance of a model
scidoe_lars: Least Angle Regression or Lasso Regression
scidoe_rsquared: R2 Computation

General Functions

scidoe_unnorm_doe_matrix: Adjusts high and low values of a design to specified maximum and minimum values
scidoe_comp_WD2_crit: Wrap-around L2 discrepancy criterion
scidoe_comp_CL2_crit: Centered L2 discrepancy criterion
scidoe_crossvalidate: K-flod cross validation
scidoe_cvplot: Plots cross validation results
scidoe_prbs: A pseudo random binary signal generator
scidoe_merge: Merges two samples
scidoe_diff: Computes the difference of two samples
scidoe_scramble: Permutes a sample
scidoe_standardize: Center and normalize a sample
scidoe_normalize: Normalises a sample

Related Potential Projets

These projects are not DOE, but may be used in the context of DOE.

Several linear regression methods (I am mostly think about the LASSO method - penalized regression).
the bootstrap method to compute the sensitivity of one statistic measure against the data.

Sources of inspiration

There are a lot of implementations available on this topic.

Design of experiments tools are available in Matlab:

These are Scilab examples of implementations which could be adapted, documented and packaged easily:

Some packages by Burkardt in Fortran or C++ :

These are sources of inspirations:

the DAKOTA project
The R-project is also a good source of ideas (for implementation of design of experiments, for codes for LASSO regression). The page

http://cran.r-project.org/web/views/ExperimentalDesign.html

gives an overview of the experimental designs available in R.

There are good C++ implementations of "on the edge" statistical methods in the ROOT framework.

Some R packages provide designs of experiments:

DiceDesign: Designs of Computer Experiments, http://cran.r-project.org/web/packages/DiceDesign/index.html, http://cran.r-project.org/web/packages/DiceDesign/DiceDesign.pdf
FrF2: Fractional Factorial designs with 2-level factors, http://cran.r-project.org/web/packages/FrF2/index.html
DoE.base: Full factorials, orthogonal arrays and base utilities for DoE packages, http://cran.r-project.org/web/packages/DoE.base/index.html
DoE.wrapper: Wrapper package for design of experiments functionality, http://cran.r-project.org/web/packages/DoE.wrapper/index.html

Authors

2012 - 2013 - Michaël Baudin
2011 - DIGITEO - Michaël Baudin
DIGITEO - Yann Collette