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Design of Experiments (DOE)

Planning experiments with systematic data collection

Passive data collection leads to a number of problems in statistical modeling. Observed changes in a response variable might be correlated with, but not caused by, observed changes in individual factors (process variables). Simultaneous changes in multiple factors might produce interactions that are difficult to separate into individual effects. Observations might be dependent, while a model of the data considers them to be independent.

Designed experiments address these problems. In a designed experiment, the data-producing process is actively manipulated to improve the quality of information and to eliminate redundant data. A common goal of all experimental designs is to collect data as efficiently as possible while providing sufficient information to accurately estimate model parameters. For example, a simple model of a response y in an experiment with two controlled factors x1 and x2 might look like this:

y=β0+β1x1+β2x2+β3x1x2+ε

Here, ε includes both experimental error and the effects of any uncontrolled factors in the experiment. The terms β1x1 and β2x2 are main effects and the term β3x1x2 is a two-way interaction effect. A designed experiment systematically manipulates x1 and x2 while measuring y, with the objective of accurately estimating β0, β1, β2, and β3. To systematically vary experimental factors, you can assign each factor a discrete set of levels. Each combination of the factor levels is called a treatment. Full factorial designs contain an experiment run for every possible treatment, while fractional factorial designs contain only treatments involving factors and interactions that have the most significant effects. For more information, see Full Factorial Designs and Fractional Factorial Designs.

Functions

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fullFactorialDOEFull factorial design of experiments (DOE) (Since R2024b)
mixtureDOEDesign of experiments (DOE) for mixture experiments (Since R2024b)
optimalDOED-optimal design of experiments (DOE) (Since R2024b)
taguchiDOE Taguchi design of experiments (DOE) (Since R2025a)
fitlmFit linear regression model using design points (Since R2024b)
addrunsAdd runs to D-optimal design (Since R2024b)
ff2nTwo-level full factorial design
fullfactFull factorial design
fracfactFractional factorial design
fracfactgenTwo-level fractional factorial design generators
bbdesignBox-Behnken design
ccdesignCentral composite design
candexchD-optimal design from candidate set using row exchanges
candgenCandidate set generation
cordexchCoordinate-exchange D-optimal design
daugmentD-optimal augmentation
dcovaryD-optimal design with fixed covariates
rowexchRow exchange D-optimal design
rsmdemoInteractive response surface demonstration
lhsdesignLatin hypercube sample
lhsnormLatin hypercube sample from multivariate normal distribution
haltonsetHalton quasirandom point set
qrandstreamQuasirandom number stream
sobolsetSobol quasirandom point set
taguchiTypesValid Taguchi design types (Since R2025a)
snrTaguchi DOE signal-to-noise ratio (SNR) (Since R2025a)
plotsnrPlot signal-to-noise ratio (SNR) for Taguchi design factors (Since R2025a)
interactionplotInteraction plot for grouped data
maineffectsplotMain effects plot for grouped data
multivarichartMultivari chart for grouped data
rsmdemoInteractive response surface demonstration
rstoolInteractive response surface modeling

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