DOE: Full & Partial (Fractional) Factorial Designs

Full Factorial Design
Full Factorial Design

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Interaction: when the effect of one factor on the outcome depends on the level of another factor.

Confounding is when we cannot differentiate between two factors

Resolution tells us the confounding we will see between factors.

Full Factorial Design

In a full factorial experiment at least one trial for all possible combinations of factors and levels. This exhaustive approach makes it impossible for any interactions to be missed as all factor interactions are accounted for.

  • Full factorial designs include all possible combinations of every level of every factor
  • Full factorial designs can require a lot of trials, which can take a lot of time
  • Full factorial designs can require a lot of trials, which can cost a lot of money
  • Requires at least one observation for every combination of factors and levels.
  • Allows for the measurement of all possible interactions.
  • Expensive and time consuming.

How Many trials in a Full Factorial Design?

Found by taking the number of levels as the base and the number of factors as the exponent:

Ex1. a design of 4 factors with 3 levels each would be: 3 x 3 x 3 x 3 = 3^4 = 81

Ex 2. 4 factors (A=3, B = 2, C=5, D= 4 levels).   3 x 2 x 5 x 4 = 120 observations.


Analyzing Full Factorial Designs


Partial or Fractional Factorial Design

One of the big drawbacks of fractional factorial design is the potential to miss important interactions.

Fractional factorials (like Latin and Graeco-Latin Squares) will not allow analysis of interactions. The interactions are confounded with other effects. (Also add to fractional factorial analysis article.)

Need partial factorial calculation.

degrees of freedom (n-1 degrees of freedom., where n is the # of levels.)

Try writing an example case study on a recipe : this many courses with this many toppings.

Moving from Full Factorial to Partial Factorial

  • There will be fewer trials
  • There will be confounding
  • Resolution will decrease

Types of Fractional Factorial Design

  • Taguchi: Uses orthogonal (balanced) arrays, but are types of fractional factorial designs.
  • Latin Squares: is a type of fractional factorial design


Analyzing Fractional Factorial Designs

  • Analyze fractional factorial designs using
    • Average effect of factors
    • Optimum score and performance
    • Sum of squares scree plot

Also see Design of Experiments

Full Factorial Designs

Linear & Quadratic Mathematical Models

Balanced & Orthogonal Designs

Fit, Diagnose Model and Center Points

Fractional Factorial Experiments


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