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The 3k Factorial Design
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Notation
Factor levels are sometime denoted 1, 2, 3
Qualitative or categorical factors are low, medium, high
Individual runs are defined by k digits combinations, such as 000 to denote the test combination in a three-variable design where all three factors are at the low level
-1, 0, +1 is the orthogonal coding for quantitative factors
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Note that by convention,
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9.2 Confounding
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An example of this method:
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An Example
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41. Factors at Two and Four Levels
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44. Nonregular Fractional Factorial Designs
Section 9.5, page 415
In regular designs, all of the elements of the alias matrix are either 0, +1 or -1.
In nonregular designs, there will be nonzero elements of the alias matrix that are not either +1 or -1.
This means that terms that are aliased are not “completely confounded”
The Plackett-Burman designs of the previous chapter are nonregular designs
Nonregular fractional factorials have some good applications in factor screening experiments
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Jones and Montgomery (2011) present 16-run two-level nonregular designs for 6 – 8 factors in 16 runs – they call these “no-confounding” designs
These are reasonable alternatives to the regular resolution IV designs
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The recommended designs do not have any complete confounding involving main effects and two-factor interactions or of two-factor interactions with each other
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55. Nonregular Designs in 9-14 Factors in 16 Runs
Section text
These are alternatives to the regular resolution III fractions
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56. Other designs are shown in the text
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57. Use of an Optimal Design Tool
An optimal design tool can be used to create a custom design for a specific situation
This requires:
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59. Examples of Optimal Designs
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63. Alias Structure for the Design in Table 9.37
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