Example of Create 2-Level Factorial Design (Specify Generators)

A quality engineer plans to conduct a 9-factor experiment. The engineer uses the 1/16th fraction of the design due to resource limitations. The engineer needs all the 2-factor interactions that involve factors A and B to be free from aliasing with other 2-factor interactions. However, the default generators in Minitab alias two-factor interactions involving factors A or B with other 2-factor interactions. Therefore, the engineer specifies different generators by creating a 5-factor design and specifying generators to add 4 more factors.

  1. Choose Stat > DOE > Factorial > Create Factorial Design .
  2. In Type of Design, select 2-level factorial (specify generators).
  3. From Number of factors, select 5.
  4. Click Designs.
  5. Select the Full factorial design.
  6. Click Generators.
  7. In Add factors to the base design by listing their generators (e.g. F=ABC), enter F = ABCD G = ABCE H = ABDE J = CDE.
  8. Click OK twice.
  9. Click Results.
  10. Select Summary table, alias table, design table, defining relation.
  11. Under Content of Alias Table, select Interactions up through order and select 2.
  12. Click OK in each dialog box.

Interpret the results

The first table gives a summary of the design. With 9 factors, a full factorial design has 512 runs. Because resources are limited, the engineer created the 1/16th fraction design with 32 runs.

The resolution of a design that has not been blocked is the length of the shortest word in the defining relation. In this example, the shortest words in the defining relation have four letters so the resolution is IV. In a resolution IV design, some main effects are confounded with 3-way interactions, but not with any 2-way interactions or other main effects. Because 2-way interactions are confounded with each other, the engineer has to evaluate any significant interactions further to define their nature.

The alias table shows that no main effects are aliased with any two-factor interactions and that 21 of the two-factor interactions are aliased with other 2-factor interactions. The design does not alias any of the two-factor interactions that involve factors A and B with any other two-factor interactions.

Note

Minitab randomizes the design by default, so when you create this design, the run order will not match the order in the design table.

Fractional Factorial Design

Design Summary Factors: 9 Base Design: 5, 32 Resolution: IV Runs: 32 Replicates: 1 Fraction: 1/16 Blocks: 1 Center pts (total): 0

Design Generators: F = ABCD, G = ABCE, H = ABDE, J = CDE

Defining Relation: I = ABCDF = ABCEG = ABDEH = CDEJ = DEFG = CEFH = ABEFJ = CDGH = ABDGJ = ABCHJ = ABFGH = CFGJ = DFHJ = EGHJ = ABCDEFGHJ

Alias Structure (up to order 2) I A B C D E F G H J AB AC AD AE AF AG AH AJ BC BD BE BF BG BH BJ CD + EJ + GH CE + DJ + FH CF + EH + GJ CG + DH + FJ CH + DG + EF CJ + DE + FG DF + EG + HJ
Design Table (randomized) Run A B C D E F G H J 1 + - - - - - - - - 2 + + - + - - + - + 3 - - - - - + + + - 4 + - - - + - + + + 5 - - - + - - + - + 6 + - + - + + - + - 7 - + + + + - - - + 8 + - - + + + + - - 9 + + + + + + + + + 10 + + + - + - + - - 11 - + - - + - + + + 12 + + + + - + - - - 13 + - - + - + - + + 14 + + + - - - - + + 15 + + - - + + - - + 16 - + - - - - - - - 17 + - + + + - - - + 18 - + - + + + + - - 19 - - + - - - - + + 20 - + - + - + - + + 21 - + + + - - + + - 22 - - + + + + + + + 23 + - + + - - + + - 24 - - + - + - + - - 25 - - - - + + - - + 26 + + - + + - - + - 27 - + + - - + + - + 28 - + + - + + - + - 29 + + - - - + + + - 30 - - - + + - - + - 31 + - + - - + + - + 32 - - + + - + - - -
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