Interpret the key results for Create 2-Level Factorial Design (Specify Generators)

Complete the following steps to verify that you created the intended design. Key outputs include the design summary and the alias structure.

Step 1: Examine the design properties

Use the summary of the design to examine the key design properties. Most properties of the design will match the selections that you made for the base design.

However, if the design includes folds or blocks, the final design resolution can differ from the resolution of the base design. Folds can increase the resolution of the design. Blocks can decrease the resolution of the design.

If the design includes any of the following elements, the total number of runs differs from the number of runs in the base design:
  • Replicates or folds: Each replicate or fold adds runs equal to the number of corner points in the base design.
  • Center points: Each center point adds 1 run to the total number of runs in the base design.
  • Blocks and center points: Each block contains the same number of center points, so if you have 4 blocks with 4 center points per block, you add 16 points to the base design.
  • Text factors and center points: Minitab adds center points at each level of a text factor in a 2-level design. Thus, each text factor doubles the number of center points in the design.
For this design, all of the design characteristics are the same as selections made during the creation of the design.
Design Summary Factors: 6 Base Design: 6, 16 Resolution: IV Runs: 16 Replicates: 1 Fraction: 1/4 Blocks: 1 Center pts (total): 0
This design has 4 blocks. Each block contains 4 runs. The resolution is different from the unblocked design because blocks are confounded with two-way interactions.
Design Summary Factors: 6 Base Design: 6, 16 Resolution with blocks: III Runs: 16 Replicates: 1 Fraction: 1/4 Blocks: 4 Center pts (total): 0 * NOTE * Blocks are confounded with two-way interactions.
This design has 4 blocks and 2 replicates. Each block contains 8 runs. Because the blocks can be partly generated from the replicates, the design resolution with blocks is IV. Because the design has 2 replicates, two runs for each factor level combination in the base design are in the final design. Thus, the number of runs is twice the number of runs for the base design.
Design Summary Factors: 6 Base Design: 6, 16 Resolution with blocks: IV Runs: 32 Replicates: 2 Fraction: 1/4 Blocks: 4 Center pts (total): 0
This design includes 2 center points. Because the design has all numeric factors, a total of 2 center points are included in the design.
Design Summary Factors: 6 Base Design: 6, 16 Resolution: IV Runs: 18 Replicates: 1 Fraction: 1/4 Blocks: 1 Center pts (total): 2
This design includes 2 center points but because one of the factors is a text factor, Minitab adds a total of 4 center points to the design. When the design includes a text factor, Minitab adds center points at the low level and at the high level of the text factor with the numeric factors set at their mid-point levels.
Design Summary Factors: 6 Base Design: 6, 16 Resolution: IV Runs: 20 Replicates: 1 Fraction: 1/4 Blocks: 1 Center pts (total): 4

Step 2: Examine the alias structure

The alias structure describes the confounding pattern that occurs in a design. Terms that are confounded are also said to be aliased.

Aliasing, also known as confounding, occurs in fractional factorial designs because the design does not include all of the combinations of factor levels. For example, if factor A is confounded with the 3-way interaction BCD, then the estimated effect for A is the sum of the effect of A and the effect of BCD. You cannot determine whether a significant effect is because of A, because of BCD, or because of a combination of both. When you analyze the design in Minitab, you can include confounded terms in the model. Minitab removes the terms that are listed later in the terms list. However, certain terms are always fit first. For example, if you include blocks in the model, Minitab retains the block terms and removes any terms that are aliased with blocks.

You can use the alias structure to verify that important terms are not aliased with each other. If the alias structure is unacceptable, consider taking one of the following actions:
  • Create the design again, but enter the factors into Minitab in a different order.
  • Use a larger fraction of the design.
  • Fold the design.
  • Specify different design generators.

To see how to determine the alias structure, go to All statistics for Create 2-Level Factorial Design (Specify Generators) and click "Defining relation".

Key results: Alias structure

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.

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 - - + + - + - - -

Step 3: Collect experimental data

When you create your design, Minitab stores the design information in the worksheet. Minitab includes columns for standard order (StdOrder), run order (RunOrder), center points (CenterPt), blocks (Blocks), and a column for each factor. For more information, go to How Minitab stores design information in the worksheet.

You can use the worksheet to guide your experiment because it lists the factor settings for each experimental run and, if you randomized the design, the order in which you should perform the runs. If you didn't randomize the design, you can do that with Modify Design. Before you perform the experiment, you should name one or more columns in the worksheet for the response data. After you enter the response data, you can use Analyze Factorial Design to analyze the design.

For example, this worksheet shows a design with 2 factors, Temperature and Time. The first row in the worksheet contains the first experimental run, where temperature is set to 100 and time is set to 5. After this run is performed, the measurement for strength can be entered into the worksheet.

C1 C2 C3 C4 C5 C6 C7
StdOrder RunOrder CenterPt Blocks Temperature Time Strength
6 1 1 1 100 5  
2 2 1 1 200 10  
9 3 0 1 150 7.5  
5 4 1 1 200 10  
1 5 1 1 200 5  

Before you perform the experiment, there are several activities you can do to help ensure that your experiment is successful.
  • Document procedures for the experiment and train the individuals who are involved in the experiment.
  • Validate the measurement system to ensure that it is accurate.
  • Review the factor level combinations to make sure they are all feasible.
  • Perform trial runs to check materials, equipment, and procedures.

For more information, go to Checklist of pre-experiment activities.

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