Example of creating a fractional factorial design
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Suppose you want to study the influence six input variables (factors) have on shrinkage of a plastic fastener of a toy. The goal of your pilot study is to screen these six factors to determine which ones have the greatest influence. Because you assume that three-way and four-way interactions are negligible, a resolution IV factorial design is appropriate. You decide to generate a 16 run fractional factorial design from Minitab's catalog.

1    Choose Stat > DOE > Factorial > Create Factorial Design.

2    From Number of factors, choose 6.

3    Click Designs.

4    In the box at the top, highlight the line for 1/4 fraction. Click OK.

5    Click Results. Choose Summary table, alias table, design table, defining relation.

6    Click OK in each dialog box.

Session window output

Fractional Factorial Design

 

 

Factors:   6   Base Design:         6, 16   Resolution:   IV

Runs:     16   Replicates:              1   Fraction:    1/4

Blocks:    1   Center pts (total):      0

 

 

Design Generators: E = ABC, F = BCD

 

 

Defining Relation:  I = ABCE = BCDF = ADEF

 

 

Alias Structure

 

I + ABCE + ADEF + BCDF

 

A + BCE + DEF + ABCDF

B + ACE + CDF + ABDEF

C + ABE + BDF + ACDEF

D + AEF + BCF + ABCDE

E + ABC + ADF + BCDEF

F + ADE + BCD + ABCEF

AB + CE + ACDF + BDEF

AC + BE + ABDF + CDEF

AD + EF + ABCF + BCDE

AE + BC + DF + ABCDEF

AF + DE + ABCD + BCEF

BD + CF + ABEF + ACDE

BF + CD + ABDE + ACEF

ABD + ACF + BEF + CDE

ABF + ACD + BDE + CEF

 

 

Design Table (randomized)

 

Run  A  B  C  D  E  F

  1  +  -  -  -  +  -

  2  -  +  +  -  -  -

  3  -  -  -  -  -  -

  4  -  -  -  +  -  +

  5  -  -  +  -  +  +

  6  +  +  -  +  -  -

  7  -  +  +  +  -  +

  8  +  -  +  +  -  -

  9  +  +  +  +  +  +

 10  -  -  +  +  +  -

 11  +  -  -  +  +  +

 12  +  +  +  -  +  -

 13  +  -  +  -  -  +

 14  +  +  -  -  -  +

 15  -  +  -  +  +  -

 16  -  +  -  -  +  +

Interpreting the results

The first table gives a summary of the design: the total number of factors, runs, blocks, replicates, and center points.

With 6 factors, a full factorial design would have 26 or 64 runs. Because resources are limited, you chose a 1/4 fraction with 16 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, all words in the defining relation have four letters so the resolution is IV. In a resolution IV design, some main effects are confounded with three-way interactions, but not with any 2-way interactions or other main effects. Because 2-way interactions are confounded with each other, any significant interactions will need to be evaluated further to define their nature.

Because you chose to display the summary and design tables, Minitab shows the experimental conditions or settings for each of the factors for the design points. When you perform the experiment, use the order that is shown to determine the conditions for each run. For example, in the first run of your experiment, you would set Factor A high, Factor B low, Factor C low, Factor D low, Factor E high, and Factor F low, and measure the shrinkage of the plastic fastener.

Minitab randomizes the design by default, so if you try to replicate this example your run order may not match the order shown.