Example of creating a blocked design
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You would like to study the effects of five input variables on the impurity of a vaccine. Each batch only contains enough raw material to manufacture four tubes of the vaccine. To remove the effects due to differences in the four batches of raw material, you decide to perform the experiment in four blocks. To determine the experimental conditions that will be used for each run, you create a 5-factor, 16-run design, in 4 blocks.

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

2    From Number of factors, choose 5.

3    Click Designs.

4    In the box at the top, highlight the line for 1/2 fraction.

5    From Number of blocks, choose 4. Click OK.

6    Click Results. Choose Summary table, alias table, design table, defining relation. Click OK in each dialog box.

Session window output

Fractional Factorial Design

 

 

Factors:   5   Base Design:         5, 16   Resolution with blocks:  III

Runs:     16   Replicates:              1   Fraction:                1/2

Blocks:    4   Center pts (total):      0

 

* NOTE * Blocks are confounded with two-way interactions.

 

 

Design Generators: E = ABCD

 

 

Block Generators: AB, AC

 

 

Defining Relation:  I = ABCDE

 

 

Alias Structure

 

I + ABCDE

 

Blk1 = AB + CDE

Blk2 = AC + BDE

Blk3 = BC + ADE

 

A + BCDE

B + ACDE

C + ABDE

D + ABCE

E + ABCD

AD + BCE

AE + BCD

BD + ACE

BE + ACD

CD + ABE

CE + ABD

DE + ABC

 

 

Design Table (randomized)

 

Run  Block  A  B  C  D  E

  1      1  +  -  -  -  -

  2      1  -  +  +  -  +

  3      1  -  +  +  +  -

  4      1  +  -  -  +  +

  5      3  -  +  -  +  +

  6      3  +  -  +  -  +

  7      3  +  -  +  +  -

  8      3  -  +  -  -  -

  9      4  +  +  +  +  +

 10      4  +  +  +  -  -

 11      4  -  -  -  +  -

 12      4  -  -  -  -  +

 13      2  +  +  -  -  +

 14      2  -  -  +  +  +

 15      2  -  -  +  -  -

 16      2  +  +  -  +  -

Interpreting the results

The first table gives a summary of the design: the total number of factors, runs, blocks, replicates, center points, and resolution. After blocking, this is a resolution III design because blocks are confounded with 2-way interactions.

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.

The first four runs of your experiment would all be performed using raw material from the same batch (Block 1). For the first run in block one, you would set Factor A high, Factor B low, Factor C low, Factor D low, and Factor E low, and measure the impurity of the vaccine.

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