What is a Taguchi design?
overview  

A Taguchi design, or an orthogonal array, is a method of designing experiments that usually requires only a fraction of the full factorial combinations. An orthogonal array means the design is balanced so that factor levels are weighted equally. Because of this, each factor can be evaluated independently of all the other factors, so the effect of one factor does not influence the estimation of another factor.

In robust parameter design, you first choose control factors and their levels and choose an orthogonal array appropriate for these control factors. The control factors comprise the inner array. At the same time, you determine a set of noise factors, along with an experimental design for this set of factors. The noise factors comprise the outer array.

The experiment is carried out by running the complete set of noise factor settings at each combination of control factor settings (at each run). The response data from each run of the noise factors in the outer array are usually aligned in a row, next to the factors settings for that run of the control factors in the inner array. For an example, see Data for Analyze Taguchi Design.

Each column in the orthogonal array represents a specific factor with two or more levels. Each row represents a run; the cell values indicate the factor settings for the run. By default, Minitab's orthogonal array designs use the integers 1, 2, 3... to represent factor levels. If you enter factor levels, the integers 1, 2, 3, ..., will be the coded levels for the design.

The following table displays the L8 (2**7) Taguchi design (orthogonal array). L8 means 8 runs. 2**7 means 7 factors with 2 levels each. If the full factorial design were used, it would have 2**7 = 128 runs. The L8 (2**7) array requires only 8 runs - a fraction of the full factorial design. This array is orthogonal; factor levels are weighted equally across the entire design. The table columns represent the control factors, the table rows represent the runs (combination of factor levels), and each table cell represents the factor level for that run.

L8 (2**7) Taguchi Design

 

A

 

B

C

D

E

F

G

1

1

 

1

1

1

1

1

1

2

1

 

1

1

2

2

2

2

 

 

 

 

 

 

 

 

 

3

1

 

2

2

1

1

2

2

4

1

 

2

2

2

2

1

1

 

 

 

 

 

 

 

 

 

5

2

 

1

2

1

2

1

2

6

2

 

1

2

2

1

2

1

 

 

 

 

 

 

 

 

 

7

2

 

2

1

1

2

2

1

8

2

 

2

1

2

1

1

2

In the above example, levels 1 and 2 occur 4 times in each factor in the array. If you compare the levels in factor A with the levels in factor B, you will see that B1 and B2 each occur 2 times in conjunction with A1 and 2 times in conjunction with A2. Each pair of factors is balanced in this manner, allowing factors to be evaluated independently.

Orthogonal array designs focus primarily on main effects. Some of the arrays offered in Minitab's catalog permit a few selected interactions to be studied. See Estimating selected interactions.

You can also add a signal factor to the Taguchi design in order to create a dynamic response experiment. A dynamic response experiment is used to improve the functional relationship between an input signal and an output response. See Creating a dynamic response experiment.