Taguchi Robust Design for Product Improvement
Taguchi robust design is used to find the appropriate control factor levels in a design or a process to make the system
less sensitive to variations in uncontrollable noise factors (i.e., to make the system robust). Ideally, a product's performance should be consistent no matter what
the noise values are. In this article, we will use ReliaSoft's
DOE++, a software product for Design of Experiments, to illustrate how to use a Taguchi Robust Design to make a
robust product.
Example
An automobile manufacturer wants to improve the quality of the painted surface of its cars. Quality is measured by the
gloss reading of the surface. The manufacturer wants the painted surface to have a higher gloss reading (i.e., maximize the response)
and to be robust against the environment. Environmental factors, particularly temperature and humidity, are known to affect the
painted surface. Thus, a robust design will be used here. For a detailed background on robust design, please see:
http://reliawiki.org/index.php/Robust_Parameter_Design
The control factors have been identified to be the flow rate of the paint, the pressure in the paint gun, the viscosity of the paint and the cure temperature.
The factors and levels are as follows:
Table 1: Control Factors
Controllable Factors 
Name 
Low Level 
High Level 
A 
Flow Rate 
30 
50 
B 
Pressure 
3 
5 
C 
Viscosity 
10 
15 
D 
Cure Temperature 
120 
160 
Two noise factors will be taken into account: the air temperature (ambient = room temperature) and humidity (ambient = room humidity).
Table 2: Noise Factors
Noise Factors 
Name 
Low Level 
High Level 
A' 
Air Temperature 
15 
30 
B' 
Humidity 
30 
90 
The design matrix for the control factor in a robust design is called the inner array, while the design matrix for the
noise factor is called the outer array. For the inner (control) array, a 2 level fractional factorial design with D=ABC is
used. For the outer (noise) array, a 2 level full factorial design is applied.
Experiment Design
Add a new standard folio in DOE++ by choosing Project
> Add Standard Folio. Follow the next steps to generate the design matrix for the experiment:
Step 1: In the Design Wizard, select Taguchi Robust Design, as shown below. Click Next.
Step 2: For the inner (control) array, select the 2 Level Factorial Design, as shown below. Click Next.
Step 3: For the inner array design, select the 2 Level Fractional Factorial Design and use the settings shown next.
Click the Factor Properties button and, in the Factor Properties window, enter the values from Table 1, as shown next.
Click OK, and then click Next.
Step 4: For the outer (noise) array, use the settings shown next.
Click the Factor Properties button and, in the Factor Properties window, enter the values from Table 2, as shown next. Click OK.
Click Next to view the design summary, then click Finish to create the standard folio. Alternatively, you can skip the design review step by
clicking Finish in the fourth step of the Design Wizard.
The following data sheet shows the final design table and the corresponding gloss readings. The gloss readings are recorded in the "Noise Condition" columns. Since we are using a 2 level factorial design for the
2 noise factors, it has 4 combinations for the noise condition.
Note that the values in the Run Order column are randomly generated. The results you obtain may be different from the
results in the example. You can conduct the experiment according to the run order in the design matrix and record all the
response values. Once the data set is collected, you can use the robust design analysis method to study the data.
Analysis and Results
The simplest analysis method for robust design is by using the socalled signal noise ratio as the response.
For more information on the signal noise ratio, please see: http://reliawiki.org/index.php/Robust_Parameter_Design#Signal_to_Noise_Ratios.
If the purpose of the experiment is to maximize the output and to decrease the variations caused by noise factors, the largerthebetter ratio can be used.
For the ith row of the inner array, it is defined as:
where m is the number of observations of the ith row. For example, for the first row in the data sheet described above, the signal noise ratio is calculated by:
To build a model for the signal noise ratio, follow the steps below.
 In the control panel, select Larger from the Signal/Noise Ratio dropdown list. In the Sort By area, select Standard Order.
 Next, select all the effects in the model by choosing Data > Select Effects. In the Effects window, define the settings as shown next. Click OK.
 In the control panel, click Calculate. Next, select Signal Noise Ratio from the Response dropdown list
in the control panel. The results in the
Analysis sheet will include all the effects in the model.
 To identify the significant effects, click Plot. From the following plot, we can see that effects A and D are significant. So we
will use only those two effects in our final model.
 To create the final model, choose Data > Select Effects. In the Effects window, click Select Significant Effects.
This setting clears all other selections except for effects A and D. Click OK.
 In the control panel, click Calculate to recalculate the results. The final results are shown next:
From the Coefficient column, we can obtain the final model for the signal noise ratio:
From the above equation, we can see that in order to maximize the signal noise ratio, factors A and D should be set to their highest values.
Conclusion
In this article, we used DOE++ to illustrate how to conduct and analyze a Taguchi robust design. First, the significant effects were
identified, and then only the significant effects were used to build the final model. Through the analysis, we found that in
order to maximize the gloss reading of the painted surface, while making it robust to environmental factors that can't be controlled, factors A and D
(flow rate and cure temperature) should be set to their highest levels. Factors C and B (pressure and viscosity) do not have any significant effects on
the final gloss reading, so their values can be set according to process requirements or budget constraints.
