# Example 9 - Taguchi Robust Design

[Download DOE++ Example File (*.rdoe)]

## Background

Taguchi robust design is used to find the appropriate control factor levels in the design to make the system less sensitive to variations in uncontrollable noise factors (i.e., to make the system robust).

Consider an experiment that seeks to determine a method to assemble an elastomeric connector to a nylon tube while delivering the requisite pull-off performance suitable for an automotive engineering application.*

The primary design objective is to maximize the pull-off force, while secondary considerations are to minimize assembly effort and reduce the cost of the connector and assembly.

The controllable and noise factors are:

For the inner (control) array, Taguchi OA L9 (3^4) is used. For the outer (noise) array, a two level full factorial design is applied.

## Experiment Design

The experimenters use DOE++ to design a Taguchi robust design. The settings and factor properties used for the inner (control) array are shown next.

The settings and factor properties used for the outer (noise) array are shown next.

The design matrix and the response data are given in the "Taguchi Robust Design Example" Folio.

## Analysis Part I

Step 1: After performing the experiment according to the design and recording the results, the experimenters enter the data set into the Standard Folio, as shown next.

The data set as entered in the DOE++ Folio.

Step 2: The larger-the-better ratio is chosen for the analysis.

Step 3: The data set is analyzed with the default risk (significance) level of 0.1, using individual terms, for each of the three responses (Y Mean, Y Std and Signal Noise Ratio).

Step 4: The Main Effect plot is created for the Y Mean (pull-off force) response using the Data Means setting, as shown next.

Step 5: The Main Effect plot is created for the Y Std response using the Data Means setting, as shown next.

Step 6: The Main Effect plot is created for the Signal Noise Ratio response using the Data Means setting, as shown next.

## Conclusions

Since the goal is to maximize both signal-to-noise ratio and the pull-off force, some trade-off may need to be made in the selecting of factor settings. Examining the main effect plots for Y Mean and Signal Noise Ratio shows that the medium level for A is clearly the best choice for maximizing signal-to-noise ratio (robustness) and the average pull-off force (Y Mean). It also has a relatively low standard deviation value. For the wall thickness, B, the medium and high level are slightly better than the low level for signal-to-noise ratio; however, the medium is preferred to high level in order to maximize the average pull-off force. From the main effect plot, the better settings for factors C and D can also be determined. In the final analysis, the best settings to maximize signal-to-noise ratio are A (medium), B (medium), C (deep) and D (low), based on the experimental results for maximizing pull-off force.

* G. Taguchi, "The Taguchi Approach to Parameter Design," Quality Progress, Dec. 1987, pp. 19-26.