Design of Experiments Guide  • Taguchi Designs • Example of a Taguchi Design
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Example of a Taguchi Design
The following example is an experiment described by Byrne and Taguchi (1986). The objective of the experiment is to find settings of predetermined control factors that simultaneously maximize the adhesiveness (pull-off force) and minimize the assembly costs of nylon tubing.
Here are the signal and noise factors in the Byrne Taguchi Data for this example:
Interfer
Tubing and connector interference. Control factor with 3 levels.
Wall
Wall thickness of the connector. Control factor with 3 levels.
Depth
Insertion depth of the tubing into the connector. Control factor with 3 levels.
Adhesive
Percent of adhesive. Control factor with 3 levels.
Time
Conditioning time. Noise factor with 2 levels.
Temperature
Temperature. Noise factor with 2 levels.
Humidity
Relative humidity. Noise factor with 2 levels.
Create the Design
1.
Select DOE > Classical > Taguchi Arrays.
2.
Select Help > Sample Data Library and open Design Experiment/Byrne Taguchi Factors.jmp.
3.
In the Taguchi Design window, click the Taguchi Design red triangle and select Load Factors.
The factors panel shows the four three-level control (signal) factors and three noise factors.
Response, and Signal and Noise Factors for the Byrne-Taguchi Example
4.
Ensure that L9-Taguchi is selected to give the L9 orthogonal array for the inner design.
5.
Click L8 to give an eight-run outer array design.
6.
Click Continue.
7.
Click Make Table to create the design table shown in Taguchi Design Before Data Entry.
The outer design has three two-level factors. A full factorial in eight runs is generated. However, it is only used as a guide to identify a new set of eight columns in the final JMP data table—one for each combination of levels in the outer design.
Taguchi Design Before Data Entry
Now, suppose the pull-off adhesive force measures are collected and entered into the columns containing missing data, as shown in Complete Taguchi Design Table (Byrne Taguchi Data.jmp). The missing data column names are appended with the letter Y before the levels (+ or –) of the noise factors for that run. For example, Y--- is the column of measurements taken with the three noise factors set at their low levels.
8.
Select Help > Sample Data Library and openDesign Experiment/Byrne Taguchi Data.jmp. Complete Taguchi Design Table (Byrne Taguchi Data.jmp) shows the completed design.
Complete Taguchi Design Table (Byrne Taguchi Data.jmp)
The column named SN Ratio Y is the performance statistic computed with the formula shown below. In this case, it is the “larger-the-better” (LTB) formula, which is –10 times the common logarithm of the average squared reciprocal:
This expression is large when all of the individual y values are large.
Analyze the Data
The data are now ready to analyze. The goal of the analysis is to find factor settings that maximize both the mean and the signal-to-noise ratio.
1.
In the Byrne Taguchi Data.jmp data table, click the green arrow to run the Model script.
Fit Model Window for Taguchi Data
The Fit Model window automatically has the appropriate effects. It includes the main effects of the four signal factors. The two responses are the mean (Mean Y) and signal-to-noise ratio (SN Ratio Y) over the outer array.
2.
Click Run.
The prediction profiler is a quick way to find settings that give the highest signal-to-noise ratio for this experiment.
3.
From the Response Mean Y red triangle menu, select Factor Profiling > Profiler.
The Prediction Profiler
The profile traces (The Prediction Profiler) indicate that different settings of the first three factors would increase SN Ratio Y. Find the optimal settings.
4.
From the Prediction Profiler red triangle menu, select Optimization and Desirability > Desirability Functions.
This adds the row of traces and a column of function settings to the profiler, as shown in Best Factor Settings for Byrne Taguchi Data. The default desirability functions are set to larger-is-better, which is what you want in this experiment. See Profiler in the Profilers book for more details about the prediction profiler.
5.
From the Prediction Profiler red triangle menu, select Optimization and Desirability > Maximize Desirability.
This automatically sets the prediction traces that give the best results according to the desirability functions.
Best Factor Settings for Byrne Taguchi Data
In this example, the settings for Interfer and Wall changed from 1 to 2. (See The Prediction Profiler and Best Factor Settings for Byrne Taguchi Data). The Depth setting changed from 1 to 3. The settings for Adhesive did not change. These new settings increased the signal-to-noise ratio from 24.0253 to 26.9075.

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Help created on 9/19/2017