Overview of Taguchi Designs
The Taguchi method defines two types of factors: control factors and noise factors:
• An inner design constructed over the control factors finds optimum settings.
• An outer design over the noise factors looks at how the response behaves for a wide range of noise conditions.
The experiment is performed on all combinations of the inner and outer design runs. A performance statistic is calculated across the outer runs for each inner run. This becomes the response for a fit across the inner design runs. Table 14.1 lists the recommended performance statistics.
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Goal
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S/N Ratio Formula
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nominal is best
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larger-is-better (maximize)
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smaller-is-better (minimize)
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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.
Figure 14.1 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 Figure 14.2.
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.
Figure 14.2 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 Figure 14.3. 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. Figure 14.3 shows the completed design.
Figure 14.3 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.
Figure 14.4 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.
Figure 14.5 The Prediction Profiler
The profile traces (Figure 14.5) 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 Figure 14.6. The default desirability functions are set to larger-is-better, which is what you want in this experiment. See the Profiler chapter 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.
Figure 14.6 Best Factor Settings for Byrne Taguchi Data
In this example, the settings for Interfer and Wall changed from 1 to 2. (See Figure 14.5 and Figure 14.6). 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.
Taguchi Design Window
The Taguchi design window updates as you work through the design steps. For more information, see “The DOE Workflow: Describe, Specify, Design”. The outlines, separated by buttons that update the outlines, follow the flow in Figure 14.7.
Figure 14.7 Taguchi Design Flow
Responses
Use the Responses outline to specify a response.
Figure 14.8 Responses Outline
The Responses outline contains the following columns:
Response Name
The name of the response. The default response name is Y. To change this name, double-click it and enter the desired name.
Goal, Lower Limit, Upper Limit
Select one of the following Goals: Larger Is Better, Nominal is Best, Smaller is Better, or None. When you create your design, JMP saves a formula for the SN Ratio to the data table that reflects your selected goal.
Importance
Because there is only one response, specifying the Importance is unnecessary because it is set to 1 by default.
Editing the Responses Outline
In the Responses outline, note the following:
• Double-click a response to edit the response name.
• Click the goal to change it.
Factors
Add factors in the Factors outline.
Signal
Specify one or more 2- or 3-level signal factors. Signal factors are system control inputs. These are factors that you can control in production.
Noise
Specify one or more noise factors. Noise factors are variables that are difficult or expensive to control in production. However, you must be able to control noise factors during the experiment.
Remove
Removes the selected factors.
The steps for specifying factors are given in Figure 14.9.
1. Click to add a signal, then select a signal type: 2 Level, or 3 Level.
Or click to add a noise.
2. Double-click to edit the factor name.
3. To change the value of a signal or noise, click and then type the new value.
Figure 14.9 Entering Factors
When you finish adding factors, click Continue.
Choose Inner and Outer Array Designs
Your choice for inner and outer arrays depends on the number and type of factors you have. Figure 14.10 shows the available inner array choices when you have eight signal factors. If you also have noise factors, choices include designs for the outer array. To follow along, enter eight two-level Signal factors and click Continue. Then highlight the design you want and again click Continue. This example uses the L12 design.
Figure 14.10 Selecting a Design for Eight Signal Factors
If you did not specify a noise factor, after you click Continue, a dialog appears that asks you to specify how many times you want to perform each inner array run. Specify two (2) for this example.
Display Coded Design
After you select a design type, the Coded Design (Figure 14.11) is shown below the Factors panel.
Figure 14.11 Coding for Eight Factor L12 Design
The Coded Design shows the pattern of high and low values for the factors in each run.
Make the Design Table
When you click Make Table, a table similar to that shown in Figure 14.12 appears. In the data table, each row represents a run. In the values for the Pattern variable, plus signs designate high levels and minus signs represent low levels.
Figure 14.12 Taguchi Design Table for Eight Factor L12 Design
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