Download Taguchi Designs

Taguchi Designs
The final design we’re going to talk about this semester is the Taguchi Design.
Introduction
One important goal of quality improvement is to design quality into every product and into the processes that build
such products. In the early 1980’s, Genechi Taguchi introduced his approach to using experimental design for…
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designing products or processes so that they are robust to environmental conditions,
designing and developing products so that they are robust to component variation, and
minimizing variation around a target value.
The philosophy that Taguchi recommends is sound and should be included in the quality improvement process.
However, he has advocated some approaches to the design of experiments that are unnecessarily complicated,
inefficient, and at times ineffective.
Example: Taguchi sought to understand the influence that parameters had on variation, not just on the mean. For
example, consider an experiment which varied two factors on a box-filling machine: Surface Area (A) and Geometry
(B). The goal was to achieve a filling rate that was closest to 14 g/s. Suppose that three difference particle sizes were
also considered, and the following data were obtained.
Particle Size 1
Particle Size 2
Particle Size 3
B
B
B
A
-1
+1
A
-1
+1
A
-1
+1
-1
13.7
13.7
-1
14.9
14.2
-1
17.4
14.4
+1
14.0
11.9
+1
16.0
11.8
+1
12.0
11.7
Source: Response Surface Methodology—Process and Product Optimization Using Designed Experiments by Raymond
H. Myers and Douglas C. Montgomery.
Questions:
1. Which combination of Surface Area (A) and Geometry (B) is most insensitive to particle size? Is this the
“best” combination?
2. Which combination of Surface Area (A) and Geometry (B) yields a mean response closest to the target of 14
g/s? Is this what you feel is the “best”?
3. Which combination of Surface Area (A) and Geometry (B) would you recommend? Explain.
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Signal to Noise Ratios (SNR)
Taguchi also suggested using a summary statistic called the signal to noise ratio which would take into account
information about both the mean and the variance. There are many different SNR, however Taguchi primarily
suggested the following, which depend on the goal of the experiment.
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Goal: To minimize the response.
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Goal: To maximize the response.
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Goal: To achieve a particular target value.
Example: Calculating Signal to Noise Ratios
Consider a study to investigate the snap action contact of a window lift switch. The response is the number of cycles
before failure, and there are four factors being considered in this experiment:
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Factor A: Contact Geometry at two levels (Standard and Long)
Factor B: Base Support at two levels (Full, 0.25mm clearance)
Factor C: Material Thickness at two levels (0.012in and 0.011 in)
Factor D: Grain Direction at two levels (with grain and across grain)
Suppose the goal is to maximize the number of cycles.
The average signal to noise ratio is given for each factor level.
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Next, suppose there is a specific target in mind, such as 125,000 cycles.
The average signal to noise ratio is given for each factor level.
Creating a Taguchi Design in Minitab
A Taguchi design can be obtained by choosing Stat  DOE  Taguchi  Create Taguchi Design… Each of the factors
under consideration have two levels, so choose 2-Level Design and specify the number of factors to 4 as shown
below.
If you click on the Display Available Designs… you’ll be able to see all the various designs which can be conducted.
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The number following the “L” indicates the number of runs in the design. The numbers in the table indicate the
minimum and maximum number of available factors for each design. For example, an L12 design can have from 2 to
11 factors with two levels each.
Click OK to return to the Taguchi Design window, and click the Designs… tab to specify the design. In this window,
click L8 under Runs. This design allows you to investigate four factors each at two levels with the fewest number of
runs.
Next, click on the Factor… tab to label each factor and each factor.
Note: Taguchi’s default is to NOT consider interaction terms. However, an initial analysis of factors should include
interactions.
Select To allow estimation of selected interactions and click on Interactions… As previously mentioned, Factor A
(Contact Geometry) is thought to have the largest impact on the window switch being studied. Therefore, in the
Taguchi Design Interactions Box, place AB, AC, and AD in as selected terms.
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Click OK twice, and the design will be placed in a new worksheet. There are enough resources for three runs at each
factor level combination being considered. Therefore, label three columns to the right of the design as Rep1, Rep2,
and Rep3 as shown below.
Analyzing a Taguchi Design in Minitab
Once you’ve entered the three replicates into Minitab, you should have the following worksheet.
To analyze the data choose Stat  DOE  Taguchi  Analyze Taguchi Design… Place each of the replicates in the
Response Data are in box.
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Similar to previous analyses, there are several options available which are summarized below.
In this window, you can specify various plots to investigate the effects of each
factor and possible interactions between factors. In our experiment, there is
specific interest in the interactions with Factor A, so make sure that AB, AC, and AD
are specified as shown in the window below.
The goal in this experiment is to maximize the fatigue life of this switch, so specify
Large is better under the Signal to Noise Ratio.
You’ll want to check the Standard deviations box in this window which will give you
information about the ln(standard deviations).
Once these options have been specified, click OK.
Note: The analysis of a Taguchi experiment typically involves analyzing three components – the mean, the variance or
standard deviation, and the signal-to-noise ratio. The signal-to-noise ratio can be thought of as an adjusted response
variable. If the goal is to maximize the response, then such a ratio should be large.
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Minitab places various tables in the session window which are given below.
In each table, Delta represents the absolute difference between the first and second level of each factor. The
magnitudes of these differences are ranked in the bottom row of each table. These tables DO NOT take into
consideration any interaction that may be present. The interaction plots and main effect plots for the Means are
shown below:
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We would like to maximize the response, thus larger means are better. It is apparent that interaction is present
between these factors. The interaction between Geometry and Support and the interaction between Geometry and
Grain appear to be significant. Furthermore, the Material Thickness appears to impact the fatigue life of these
switches the most, not Geometry as initially thought.
The following plots consider the ln(Standard Deviations) in the response. Here, we want to minimize variability, so
small values are better.
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From the interaction plots, it appears that Geometry and Thickness may exhibit some interaction. If this interaction
is ignored, then Contact Geometry = Long, Support = Full, Thickness = 0.012in, and Grain = Cross appear to be best.
Again, Thickness appears to influence the variability in the response the most.
The Signal-to-noise ratios allow us to consider the effect on the mean and variance simultaneously. We want the
Signal-to-noise ratios to be large.
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Final Comments:
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We discovered that several interactions were important to the fatigue life of these switches. Realize, if we
would have used the default Taguchi design in Minitab, then such interactions would have been missed!
It appears that Material Thickness has the most significant impact on the fatigue life, not Contact Geometry
as initially thought.
Even at the best experimental setting, the number of cycles is roughly 50,000 short of the goal of 125,000.
Most often you can save time, money and resources using a design other than a Taguchi Design.
Example: The accuracy of an online sensor for measuring solids is thought to be a function of the following variables:
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Sight glass: Type A, Type B
Orifice type: 22 degrees, 25 degrees
Installation torque: 120 lbs., 150 lbs.
Line location: Vertical, 100 Off vertical
The data can be found in the file Taguchi_Sensor.mpj on the course website.
Questions:
4. Does sight glass appear to have a significant interaction with the other three variables?
5. What is the best process condition to minimize the response?
6. What is the best process condition to minimize the SNR?
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