Unit 1 (part 3): The Taguchi Method: Which Input Has the Greatest
Effect?
Concepts:
The Taguchi method allows us to predict our ideal combination of
independent variables (or input variables) to give the best result on a
dependent variable. It can also be used to find which input variable has the
greatest effect.
Objectives:
Students should explore the use of the Taguchi method to find which
independent variable has the greatest effect on the dependent variable.
Equipment/Materials:
 Computers with Internet access and Microsoft Excel
Useful websites:
Many Excel tutorials are online: for help with a specific Excel command or
formula, it’s usually helpful to type the term into www.Google.com for
quick, efficient tips.
One good introductory Excel tutorial on Youtube can be seen at:
http://www.youtube.com/watch?v=FNPNS6MT1Kk&feature=related
(others are also available: go to www.youtube.com and search for
“introduction to excel”)
The Michigan Chemical Process Dynamics and Controls Open Text Book:
http://controls.engin.umich.edu/wiki/index.php/Design_of_experiments_via
_taguchi_methods:_orthogonal_arrays
Wikipedia: Genichi Taguchi: http://en.wikipedia.org/wiki/Genichi_Taguchi
A more complex site with many array choices:
http://www2.research.att.com/~njas/oadir/index.html
© 2010, Ohio Northern University: Dr. Debra Gallagher, Dr. Robert Verb, Dr. Ken Reid and Ben McPheron
Taguchi’s Robust Design Method (see “Extend”)
http://www.mne.psu.edu/simpson/courses/ie466/ie466.robust.handout.pdf)
Activity Sheets:
Taguchi Exercise: Input with the Greatest Effect
Material:
Computers with Internet access
Computers with Microsoft Excel
Engage:
Review the concepts of experiments, dependent and independent variables
and defining the number of levels of each variable. Review the answers
from the previous class to the following questions:
1. Why would it be important to identify the variable that causes the
most change in the dependent variable we’re studying?
2. Can you see any information in the ice cream example from the last
lesson that gives a hint about which variable causes the biggest
change?
If the students in class have little or no experience in using Microsoft Excel,
you may want to review the video tutorials in “Useful websites” in class, and
have the students work through the tutorials along with the video.
Explore:
1. Review the ‘ice cream experiments’ from the teacher background with
students in the classroom. Lead the students through the final values
of signal-to-noise ratios and identification of the variable with the
greatest effect.
2. During the ice cream example, emphasize that the Taguchi method
was also useful to reduce the number of experiments we had to do.
Had we done full-factorial experiments, this procedure would also
work, but there would be many more calculations to perform.
© 2010, Ohio Northern University: Dr. Debra Gallagher, Dr. Robert Verb, Dr. Ken Reid and Ben McPheron
3. Have students work through the questions on the “Taguchi Exercise”
worksheet.
4. Working in pairs, ask each student team discuss signal to noise ratio.
For instance, what ‘noise’ could be present in a tank with algae?
(Examples: a breeze could be blowing on a tank, contaminants could
be introduced while testing, etc.). As the list grows, discuss which
variables could be controlled and tested (i.e., airstone in the tank vs.
no airstone in the tank) and those that cannot be controlled, and can
only be considered noise (unexpected contaminants).
Explain:
1. Discuss the results of the ice cream experiment.
2. Review the solution of the Taguchi Exercise: Input with the Greatest
Effect worksheet.
Extend:
The analysis done here is sometimes represented graphically, with a
series of plots showing the values of SN for each factor. An example of this
analysis can be seen in section 32.4.2 of Taguchi’s Robust Design Method
(available at
http://www.mne.psu.edu/simpson/courses/ie466/ie466.robust.handout.pdf)
Evaluate:
1. Use student solutions to the Taguchi Experiment Exercise.
© 2010, Ohio Northern University: Dr. Debra Gallagher, Dr. Robert Verb, Dr. Ken Reid and Ben McPheron
Teacher Notes:
Design of experiments (DoE) or experimental design is very commonly used to figure
out how a number of variables work together toward some result. We have seen that we
can minimize the number of experiments we need to perform, and we can use the results
to predict the best combination of variables.
The data collected while using the Taguchi Method can be used to find the input
variable in which a change results in the biggest change in the final, dependent variable.
The basic process is:
-
-
Collect data using the Taguchi method
o You will need to collect 3 or more results from each experimental setup
(in other words, run each experiment 3 or more times).
Follow the instructions to set up an Excel spreadsheet.
Types of experimentation:
(Review) - Running the Experiments:
First, determine how you will measure the dependent variable. In most cases, you want a
maximum or minimum number: which experiment grew the most algae, which
experiment resulted in the lowest cost. For our ice cream example, you may have to
assign the deliciousness of the ice cream cone a scale of 1 – 100.
Use the input variable values indicated in the Taguchi chart to run each experiment. For
example, on the above ice cream experiment, you would eat:
 Vanilla soft-serve on a sugar cone, with dip,
 Chocolate, regular ice cream on a sugar cone with sprinkles,
 Vanilla, regular ice cream on a sugar cone (plain),
 etc.
… and record the deliciousness of the ice cream cone in each of the 9 cases.
To find the input variable with the greatest effect, we will need to do multiple tests of
each case – 3 or more is recommended.
Analyzing the results:
Let’s assume we made 3 ice cream cones testing each of our test conditions, and collected
the following data (and averaged all of the experiments for each setup):
The average is shown. The Excel formula for calculating the average is:
=average( )
© 2010, Ohio Northern University: Dr. Debra Gallagher, Dr. Robert Verb, Dr. Ken Reid and Ben McPheron
After typing =average( block the group of 3 numbers using the mouse ) (in our first
row, select 88, 86 and 86).
L9 (filled in, with random values in blank boxes) Each level is named 1, 2 or 3 (for the next table)
Exp
Cone
1 Sugar 1
Ice cream
Topping
Texture
Vanilla 1
Dip 1
Soft 1
1
88
2
86
3
avg
86 86.67
2 Sugar 1
Chocolate 2
Sprinkles 2
Regular 2
78
77
75 76.67
3 Sugar 1
Vanilla 1
None 3
Regular 2
82
84
85 83.67
4 Regular 2
Vanilla 1
Sprinkles 2
Soft 1
77
81
76 78.00
5 Regular 2
Chocolate 2
None 3
Soft 1
57
54
52 54.33
6 Regular 2
Vanilla 1
Dip 1
Regular 2
80
80
81 80.33
7 Sugar 1
Vanilla 1
None 3
Regular 2
82
84
85 83.67
8 Regular 2
Chocolate 2
Dip 1
Soft 1
68
62
57 62.33
9 Regular 2
Vanilla 1
Sprinkles 2
Soft 1
77
81
76 78.00
Finding the signal to noise ratio (SN):
A basic explanation of the signal-to-noise ratio is: a ratio of the change in output due to
the changing variable vs. changes in things we cannot control.
For example, if we recorded speed of a bike based on speed of the pedals, we expect that,
the faster we pedal, the faster the bike travels. However, if we record this data in a very
hilly area, the rider might coast, shift gears, or maybe a strong wind would blow and
make him/her speed up or slow down. If we took a lot of data, we expect we could show:
the faster you pedal, the faster your bike goes. But the data would not be perfect – there
was some noise (hills, coasting, gears, wind) that had some effect. The signal (pedal
speed) was affected by the noise (everything else).
The signal-to-noise (SN) ratio is found by:
Where:
i
tells us which row we are working with (which experiment).
is the mean (or average) of the row (shown in the data table above)
is the standard deviation of the row
We can find each of these values using Excel.
© 2010, Ohio Northern University: Dr. Debra Gallagher, Dr. Robert Verb, Dr. Ken Reid and Ben McPheron
Step 1: Our goal is to find a value for SN for each row of our table. We will need to
calculate the average and the standard deviation before we can determine the SN.
To find the average of a group of numbers (in our case, 3 numbers) use
To find the standard deviation, use
=average( )
=stdev( )
The table below shows row 3 (i=3): the data is highlighted. The average of these 3 values
is 83.67, and the standard deviation is 1.53.
Exp
1
Cone
Sugar 1
Ice cream Topping
Vanilla 1 Dip 1
Texture
Soft 1
1
88
2
86
3
avg
86 86.67
st dev
1.15
2
Sugar 1
Chocolate 2
Sprinkles 2
Regular 2
78
77
75 76.67
1.53
3
Sugar 1
Vanilla 1
None 3
Regular 2
82
84
85 83.67
1.53
4
Regular 2
Vanilla 1
Sprinkles 2
Soft 1
77
81
76 78.00
2.65
5
Regular 2
Chocolate 2
None 3
Soft 1
57
54
52 54.33
2.52
6
Regular 2
Vanilla 1
Dip 1
Regular 2
80
80
81 80.33
0.58
7
Sugar 1
Vanilla 1
None 3
Regular 2
82
84
85 83.67
1.53
8
Regular 2
Chocolate 2
Dip 1
Soft 1
68
62
57 62.33
5.51
9
Regular 2
Vanilla 1
Sprinkles 2
Soft 1
77
81
76 78.00
2.65
=average( )
=stdev()
We now have all of the info we need to find the signal-to-noise ratio.
The formula for the SN ratio is:
=10*LOG((J18*J18)/(K18*K18))
… where J18 = the cell address of the average, and K18 is the cell address of the standard
deviation. Be careful to type the parenthesis in correctly!
For our example, this formula gives us:
= 10 * log ((83.67*83.67) / (1.53*1.53)) = 34.76
(note: using Excel may give slightly different answers: for example, the result shown
below is 34.771. Excel keeps track of the digits beyond those we see in the chart)
© 2010, Ohio Northern University: Dr. Debra Gallagher, Dr. Robert Verb, Dr. Ken Reid and Ben McPheron
The table below shows each row with
- average
- standard deviation
- Signal to Noise ratio
Exp
Cone
Ice
cream
Topping
Texture
1
2
3
avg
st dev
SN
1
2
3
4
5
6
7
8
9
1
1
1
2
2
2
1
2
2
1
2
1
1
2
1
1
2
1
1
2
3
2
3
1
3
1
2
1
2
2
1
1
2
2
1
1
88
78
82
77
57
80
82
68
77
86
77
84
81
54
80
84
62
81
86
75
85
76
52
81
85
57
76
86.67
76.67
83.67
78.00
54.33
80.33
83.67
62.33
78.00
1.15
1.53
1.53
2.65
2.52
0.58
1.53
5.51
2.65
37.508
34.012
34.771
29.391
26.685
42.869
34.771
21.075
29.391
Step 2:
After calculating the SN ratio for each experiment, the average SN value is calculated for
each factor and level. We will want to find:
SN cone,1
SN cone,2
SN icecream,1
SN icecream,2
SN topping,1
SN topping,2
SN topping,3
SN texture,1
SN texture,2
Let’s look at SN values for texture: we’ll average each value for which texture was
choice 1 (soft – shown in blue), then for each where it was 2 (regular – shown in gold):
© 2010, Ohio Northern University: Dr. Debra Gallagher, Dr. Robert Verb, Dr. Ken Reid and Ben McPheron
SN texture,1 = (37.508 + 29.391 + 26.685 + 21.075 + 29.391) / 5 = 28.81
SN texture,2 = (34.012 + 34.771 + 42.869 + 34.771) / 4 = 36.61
Next, let’s find SN values for topping:
SN topping,1 = (37.508 + 42.869 + 21.075) / 3 = 33.82
SN topping,2 = (34.012 + 29.391 + 29.391) / 3 = 30.931
SN topping,2 = (34.771 + 26.685 + 34.771) / 3 = 32.076
… the complete list is shown below:
SN cone,1
35.266
SN cone,2
29.882
SN icecream,1
34.784
SN icecream,2
27.258
SN topping,1
33.817
SN topping,2
30.931
SN topping,3
32.076
SN texture,1
28.810
SN texture,2
36.606
© 2010, Ohio Northern University: Dr. Debra Gallagher, Dr. Robert Verb, Dr. Ken Reid and Ben McPheron
Step 3: Find the variable with the greatest change in signal-to-noise ratio
We will find the difference between the highest and lowest SN for each variable. The
most basic way is to fill in a table with the above values
as shown:
-
-
Cone
Ice cream
Topping
Texture
1
2
3
35.226
29.882
34.784
27.258
33.817
30.931
32.076
28.81
36.606
Δ
rank
5.344
3
7.526
2
2.886
4
7.796
1
Excel note:
To automatically find Δ, you can use
the following formula:
=MAX(O18:O20)-MIN(O18:O20)…
where O18:O20 would be replaced by
the values in your Excel table. This
automatically finds the maximum
value in the range and subtracts the
minimum.
The values in the table are the SN values we’ve just calculated.
The values for Δ (the Greek letter ‘delta’, which typically means ‘change in value’ in
mathematics) are the maximum value – the minimum value of SN’s
The rank is a ranking of largest to smallest value of delta.
The ranking shows us that the texture of the ice cream has the greatest effect on the score
for taste, while the topping has the smallest effect!
© 2010, Ohio Northern University: Dr. Debra Gallagher, Dr. Robert Verb, Dr. Ken Reid and Ben McPheron