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.
!"ecti#es:
Students should explore the use of the Taguchi method to find which
independent variable has the greatest effect on the dependent variable.
E$uip%ent&Materia's:
Computers with Internet access and Microsoft Excel
Usefu' (e!sites:
Man Excel tutorials are online! for help with a specific Excel command or
formula" it#s usuall helpful to tpe the term into www.$oogle.com for
%uic&" efficient tips.
'ne good introductor Excel tutorial on (outube can be seen at!
http!))www.outube.com)watch*v+,-.-S/MT01&2feature+related
(others are also available! go to www.outube.com and search for
3introduction to excel4)
The Michigan Chemical .rocess 5namics and Controls 'pen Text 6oo&!
http!))controls.engin.umich.edu)wi&i)index.php)5esign7of7experiments7via
7taguchi7methods!7orthogonal7arras
8i&ipedia! $enichi Taguchi! http!))en.wi&ipedia.org)wi&i)$enichi7Taguchi
9 more complex site with man arra choices!
http!))www:.research.att.com);n<as)oadir)index.html
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Taguchi#s @obust 5esign Method (see 3Extend4)
http!))www.mne.psu.edu)simpson)courses)ieB//)ieB//.robust.handout.pdf)
)cti#it* +heets:
Taguchi Exercise! Input with the $reatest Effect
Materia':
Computers with Internet access
Computers with Microsoft Excel
Engage:
@eview the concepts of experiments" dependent and independent variables
and defining the number of levels of each variable. @eview the answers
from the previous class to the following %uestions!
0. 8h would it be important to identif the variable that causes the
most change in the dependent variable we#re studing*
:. Can ou see an 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"
ou ma want to review the video tutorials in 3?seful websites4 in class" and
have the students wor& through the tutorials along with the video.
E,p'ore:
0. @eview the Cice cream experiments# from the teacher bac&ground with
students in the classroom. Dead the students through the final values
of signalEtoEnoise ratios and identification of the variable with the
greatest effect.
:. 5uring the ice cream example" emphasiFe that the Taguchi method
was also useful to reduce the number of experiments we had to do.
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Gad we done fullEfactorial experiments" this procedure would also
wor&" but there would be man more calculations to perform.
H. Gave students wor& through the %uestions on the 3Taguchi Exercise4
wor&sheet.
B. 8or&ing in pairs" as& each student team discuss signal to noise ratio.
,or instance" what Cnoise# could be present in a tan& with algae*
(Examples! a breeFe could be blowing on a tan&" contaminants could
be introduced while testing" etc.). 9s the list grows" discuss which
variables could be controlled and tested (i.e." airstone in the tan& vs.
no airstone in the tan&) and those that cannot be controlled" and can
onl be considered noise (unexpected contaminants).
E,p'ain:
0. 5iscuss the results of the ice cream experiment.
2. @eview the solution of the Taguchi Exercise: Input with the
Greatest Effect wor&sheet.
E,tend:
The analsis done here is sometimes represented graphicall" with a
series of plots showing the values of S- for each factor. 9n example of this
analsis can be seen in section H:.B.: of Taguchi#s @obust 5esign Method
(available at
http!))www.mne.psu.edu)simpson)courses)ieB//)ieB//.robust.handout.pdf)
E#a'uate:
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0. ?se student solutions to the Taguchi Experiment Exercise.
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Teacher -otes:
.esign of e,peri%ents (.oE) or e,peri%enta' design is ver commonl used to figure
out how a number of variables wor& together toward some result. 8e have seen that we
can minimiFe 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!
E Collect data using the Taguchi method
o (ou will need to collect H or more results from each experimental setup
(in other words" run each experiment H or more times).
E ,ollow the instructions to set up an Excel spreadsheet.
T*pes of e,peri%entation:
(/e#ie() 0 /unning the E,peri%ents:
,irst" determine how ou will measure the dependent variable. In most cases" ou want a
maximum or minimum number! which experiment grew the most algae" which
experiment resulted in the lowest cost. ,or our ice cream example" ou ma have to
assign the deliciousness of the ice cream cone a scale of 0 I 0>>.
?se the input variable values indicated in the Taguchi chart to run each experiment. ,or
example" on the above ice cream experiment" ou would eat!
Aanilla softEserve on a sugar cone" with dip"
Chocolate" regular ice cream on a sugar cone with sprin&les"
Aanilla" regular ice cream on a sugar cone (plain)"
etc.
J and record the deliciousness of the ice cream cone in each of the K cases.
To find the input variable with the greatest effect" we will need to do multiple tests of
each case I H or more is recommended.
)na'*1ing the resu'ts:
Det#s assume we made H 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( )
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9fter tping =average( block the group of 3 numbers using the mouse ) (in our first
row" select LL" L/ and L/).
L9 (filled in, with random alues in !lan" !oxes# Each leel is named $, 2 or % (for the
next ta!le#
Exp Cone Ice
cream
Topping Texture 1 2 3 avg
0
Sugar 0 Aanilla 0 5ip 0 Soft 0 LL L/ L/ 23435
:
Sugar 0 Chocolate : Sprin&les : @egular : ML MM MN 53435
H
Sugar 0 Aanilla 0 -one H @egular : L: LB LN 23435
B
@egular : Aanilla 0 Sprin&les : Soft 0 MM L0 M/ 52466
N
@egular : Chocolate : -one H Soft 0 NM NB N: 78433
/
@egular : Aanilla 0 5ip 0 @egular : L> L> L0 26433
M
Sugar 0 Aanilla 0 -one H @egular : L: LB LN 23435
L
@egular : Chocolate : 5ip 0 Soft 0 /L /: NM 39433
K
@egular : Aanilla 0 Sprin&les : Soft 0 MM L0 M/ 52466
:inding the signa' to noise ratio (+-):
9 basic explanation of the signalEtoEnoise ratio is! a ratio of the change in output due to
the changing variable vs. changes in things we cannot control.
,or example" if we recorded speed of a bi&e based on speed of the pedals" we expect that"
the faster we pedal" the faster the bi&e travels. Gowever" if we record this data in a ver
hill area" the rider might coast" shift gears" or mabe a strong wind would blow and
ma&e him)her speed up or slow down. If we too& a lot of data" we expect we could show!
the faster ou pedal" the faster our bi&e goes. 6ut the data would not be perfect I there
was some noise (hills" coasting" gears" wind) that had some effect. The signal (pedal
speed) was affected b the noise (everthing else).
The signalEtoEnoise (S-) ratio is found b!
8here!
i tells us which row we are wor&ing with (which experiment).
is the mean (or average) of the row (shown in the data table above)
is the standard deviation of the row
8e can find each of these values using Excel.
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Step 1: 'ur goal is to find a value for S- for each row of our table. 8e will need to
calculate the average and the standard deviation before we can determine the S-.
To find the average of a group of numbers (in our case" H numbers) use +average( )
To find the standard deviation" use +stdev( )
The table below shows row H (i+H)! the data is highlighted. The average of these H values
is LH./M" and the standard deviation is 0.NH.
Exp Cone Ice
cream
Topping Texture 1 2 3 avg st dev
0 Sugar
0
Aanilla
0
5ip
0
Soft
0
LL L/ L/ 2343
5
1417
: Sugar
0
Chocolate
:
Sprin&les
:
@egular
:
ML MM MN 5343
5
1473
H Sugar
0
Aanilla
0
-one
H
@egular
:
L: LB LN 2343
5
1473
B @egular
:
Aanilla
0
Sprin&les
:
Soft
0
MM L0 M/ 5246
6
9437
N @egular
:
Chocolate
:
-one
H
Soft
0
NM NB N: 7843
3
9479
/ @egular
:
Aanilla
0
5ip
0
@egular
:
L> L> L0 2643
3
6472
M Sugar
0
Aanilla
0
-one
H
@egular
:
L: LB LN 2343
5
1473
L @egular
:
Chocolate
:
5ip
0
Soft
0
/L /: NM 3943
3
7471
K @egular
:
Aanilla
0
Sprin&les
:
Soft
0
MM L0 M/ 5246
6
9437
&aerage( #
&stde(
#
8e now have all of the info we need to find the signalEtoEnoise ratio.
The formula for the S- ratio is!
+0>OD'$((P0LOP0L))(10LO10L))
J where P0L + the cell address of the average" and 10L is the cell address of the standard
deviation. 6e careful to tpe the parenthesis in correctlQ
,or our example" this formula gives us!
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+ 0> O log ((LH./MOLH./M) ) (0.NHO0.NH)) + HB.M/
(note! using Excel ma give slightl different answers! for example" the result shown
below is HB.MM0. Excel &eeps trac& of the digits beond those we see in the chart)
The table below shows each row with
E average
E standard deviation
E Signal to -oise ratio
Exp Cone Ice
cream
Toppin
g
Textur
e
1 2 3 avg st dev SN
0 0 0 0 0 LL L/ L/ 23435 1417 %'.()*
: 0 : : : ML MM MN 53435 1473 %+.)$2
H 0 0 H : L: LB LN 23435 1473 %+.''$
B : 0 : 0 MM L0 M/ 52466 9437 29.%9$
N : : H 0 NM NB N: 78433 9479 2,.,*(
/ : 0 0 : L> L> L0 26433 6472 +2.*,9
M 0 0 H : L: LB LN 23435 1473 %+.''$
L : : 0 0 /L /: NM 39433 7471 2$.)'(
K : 0 : 0 MM L0 M/ 52466 9437 29.%9$
Step 2:
9fter calculating the S- ratio for each experiment" the average S- value is calculated for
each factor and level. 8e will want to find!
S-
cone"0
S-
cone":
S-
icecream"0
S-
icecream":
S-
topping"0
S-
topping":
S-
topping"H
S-
texture"0
S-
texture":
Det#s loo& at S- values for texture! we#ll average each value for which texture was
choice 0 (soft I shown in blue)" then for each where it was : (regular I shown in gold)!
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S-
texture"0
+ (HM.N>L R :K.HK0 R :/./LN R :0.>MN R :K.HK0) ) N + :L.L0
S-
texture":
+ (HB.>0: R HB.MM0 R B:.L/K R HB.MM0) ) B + H/./0
-ext" let#s find S- values for topping!
S-
topping"0
+ (HM.N>L R B:.L/K R :0.>MN) ) H + HH.L:
S-
topping":
+ (HB.>0: R :K.HK0 R :K.HK0) ) H + H>.KH0
S-
topping":
+ (HB.MM0 R :/./LN R HB.MM0) ) H + H:.>M/
J the complete list is shown below!
S-
cone"0 %(.2,,
S-
cone": 29.**2
S-
icecream"0 %+.'*+
S-
icecream": 2'.2(*
S-
topping"0 %%.*$'
S-
topping": %).9%$
S-
topping"H %2.)',
S-
texture"0 2*.*$)
S-
texture": %,.,),
= :>0>" 'hio -orthern ?niversit! 5r. 5ebra $allagher" 5r. @obert Aerb" 5r. 1en @eid and 6en Mc.heron

Step H! ,ind the variable with the greatest change in signalEtoEnoise ratio
8e will find the difference between the highest and lowest S- for each variable. The
most basic wa is to fill in a table with the above values
as shown!
Cone Ice cream Topping Texture
$ %(.22, %+.'*+ %%.*$' 2*.*$
2 29.**2 2'.2(* %).9%$ %,.,),
% %2.)',
- (.%++ '.(2, 2.**, '.'9,
ran" % 2 + $

E The values in the table are the S- values we#ve <ust
calculated.
E The values for S (the $ree& letter Cdelta#" which tpicall means Cchange in value# in
mathematics) are the maximum value I the minimum value of S-#s
E The ran& is a ran&ing of largest to smallest value of delta.
The ran&ing shows us that the texture of the ice cream has the greatest effect on the score
for taste" while the topping has the smallest effectQ
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Excel note:
To automatically find , you can use the
following formula:
=MAX(O!:O"#$%M&'(O!:O"#$(
where O!:O"# would )e re*laced )y
the +alues in your Excel ta)le, This
automatically finds the maximum +alue
in the range and su)tracts the minimum,