Lab Course IC-211 Planning the Experiment Final3

Lab Course ICLab Course IC--211 211

How to Plan an Experiment?How to Plan an Experiment?

AndAnd

How to How to AnalyseAnalyse the Measured Data?the Measured Data?

By

Prof. Prakash R. Apte

EE Department

How to Plan an experiment?How to Plan an experiment?

How to How to analyseanalyse the measured data?the measured data?

• Planning the Experiment

• Let us plan the experiments to maximize the discharge “Q” from a Capillary

STEP 1STEP 1 : Identify Problem: Identify Problem

• We would like to determine the function Q(H, R, µ, L)

• From a given set of values of “H”, “R”, “µ” and “L”, we would like to determine the best combination that would give MAXIMUM discharge “Q MAX”

Hydrostatic

Pressure “H” Capillary

Radius

“R”

Viscosity of

Liquid “µ”

Quantity of

Liquid “Q”

collected

after, say, 10min

Length

of Capillary “L”

Capillary



STEP 2STEP 2 : Identify Control Factors: Identify Control Factors

• Let us take 3 values each for “H”, “R”, “µ” and “L”, as shown in

the table below

Control Factors

And

Levels

Hydrostatic

Pressure “H”

Capillary

Radius “R”

Liquid type or

Viscosity “µ”

Capillary

Length “L”

Level 1 500 mmHg 50 µm Water = .89 cP 100 mm

Level 2 200 mmHg 60µm Methanol = .54 cP 150 mm

Level 3 50 mmHg 80 µm Ethanol = 1.08 cP 200 mm



STEP 3STEP 3 : Identify NOISE Factors: Identify NOISE Factors

• Identify a NOISE factor that can affect the measured output, but

we have no control over it (say from 1 day to another)

� we can take “Temperature of Liquid” as Noise Factor

as it will affect the viscosity (and may be the radius)

� allow it to take 3 values as “35C, 45C and 55C”

NOISE Factor

and

Levels

Temperature of Liquid “T”

Level 1 35 C

Level 2 45 C

Level 3 55 C



STEP 4STEP 4 : Prepare for Experiments : Prepare for Experiments

Create 3 values of “H” �� “water head” of (500, 200, 50) mmHg

Create 3 values of “R” �� “Radii” of (50, 60, 80) µm

Create 3 values of “µ” �� “water/methanol/ethanol” of

(.89, .54, 1.08) cP

Create 3 values of “L” �� “Capillary Lengths” of (100, 150, 200) mm

STEP 4STEP 4 : Prepare for Measurements: Prepare for Measurements

Stopwatch 450cc graduated Beaker


How to How to analyseanalyse the measured data?the measured data?STEP 5STEP 5 : Select Orthogonal Array L9: Select Orthogonal Array L9

| | | Control Factors | Control Factors | | | | Noise Factors &| |Noise Factors &| |

| | “Q| | “Q” Measured | |” Measured | |Obj. Obj. FuncFunc..||Expt

No.

A B C D NZ1

Measure

Q1

NZ2

Measure

Q2

NZ3

Measure

Q3

CALCULATE

η

1 1 1 1 1 Q1,1 Q1,2 Q1,13 η1

2 1 2 2 2 ? ? ? η2

3 1 3 3 3 ? ? ? η3

4 2 1 2 3 Q4,1 Q4,2 Q4,3 η4

5 2 2 3 1 ? ? ? η5

6 2 3 1 2 ? ? ? η6

7 3 1 3 2 ? ? ? η7

8 3 2 1 3 ? ? ? η8

9 3 3 2 1 Q9,1 Q9,2 Q9,3 η9



Expt

no.

H R µ L 35 C 45 C 55 C Obj. Func.

1 500 50 Water 0.89 100 ? ? ? 15

2 500 60 Methanol 0.54 150 ? ? ? 22

3 500 80 Ethanol 1.08 200 ? ? ? 20

4 200 50 Methanol 0.54 200 Yi,1

=10.5

Yi,1

=11

Yi,1

=11.511

5 200 60 Ethanol 1.08 100 ? ? ? 15

6 200 80 Water 0.89 150 ? ? ? 22

7 50 50 Ethanol 1.08 150 ? ? ? 1

8 50 60 Water 0.89 200 ? ? ? 5

9 50 80 Methanol 0.54 100 ? ? ? 24

STEP 5STEP 5 : : Assign Control factors to L9 ArrayAssign Control factors to L9 Array

| | Control Factors | | “Q” Measured | || | Control Factors | | “Q” Measured | |Obj. Obj. FuncFunc..||


How to How to analyseanalyse the measured data?the measured data?•• STEP 6STEP 6 : Conduct the 9 experiments : Conduct the 9 experiments

and collect the dataand collect the data

�� For example : For example : exptexpt #4 uses H=#4 uses H=200, R=50, µ = 0.54 and L=200

�� measured Q’s could be Yi,1 =10.5, Yi,2 =11, Yi,3 =11.5 �� mean ηηii= 11

�� Similarly, ALL 9 rows are filled with data and Similarly, ALL 9 rows are filled with data and

objobj funcfunc. is taken as the mean of 3 readings of Q in each row. is taken as the mean of 3 readings of Q in each row

(dummy data for obj. (dummy data for obj. funcfunc. are given in last column of table on previous page . are given in last column of table on previous page to demonstrate a sample analysis) to demonstrate a sample analysis)

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Footnote: Taguchi uses LogFootnote: Taguchi uses Log--form of obj. form of obj. funcfunc. .

�� for for iithth row row ηηii

= = --10 Log10 { 1/3 (1/y10 Log10 { 1/3 (1/yi,1i,1^2 + 1/y^2 + 1/yi,2i,2^2 + 1/y^2 + 1/yi,3i,3^2) }^2) }



STEP 7STEP 7 : : AnalyseAnalyse the datathe data

�� Calculate Factor Effects (for each level of control factors)Calculate Factor Effects (for each level of control factors)

��How? How?

Factor Effect of H=500 mmHg can be found by following simple algorithmFactor Effect of H=500 mmHg can be found by following simple algorithm

�� H=500 mmHg occurs in rows 1, 2 and 3H=500 mmHg occurs in rows 1, 2 and 3

So, take the mean of obj. So, take the mean of obj. funcfunc. for rows 1,2,3 . for rows 1,2,3 �� m(H=500) = (15 + 22 +20)/3 = 19m(H=500) = (15 + 22 +20)/3 = 19

Similarly, Similarly,

H=200 mmHg occurs in rows 4, 5 and 6 H=200 mmHg occurs in rows 4, 5 and 6

So, take the mean of obj. So, take the mean of obj. funcfunc. For rows 4,5,6 . For rows 4,5,6 �� m(H=200) = (11 + 15 + 22)/3 = 16m(H=200) = (11 + 15 + 22)/3 = 16

Similarly, Similarly, �� m(H=100) = (1+ 5 + 24)/3 = 10m(H=100) = (1+ 5 + 24)/3 = 10

�� Do the same for all remaining Control factors and their 3 levelsDo the same for all remaining Control factors and their 3 levels

�� Make the plot (shown on next slide)Make the plot (shown on next slide)


How to How to analyseanalyse the measured data?the measured data?STEP 7STEP 7 : : AnalyseAnalyse the datathe data

�� Calculate Factor Effects (for each level of control factors)Calculate Factor Effects (for each level of control factors)

�� Do the same for all remaining Control factors and their 3 levelsDo the same for all remaining Control factors and their 3 levels

Factor Effects of R can be found by following simple algorithmFactor Effects of R can be found by following simple algorithm

�� R=50 R=50 µm occurs in rows 1, 4 and 7m occurs in rows 1, 4 and 7

So, take the mean of obj. So, take the mean of obj. funcfunc. for rows 1,4,7 . for rows 1,4,7 �� m(R=50) = (15 + 11 +1)/3 = 9m(R=50) = (15 + 11 +1)/3 = 9

Similarly, Similarly,

R=60 R=60 µm occurs in rows 2, 5 and 8m occurs in rows 2, 5 and 8

So, take the mean of obj. So, take the mean of obj. funcfunc. for rows 2,5,8 . for rows 2,5,8 �� m(R=60) = (22 + 15 + 5)/3 = 14m(R=60) = (22 + 15 + 5)/3 = 14

Similarly, for rows 3,6,9 Similarly, for rows 3,6,9 �� m(R=80) = (20+ 22 + 24)/3 = 22m(R=80) = (20+ 22 + 24)/3 = 22

�� Similarly, m(Similarly, m(µ=0.89 water) = 14, m(m(µ=0.54 methanol) = 19, m(m(µ=1.08 ethanol) = 12

�� Similarly, m(LSimilarly, m(L=100) = 18, m(m(L=150) = 15, m(m(L=200) = 12

��Make the plot (shown on next slide)Make the plot (shown on next slide)

19

16

109

14

22

14

19

12

18

15

12

Ov Mean = 15

0

5

10

15

20

25

H =

50

0 m

mH

g

H =

20

0 m

mH

g

H =

50

mm

Hg

R =

50

um

R =

60

um

R =

80

um

µ =

wa

ter

(0.8

9 c

P)

µ =

Me

tha

no

l (0

.54

cP

)

µ =

Eth

an

ol (

1.0

8 c

P)

L =

10

0m

m

L =

15

0m

m

L =

20

0m

m

Ov-M

ea

n

S/N

Ratio (

LA

RG

ER

-the-b

ett

er)

in d

B

Control Factor Levels

Factor Effect Plot for CAPILLARY DISCHARGE "Q"



STEP 8STEP 8 : Best settings and Best result: Best settings and Best result

�� From the PLOT From the PLOT

�� best settings are H=500, R=80, µ = 0.54, L = 100

�� best result = Ov mean m + {m(H=500) – m } + {m(R=80) – m }

+ {m(µ =0.54) – m } + {m(L=100) – m }

�� best result = 15 + { 19 – 15 } + { 22 – 15 } + { 19 – 15 } + { 18 – 15 }

�� best result = 15 + { 4 } + { 7 } + { 4 } + { 3 }

�� best result = 33 (while max of 9 rows = 24)

STEP 8STEP 8 : : Conduct the “confirmation experiment” with Best settings Conduct the “confirmation experiment” with Best settings

and the result should match “Predicted best result=33and the result should match “Predicted best result=33””

End of presentationEnd of presentation

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Lab Course IC-211 Planning the Experiment Final3