Design Experiments Using Minitab

Yanling Zuo(左燕玲 ), PhDMinitab Inc.

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Taguchi

Case Study

A quality team is studying how a catalytic reaction converts

substrate into a final product.

A sketch of the converter

Feed 100% Reactants 70% products, 30% reactants

catalyst

Rev/min

Temperature

Case Study…

Factors identified after brainstorming:

Feed rate – Flow rate settings for feed tank (10,15 ml/min)

Catalyst (A, B)

Agitation rate (100, 120)

Temperature (140º, 180º C)

Percent concentration (3%, 6%)

Case Study...

Response:

Percent of substrate reacted

Data collection:

The team has enough budget to perform 35 runs. They

could run a full factorial design (25=32). However, a better

approach is to run a fractional design, analyze results,

and decide on subsequent experimentation.

What’s next?

Create a ½ fraction design.

Case Study…

Create the design with Minitab

Go to Stat > DOE > Factorial >

Create Factorial Design

Case Study…

Output

Note: Main effects confounded with 4-way interaction,

2-way interaction with 3-way interaction

Case Study…

Worksheet

Case Study…

Analyze the design with Minitab

Go to Stat > DOE > Factorial >

Analyze Factorial Design

Case Study…

Normal Probability Plot of Effects

20151050-5-10

99

95

90

80

70605040

30

20

10

5

1

Effect

Perc

ent

A FeedrateB Catalyst

C AgitationD TempE Conc%

Factor Name

Not SignificantSignificant

Effect Type

DE

BD

E

D

B

Normal Plot of the Effects(response is Reacted, Alpha = .05)

Lenth's PSE = 1.875

Case Study…

Pareto chart of Effects

C

CD

AC

AD

BE

AE

AB

BC

A

CE

E

DE

BD

D

B

20151050

Term

Effect

4.82

A FeedrateB Catalyst

C AgitationD TempE Conc%

Factor Name

Pareto Chart of the Effects(response is Reacted, Alpha = .05)

Lenth's PSE = 1.875

Case Study...

Significant factors:

Catalyst (B)

Temp (D)

Concentration (E)

Catalyst x Temp (BD)

Temp x Concentration (DE)

What’s next:

Remove non-significant effects and refit models.

Case Study...

Output:

Case Study...

Estimated coefficients:

Reacted = -88.37 – 32.75 x Catalyst + 1.02 x Temp

+23.25 x Conc + 0.27 x Catelyst x Temp

-0.16 x Temp x Conc.

(Can be used to predict percent reacted settings)

Case Study...

Residual plots

What’s next?

Create factorial plots to find best settings.

5.02.50.0-2.5-5.0

99

90

50

10

1

Residual

Perc

ent

9080706050

4

2

0

-2

-4

Fitted Value

Resi

dual

420-2-4

4

3

2

1

0

Residual

Fre

quency

16151413121110987654321

4

2

0

-2

-4

Observation Order

Resi

dual

Normal Probability Plot Versus Fits

Histogram Versus Order

Residual Plots for Reacted

Case Study...

Factorial Plots

Case Study...180140 63

90

75

60

90

75

60

Catalyst

Temp

Conc%

AB

Catalyst

140180

Temp

Interaction Plot for ReactedData Means

6

3

180

140

BA

Conc%

Temp

Catalyst

80.0

66.055.5

47.0

94.0

62.053.0

64.5

Cube Plot (data means) for Reacted

Case Study...

Conclusions:

Feed rate and agitation do not have a significant impact

Catalyst B, a temperature of 180ºC, and 3%

concentration maximize substrate consumption.

Followup experiment:

The team had budget for 19 additional runs. They used

Catalyst B and run a 22 full factorial design with 2 center

points to detect curvature in the response. They centered

experiment at currently known optimal settings,180ºC, 3%.

Case Study...

Numerical output for the follow up experiment:

Case Study...

Graphical output:

190180170

95

90

85

80

75

432

Temp

Mean

Conc%CornerCenter

Point Type

Main Effects Plot for ReactedData Means

432

95

90

85

80

75

70

Conc%

Mean

170 Corner180 Center190 Corner

Temp Point Type

Interaction Plot for ReactedData Means

4

2

190170

Conc%

Temp

94

79

8175

73

CenterpointFactorial Point

Cube Plot (data means) for Reacted

Case Study...

Assessing Power:

Design:

2 x 2, 1 replicate,

2 center points.

Variance (MSE) = 1.28

St Dev = 1.131

Size of effect:

A change of 3% in reacted substrate.

Case Study...

This design has low power (0.165).

3210-1-2-3

1.0

0.8

0.6

0.4

0.2

0.0

Effect

Pow

er

Alpha 0.05StDev 1.131

# Factors 2# Corner Pts 4# Blocks none# Terms Omitted 0

Center Points Yes

Term Included In Model

Assumptions

1, 2Ctr Pts Per BlkReps,

Power Curve for 2-Level Factorial Design

Case Study...

Conclusions:

A quadratic effect on catalytic reaction due to temperature

and concentration is present.

This design has low power, not the best choice. A better

design would include 2 replicates, but would require 12 runs

(assuming 2 center points per replicate) rather than 6.

Additional consideration:

Consider using response surface methodology to model the

curvature.