What to do when you haven’t got a clue.

Terry A. RingChem. Eng.

University of Utahwww.che.utah.edu/~ring/Statistically Designed Experiments

My First Job

• My First Task• Process that I

knew nothing about.– Nodulization– Drying– Sintering

• Plant– 3m (0.5m tall)

• Pilot Plant– 1m(0.3m tall)

Conveyor Belt

ShaftKiln

1800C

Water spray

Drying Oven

Al2O3 Powder

Process

• Problem– Control Ball Size

– Minimize H2O

– Minimize Pore Volume

– Low Dust Emissions

• 6 mo. to solve problem

Conveyor Belt

ShaftKiln

1800C

Water Spray

Drying Oven

3 cm

2.5 cm

Al2O3 powder

Variables

• Variables– Water flow rate

• Concentration of additives

– Powder Flow Rate– RPM– Time in Dryer– Temp Dryer– Time in Shaft Kiln– Temp of Shaft Kiln

• 6 mo. to solve problem

Conveyor Belt

ShaftKiln

1800C

Water Spray

Drying Oven

3 cm

2.5 cm

Al2O3 powder

What to do?

• Literature Review on Nodulization– 1 paper– 1 PhD thesis

– m(d,t) is the mass of sphere of diameter d

• How do I solve this?• What do I do now?

V

tdmQtdmddkdxtxm

e

edxk

dt

tddm kkk

bo

xdb

o

),(),()/(),(]

1

1[)/(

),(1

/

0

Now what do you do?

• Get Help– Plant Operator in Baton Rouge, Louisiana

• Nothing Useful

– Technician that last ran the Pilot Plant• Water flow rate seemed to be critical.

– Talk to others at the research site• Idea at lunch to use statistically designed

experiments– Consultant gave lecture 2 years ago at site.

Statistically Designed Experiments

• Save time and money

• Find out what variables are important– Tell you if you have all the important variables– Tell you if some variables are not important– Tell you if variable interact

• Non-linear effects

• Gives a Model for prediction purposes

• Allows optimization of the process

Used today in

• Pharma– Drug Development

• Silicon Chip Processing– From Wafers to chips

• It is the basis of 6 sigma’s statistical process analysis

Traditional Experimentation

• Move one variable at a time• Keep other variables constant• No of experiments = LV

– V=Variables– L=Levels

• Traditional Experimentation– 57=78,125 experiments– 37=2,187 experiments– Need to reduce the number of variables

Levels of x2

y Response

Saves Time and Money

• No of experiments = LV

– V=Variables– L=Levels

• Traditional Experimentation– 53=125 experiments

• Statistically Designed Experiments• 23= 8 experiments + 2 (repeats)=10 expts.• 23= 8 experiments x 2 (repeats)=16 expts.

– Vary all variables simultaneously then mathematically sort things out

Levels of x2

yi Response

Process for Design of Experiments

• Select Variables – RMP, Water Flow, Drying Time, Sintering Time

• Select range of to manipulate the variables– Low value (-) sometimes scaled variable -1– High value (+) sometimes scaled variable +1

• Select Measurements to be made– Ball Diameter, Pore Volume, H2O content,

Dust

• Run Experiments in a Randomized Order

Variables for 23 Design

Mathematics

• Calculate Effects of each variable on each measurement

• Ei=Σyi(+)- Σyi(-)

• Prediction Equation• y(x)=E1x1+ E2x2+ E3x3+ …• E1E2x1x2+ E1E3x1x3+ E2E3x2x3+• E123 x1x2x3

• Generate Response Surface Map• Optimize

Response Surface Map

Various Software to do this

• ** Stat-ease from Stat-ease Inc. – (3 mo free license)

• DOE from BBN Software Products• Reliasoft• MiniTab• Statistica from Statsoft• DoE from Camo• Others

Why do you do experiments?

• Understand how process responds to changes in variables

• Develop a mathematical description of the process

• Verify a model– Determine various coefficients in the model

Physical Model vs DoE model

• Physics based Model– Often physics is too difficult to model– Often equations are too difficult to solve– Use of simplified model is all too often occurrence

• DoE Model– Little physical significance to Effects in equation– Good only inside box

• Minor extrapolation is possible

Use Physics to guide variable choice

• Suppose you know the physics behind the model– Choose a variable and response that are linearly related.

• Suppose we vary temperature and are looking at the output from a bleaching operation– Use 1/T as a variable– Use Cbleach as a variable– Use ln[whiteness] as measured response– This approach will determine the activation energy as the

temperature effect and the rate constant as the concentration effect.

– The standard errors will be determined giving the error on the activation energy and the rate constant.