Transcript What to do when you haven’t got a.ppt

What to do when you haven’t
got a clue.
Terry A. Ring
Chem. Eng.
University of Utah
www.che.utah.edu/~ring/Statistically Designed Experiments
My First Job
• My First Task
• Process that I
knew nothing
about.
– Nodulization
– Drying
– Sintering
• Plant
Al2O3 Powder
Water spray
Drying Oven
Conveyor Belt
– 3m (0.5m tall)
• Pilot Plant
– 1m(0.3m tall)
Shaft
Kiln
1800C
Process
Al2O3 powder
• Problem
– Control Ball Size
– Minimize H2O
– Minimize Pore
Volume
– Low Dust
Emissions
Water Spray
3 cm
Drying Oven
Conveyor Belt
• 6 mo. to solve
problem
Shaft
Kiln
1800C
2.5 cm
Variables
Al2O3 powder
• Variables
Water Spray
– Water flow rate
• Concentration of
additives
–
–
–
–
–
–
Powder Flow Rate
RPM
Time in Dryer
Temp Dryer
Time in Shaft Kiln
Temp of Shaft Kiln
3 cm
Drying Oven
Conveyor Belt
• 6 mo. to solve
problem
Shaft
Kiln
1800C
2.5 cm
What to do?
• Literature Review on Nodulization
– 1 paper
– 1 PhD thesis

d / x
dm(d , t )
1 e
b
  k ( x / d o )b [
]
m
(
x
,
t
)
dx

k
(
d
/
d
)
m( d , t ) 
o
1
dt
1 e
0
– m(d,t) is the mass of sphere of diameter d
• How do I solve this?
• What do I do now?
 Q m (d , t )
k
k
k
V
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
y Response
• Traditional Experimentation
– 57=78,125 experiments
Levels of x2
7
– 3 =2,187 experiments
– Need to reduce the number of variables
Saves Time and Money
• No of experiments = LV
– V=Variables
– L=Levels
yi Response
• Traditional Experimentation
– 53=125 experiments
Levels of x2
• 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
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.