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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

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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 Shaft Kiln 1800C Water spray Drying Oven Al 2 O 3 Powder

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Process Problem –Control Ball Size –Minimize H 2 O –Minimize Pore Volume –Low Dust Emissions 6 mo. to solve problem Conveyor Belt Shaft Kiln 1800C Water Spray Drying Oven 3 cm 2.5 cm Al 2 O 3 powder

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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 Shaft Kiln 1800C Water Spray Drying Oven 3 cm 2.5 cm Al 2 O 3 powder

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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?

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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.

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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

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Used today in Pharma –Drug Development Silicon Chip Processing –From Wafers to chips It is the basis of 6 sigma’s statistical process analysis

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Traditional Experimentation Move one variable at a time Keep other variables constant No of experiments = L V –V=Variables –L=Levels Traditional Experimentation –5 7 =78,125 experiments –3 7 =2,187 experiments –Need to reduce the number of variables Levels of x 2 y Response

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Saves Time and Money No of experiments = L V –V=Variables –L=Levels Traditional Experimentation –5 3 =125 experiments Statistically Designed Experiments 2 3 = 8 experiments + 2 (repeats)=10 expts. 2 3 = 8 experiments x 2 (repeats)=16 expts. –Vary all variables simultaneously then mathematically sort things out Levels of x 2 y i Response

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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, H 2 O content, Dust Run Experiments in a Randomized Order

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Variables for 2 3 Design

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Mathematics Calculate Effects of each variable on each measurement E i =Σy i(+) - Σy i(-) Prediction Equation y(x)=E 1 x 1 + E 2 x 2 + E 3 x 3 + … E 1 E 2 x 1 x 2 + E 1 E 3 x 1 x 3 + E 2 E 3 x 2 x 3 + E 123 x 1 x 2 x 3 Generate Response Surface Map Optimize

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Response Surface Map

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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

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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

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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

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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 C bleach 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.

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It is very difficult to measure the small change in volume of the mercury. If the mercury had the shape of a sphere, the change in diameter would be very.

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