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The Straight Way to a Final Result: Mixture Design of Experiments

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Running experiments is an essential part of all development, improvement, upscaling and research. Very often, experiments are run following traditional legacy designs. Only one factor gets changed over a series of experiments. Single-factor experiments are not possible with mixture designs as all the components have to add up to the total.

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The Straight Way to a Final Result: Mixture Design of Experiments

  1. 1. Copyright © 2012, SAS Institute Inc. All rights reserv ed. THE STRAIGHT WAY TO A FINAL RESULT: MIXTURE DESIGN OF EXPERIMENTS Bernd Heinen Sr. Systems Engineer bernd.heinen@jmp.com
  2. 2. Copyright © 2012, SAS Institute Inc. All rights reserv ed. Running experiments is an essential part of all development, improvement, upscaling and research activitiy. Very often, still today, experiments are run following traditional legacy designs. This goes to the extent that only one factor gets changed over a series of experiments. Single factor experiments are not possible in mixture designs as all the components have to add up to the total amount. If the volume of one component goes up others need to go down. Are you designing each experiment? Do you exactly know what your design space looks like? Are you aware of constraints? Is your experimental design optimized for the design space and the constraints given? Do you know in advance how many experiments you will need to definitively answer your questions? Are you making the best use of the data generated? Are you using your experimental data for interactive what-if scenario analyses? Let‘s go!
  3. 3. Copyright © 2012, SAS Institute Inc. All rights reserv ed. Mixture experiments have the specific side condition that the levels of their factors are not independent from each other. If the amount of one component is known, there are only limited options for the rest. If all but one components are known the last one has no options any more. Frequency distribution of fractions of three components used for twelve experiments With a fraction of 50% selected for the first component there are only few combinations left for the other two The contribution of the last component is determined by the others.
  4. 4. Copyright © 2012, SAS Institute Inc. All rights reserv ed. The Ternary Plot is a graphical representation of mixtures that allows to represent three factors (three dimensions) in one graph. Dots mark the combinations at which experiments have been carried out. Their color is an indicator for the level of the response variable as well. Isometric lines show the interpolated „landscape“ of a result (or response) variable over the experimental space as it is derived from the experiments. Current mixture setting of the slider Expected result for response variable at optimal settings
  5. 5. Copyright © 2012, SAS Institute Inc. All rights reserv ed. Oil 0 00 1 1 1 To set up a mixture design does not require any statistical knowledge. The single components need to be listed and it is relevant to state if interactions are expected. If every component could take any proportion from 0 to 1 (equivalent of 0% to 100%) then the whole experimental space will be covered as it is spanned by the Ternary Plot. The experiments will be arranged such that the vertices and the edges will be covered. List of all pairwise interactions
  6. 6. Copyright © 2012, SAS Institute Inc. All rights reserv ed. Water0 0.25 Vinegar 0.375 0.125 Oil 0.75 0.5 Often components contribute with different fractions to the mixture. If accordingly specified, the experimental space is a limited area. Experimental mixtures then cover the vertices and the center.
  7. 7. Copyright © 2012, SAS Institute Inc. All rights reserv ed. Oil : Vinegar ≥ 3 : 1 Oil : Vinegar ≤ 2 : 1 Constraints that link components among each other further restrict the experimental space. Again, the test mixtures cover the vertices, the edges and the center.
  8. 8. Copyright © 2012, SAS Institute Inc. All rights reserv ed. Factor Profiler and Mixture Profiler set to center experiment Factor Profiler and Mixture Profiler set to maximum response When the experiments have been run and the response variable was measured and captured the result is used to answer the questions behind the experiment. In this example „how do we get the maximal response?“ Linked profilers let you find the desired optimum and explore the behaviour of the mixture in the vicinity of the optimal point. Also the whole experimental space can be analyzed to gain better understanding of the system‘s behaviour.
  9. 9. Copyright © 2012, SAS Institute Inc. All rights reserv ed. More mixture factors and more response variables don‘t make it more difficult. The whole design process scales to arbitrary volumes. It‘s just a bit more typing.
  10. 10. Copyright © 2012, SAS Institute Inc. All rights reserv ed. Profilers still show the response variables from all aspects,yet the factor profiler (top left) gives the best overview and access to data and models. Here all profilers are set to center values.
  11. 11. Copyright © 2012, SAS Institute Inc. All rights reserv ed. Same dashboard as before, all profilers set to the optimum value, i.e. hardness close to ist target value of 50 at minimal achievable cost.
  12. 12. Copyright © 2012, SAS Institute Inc. All rights reserv ed. Very often a mixture is not used „as is“ but as part of a process.
  13. 13. Copyright © 2012, SAS Institute Inc. All rights reserv ed. Responses along with their goals, factors with their roles and test ranges and constraints are defined just as in the simpler examples before. Mixture components and process variables are specified in the same manner.
  14. 14. Copyright © 2012, SAS Institute Inc. All rights reserv ed. Mixture ComponentsProcess Factors All factors set to optimal values. Yellow are the most influential ones. Time doesn‘t impact any of the response variables so it can be set to the shortest time possible to save money.
  15. 15. Copyright © 2012, SAS Institute Inc. All rights reserv ed. Know the design space Place experiments where exactly they are needed. Make as few experiments as possible, but no less (adapted from Einstein) Summary 1
  16. 16. Copyright © 2012, SAS Institute Inc. All rights reserv ed. THE ULTIMATE CHALLENGE COMBINE MIXTURE AND PROCESS FACTORS IN ONE EXPERIMENT Mixture Process Summary 2
  17. 17. Copyright © 2012, SAS Institute Inc. All rights reserv ed. Put all relevant factors into one consistently designed experiment Get answers in a predictable process Get Information Get in Touch www.jmp.com www.jmp.com/trial Webcast on Demand JMP Offices JMP DOE Brief JMP Contact JMP YouTube Channel Bernd Heinen Linkedin Bernd Heinen Xing Summary 3

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