1: Alert about DOE FAQ Alert: Now going to bimonthly issues

2: FAQ: Model selection and reduction from response surface method (RSM) experiments

Original Question:

From a Mechanical Engineer studying for a Master’s Degree:
“How do you know which terms you have to select?  I notice in the predictive model you revised for me, that only some terms are selected by Design-Expert.  Is there any method you follow for model reduction?”

Answer:

From Stat-Ease Consultant Brooks Henderson:
“I usually start with the model suggested (underlined) by Design-Expert (“DX”) on the Fit Summary screen.  Then, I remove any terms that are not-significant.  You can let DX remove non-significant terms by turning on “Backward” selection with the alpha out value that you choose.  For example, below I started with the two-factor (“2FI”) model and it will remove any terms with p-values higher than 0.1000 (Alpha out value).  Make sure to click “yes” if asked about hierarchy and any terms needed for hierarchy will be put back in the model (even if they are insignificant.)

Backward selection for model reduction

As I am selecting a model, I’m looking to only keep significant terms or terms needed for hierarchy and looking for good agreement between adjusted and predicted R-squared values (less than 0.2 difference).  I would also like the raw R-squared values to be as high as possible and the Adequate Precision to be greater than 4.  After that, I check the diagnostics and that’s really all there is to it.”

(Learn more about model selection by attending the two-day computer-intensive workshop “Response Surface Methods for Process Optimization”. Click on the title for a complete description.  Link from this page to the course outline and schedule.  Then, if you like, enroll online.)

3: FAQ: How to tell if mixture components are synergistic

Original Question:

From a Pesticide Formulator:
“When using the simplex lattice design, combining two or more components, is there a way to determine if results are synergistic or additive?”

Answer:

From Stat-Ease Consultant Shari Kraber:
  “Look at the coefficients of two-component terms (like AB) in the ANOVA. If the pseudo coefficient is positive, the results are synergistic.  If the coefficient is negative, the results are antagonistic.  Alternatively, you can look at the 3D model graph and see if the curves are going up or down.”

PS from Mark: This formulator hopes to kill bugs—the more the better, so Shari is dead on (pun intended) with her answer.  However, for responses that must be minimized, synergism comes from negative coefficients for non-linear blending terms.  For example, see the case study on blending gold with copper at the outset of our Primer on Mixture Design.  The goal is to reduce the melting point of a metal mixture used by goldsmiths to solder jewelry-parts.

(Learn more about mixture design and model interpretation by attending the computer-intensive two-day workshop "Mixture Design for Optimal Formulations."  Click on the title for a complete description of this class.  Link from this page to the course outline and schedule.  Then, if you like, enroll online.)

4: Expert-FAQ: Cannot run RSM within entire cubical region—how to set a multifactor constraint that cuts out infeasible region

Original Question:

From a Compounding Engineer:
“I would like to run a three-factor response surface method (RSM) design in the ranges of A: 100-200, B: 100-300 and C: 400-500.  However, because of machine limitations, we cannot process in the entire cubical region.  I would still like to run this design since we generally get the best properties along the hypotenuse of the triangle.  Aliasing, as far as I am concerned, looks ok for a quadratic model.  But the design will not be orthogonal.  What are the risks of running DOE's like this?”

Answer:

From Stat-Ease Consultant Wayne Adams:
 “Rather than setting up a cubical experiment and deleting 'bad' runs with combinations that cannot work, build the design with constraints by entering an inequality under the Edit Constraints tool.  The biggest problem with simply deleting runs is that the numeric optimization may allow solutions to occur in the 'impossible' region.

Here’s the process for dealing with your particular constraints: Identify the 'bad' vertex—in this case A cannot be low while B is high.  Thus you must exclude the 100, 300 vertex on the A x B face of the cube.  The C factor is not involved in this constraint.

After drawing a constraint line, figure out for each factor whether the 'good' area is less than or greater than the constraint line.

For greater-than constraints (the constraint for A) the formula is (A – LL) / (CP – LL), for less-than constraints (the constraint for B) the formula is (UL-B) / (UL – CP), where  UL is upper limit, LL is lower limit, and CP is Constraint Point.

For A the numbers are A - 100 / (200 – 100) = A – 100 / 100.  The formula for factor B is (300 - B) / (300 – 100) = (300 - B) / 200.

Placing these formula into the inequality and simplifying yields this inequality:
  1 <= (A – 100) / 100 + (300 – B ) / 200

Multiplying through by 200 produces this result:
  200 <= 2A – 200 + 300 – B

Finally, subtracting 100 from both sides of the equation reduces it to:
  100 <= 2A - B

This is what you should enter for your particular constraints.”


Entering a multifactor constraint


Constrained region with design points shown for factors A & B—C fixed at its high (+1) level

PS from Mark: In Version 8 of Design-Expert software, we now provide a very handy tool designed by Wayne that does all this constraint-calculating for you.  To see a demonstration, follow this link to the “Multifactor RSM (Optimal design)” tutorial.

5: Book giveaway: Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3rd Ed. by Myers, Montgomery and Anderson-Cook

(Sorry, due to the high cost of shipping, this offer applies only to residents of the United States and Canada.)

Simply reply to this e-mail by March 1st if you'd like one of three copies of Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3rd Ed. by Myers, Montgomery and Anderson-Cook.  We no longer re-sell this text due to its ready availability via the publisher, Wiley, and online booksellers such as Amazon.  See Wiley’s details on the textbook here.

(Reminder: If you reside outside the US or Canada, you are NOT eligible for the drawing because it costs too much to ship the books.)