>>>>>>>>>>>>>>>>>>>>>>>>>>DOE FAQ Alert<<<<<<<<<<<<<<<<<<<<<<<<<< Issue: Volume 1, Number 2 Date: April 2001 From: Mark J. Anderson, Stat-Ease, Inc. (http://www.statease.com) "Statistics Made Easy" (tm) Dear Experimenter, Here's our second issue in an ongoing series of e-mails with answers to frequently asked questions (FAQs) about doing design of experiments (DOE), plus alerts to timely information and free software updates. Starting this issue, topics that delve into statistical detail will be rated "X" for eXpert. Read these only if you dare to eXpand the eXtent of your knowledge of statistics for eXperimenters. Before I get into the meat of this message, I offer this appetizer: click http://mathdl.maa.org/mathDL/4/ offered by the Journal of Online Mathematics and its Applications (JOMA). See neat graphics made by various applets that illustrate various functions. Test your knowledge of math! Here's what I cover in the body text of this DOE FAQ Alert: 1. FAQ: Botched runs in fractional two-level factorial designs - When to enter actual versus planned factor level 2. X-FAQ: How to set up a Latin square with Design-Expert(R) 3. X-FAQ: Choosing alpha for a Central Composite Design (CCD) (Response Surface Method (RSM)) 4. Software alert (2nd): Upgrade patch available for Design-Expert version 6 software (link to free download) 5. Info alert: "DOE It Yourself" ideas 6. Events alert: A heads-up on DOE talks and demos 7. Workshop alert: FREE textbook for early enrollees of "Robust Design, DOE Tools for Reducing Variation" workshop - a must for students of the SIX SIGMA approach to quality improvement. You received this newsletter because of your expressed interest in DOE via an inquiry to Stat-Ease, or registration as a user of the company's software and/or status as a graduate of its DOE workshops. It's easy to unsubscribe (leave our list) - just follow the instructions at the bottom (footer) of this message. PLEASE DO NOT REPLY DIRECTLY TO ME TO UNSUBSCRIBE, CLICK ON THE MAILTO LINK AT THE END OF THIS E-MAIL. Feel free to forward the DOE FAQ Alert e-mail to any friends and colleagues who need tools for doing DOE. They can then subscribe (join our list) if they like by going to the Internet link shown at the end of this message. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1 - FAQ: Botched runs in fractional two-level factorial designs - When to enter actual versus planned factor levels -----Original Question (Part a)----- From: California "We conducted a 4-factor [8 run] half-fractional factorial. During one run the temperature rose above the upper limit. Do you think that it is wise to delete this run, or would it be best to plug in the data, knowing that the run parameters [factor levels] were not accurate [off target]?" Answer: When an input value deviates significantly from set point, you should enter the actual data. Design-Expert ("DX") or Design-Ease(R) ("DE") will then take this deviation into account when it calculates effects. However, don't bother changing input values when they exhibit normal variation. For example, let's say you set your temperature at 100 but it measures 99.8, 100.1, etc. In this case leave the input values at 100 because this is how you will set your temperature in future, assuming it comes out best. The variation in set point will be expressed as variation in your response, which gets taken into account in the statistical analysis. If you are not sure whether to change the input levels to what you actually observe, try it both ways, but be sure to save your original design first before you make the changes. One more suggestion regarding deviant inputs: Check the outlier t value on the response(s). If it falls outside of the suggested limits (plus or minus 3.5), consider ignoring the run(s). This can be done very easily in version 6 of DE or DX by right-clicking the button to the left of any given row(s) and choosing Toggle Ignore. Warning - missing runs may create unforeseen problems with aliasing as you will see in next month's FAQ, "The negative impact of ignored run(s) on alias structure and how to repair the damage," an X-rated sequel to this question. (Learn more about fractional factorial design by attending the 3-day computer-intensive workshop "Experiment Design Made Easy". Go to http://www.statease.com/clas_edme.html for a description and links to the course outline and schedule.) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 2 - X-FAQ: How to set up a Latin square with Design-Expert -----Original Question----- From: Arizona "I am using the student version of DX-6 with the DOE text by Montgomery for a class at Arizona State University. I was just curious if the software can accommodate Latin square designs. My attempts at using the general factorial window for Latin squares were not successful." Answer: You can do a Latin square design with Design-Expert (or Design-Ease). To learn how, refer to the mini-tutorial at http://www.statease.com/rocket.html , which shows a case study on burn rate of five different formulations of rocket propellant used in aircrew escape systems.* In this case, a 5 x 5 Latin square blocks out two nuisance factors: batch of raw material and operator. PS. Latin square refers to the arrangement of the Latin letters A, B, C,... into a square array such that each letter appears once in each column and once in each row of the square. It was first used in agricultural research to adjust for fertility differences in two physical directions. To see a neat picture of an actual Latin Square field experiment go to http://www.stat.ucla.edu/history/latin_square.gif . *(From Section 4-2, page 144 of Montgomery's "Design and Analysis of Experiments." You can buy this book, and others on DOE, from the e-commerce site at http://www.statease.com/prodbook.html .) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 3 - X-FAQ: Choosing alpha for a Central Composite Design (CCD) (Response Surface Method (RSM)) -----Original Question----- From: North Carolina "I am having a tough time trying to decide between two CCDs (one with alpha=1.682 and the other with alpha=1). I have three factors, each of which can vary from 0 to 2. Negative values are inadmissible for the factors. The first design is generated with alpha=1 (face-centered cuboidal design). The second design is generated by checking the "Factors ranges entered in terms of alpha" box and setting alpha=1.682 (spherical design). When I evaluate the designs, the StdErr graphs for the second design look a little "worse" than the first one. However, the power seems to be higher for the second design." Answer: First of all, you are to be commended for recognizing that if you set the factorial levels (plus or minus one) at your operating constraint of 0 and 2, the axial (star) points in the resulting CCD (with default alpha=1.682) would go out of bounds. By changing alpha to 1, you pull the axial points into the face of the cube, which creates a design that's no longer rotatable (spherical). This face-centered design produces a cuboidal standard error pattern. The other option, inscribing the CCD within the 0 to 2 cube (by entering these values as the alphas), preserves rotatability and other desirable statistical properties, but leaves the corners uncovered. When you choose standard CCD's like this, we advise that you stay within the "cube" (the factorial portion) for making predictions because this is where you get the best information. Your region of interest then becomes quite small (only about 20% by volume!) for the inscribed CCD with alpha =1.68 versus the face-centered design option. The bottom line from a purely practical perspective then might favor your first choice, the face-centered CCD, which hits the extreme vertices (corners of the cube). However, the choice depends on your region of interest and subjective preferences. In any case, Design-Expert's unique Design Evaluation provides lots of fodder (statistical measures) for discussion on this issue. (For more details, including helpful pictures, on the various options for setting up central composite designs (CCD's) see http://www-09.nist.gov/div898/handbook/pri/section3/pri3361.htm a section of the "Engineering Statistics Handbook" co-sponsored by the National Institute of Standards and Technology (NIST) and Sematech, an R&D consortium of semiconductor manufacturers. Learn more about RSM, including design evaluation, by attending the 3-day workshop "Response Surface Methods for Process Optimization". See http://www.statease.com/clas_rsm.html for a description and links to the course outline and schedule.) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 4 - Software alert (2nd): Free patch for Stat-Ease version 6 If you own a permanently licensed copy (individual or networked) of Design-Ease(R) or Design-Expert version 6 (DE6 or DX6), go to www.statease.com/soft_ftp.html#dx6updt for downloads that will patch your software with the latest enhancements. If you do not currently use Stat-Ease software, download a fully-functional free trial of DX6 at http://www.statease.com/dx6trial.html which you can use at no cost for 30 days. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 5 - Info alert: "DOE It Yourself" ideas Go to http://www.statease.com/pubs/doe-self.pdf to view or download a collection of fun science projects that you can do at home with your children or in class with your students. You don't need any unusual equipment. The details are sketchy but they should be sufficient for creative experimenters. Use your imagination! If you have your own favorite DOE that anyone can do, send me the details. I'll add it to the list. ---Mark ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 6 - Events alert: A heads-up on DOE talks and demos Click http://www.statease.com/events.html for a listing of where Stat-Ease consultants will be giving talks and doing DOE demos. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 7 - Workshop alert: FREE textbook for early enrollees of the "Robust Design, DOE Tools for Reducing Variation" workshop - a must for students of SIX SIGMA approach to quality improvement. Sign up for the Robust Design, DOE Tools for Reducing Variation (RDRV) workshop,* to be held in Philadelphia on June 5-7, and get a free copy of Montgomery and Myers "Response Surface Methodology" book. This offer, worth almost $100, expires on May 7, so don't delay in enrolling. Call 612-378-9449 and ask Sherry Klick, Stat-Ease workshop coordinator, if we still have openings for this workshop, a must for students of the SIX SIGMA approach to quality improvement. *(See http://www.statease.com/clasrdrv.html for a description and outline for "Robust Design, DOE Tools for Reducing Variation," a three-day computer-intensive workshop.) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I hope you learned something from this issue. Address your questions and comments to me at: Mark@StatEase.com PLEASE DO NOT SEND ME REQUESTS TO SUBSCRIBE OR UNSUBSCRIBE - FOLLOW THE INSTRUCTIONS AT THE END OF THIS MESSAGE. If you missed the first DOE FAQ Alert, issued in early March, go to http://www.statease.com/news/faqalert1.txt . Sincerely, Mark Mark J. Anderson, PE, CQE Principal, Stat-Ease, Inc. ( http://www.statease.com ) Minneapolis, Minnesota USA "Experiment is the sole interpreter of the artifices of nature." - Leonardo Da Vinci Trademarks: Design-Ease and Design-Expert are registered trade- marks of Stat-Ease, Inc. Acknowledgements to contributors: - Students of Stat-Ease training and users of Stat-Ease software - Fellow Stat-Ease consultants Pat Whitcomb and Shari Kraber (see http://www.statease.com/consult.html for resumes) - Statistical advisor to Stat-Ease: Dr. Gary Oehlert ( http://www.statease.com/garyoehl.html ) - Stat-Ease programmers, especially Tryg Helseth ( http://www.statease.com/pgmstaff.html ) - Heidi Hansel, Stat-Ease communications specialist, and all the remaining staff ( http://www.statease.com/se_staff.html ) DOE FAQ Alert - Copyright 2001 Stat-Ease, Inc. All rights reserved. Subscribe (join our list) by going to: http://www.statease.com/doealert.