Here's another set of frequently asked questions (FAQs) about doing design of experiments (DOE), plus alerts to timely information and free software updates. If you missed previous DOE FAQ Alerts, please click on the links at the bottom of this page. If you have a question that needs answering, click the Search tab and enter the key words. This finds not only answers from previous Alerts, but also other documents posted to the Stat-Ease web site.
Feel free to forward this newsletter to your colleagues. They can subscribe by going to http://www.statease.com/doealertreg.html. If this newsletter prompts you to ask your own questions about DOE, please address them via mail to: StatHelp@StatEase.com.
Here's an appetizer to get this Alert off to a good start:
See http://www.scaled.com/projects/tierone/ for details on SpaceShipOne, the first private spacecraft to exceed an altitude of 328,000 feet twice within the span of a 14-day period, thus claiming the ten-million dollar Ansari X-Prize. Check out the photos and video of this historic event in aerospace. SpaceShipOne, solely funded by Microsoft mogul Paul Allen, was designed by aviation legend Burt Rutan and built by his company, Scaled Composites. Composites are becoming the material of choice for aircraft as evidenced by Boeing's new Dreamliner. See http://www.boeing.com/commercial/787family/index.html for information on this new airplane, designated "7E7."
Here's what I cover in the body text of this DOE FAQ Alert (topics that delve into statistical detail are designated "Expert"):
1. FAQ: How many replicates to perform versus signal to noise
2. FAQ: Combining components in a mixture design
3. Info alert: Response surface methodology (RSM) is featured in two articles, one for a biotech application, the other on optimal design in the presence of multifactor linear constraints
4. Events alert: Link to a schedule of Stat-Ease appearances
5. Workshop alert: Experiment Design Made Easy is coming to Anaheim in December and San Jose in January
PS. Quotes for the month regarding political polls:
—In terms their readers will understand, Time magazine tries to explain sampling error in US Presidential polls.
—The National Council on Public Polls advises journalists on sampling error and how they should report close races.
"I caught your article in the September Stat-Teaser newsletter on 'Power—How Many Runs Do I Need' [posted at http://www.statease.com/news/news0409.pdf]. The article covers the relationship between number of runs and signal-to-noise (S/N) ratio, and how to take S/N ratio into account when selecting number of runs. How does this compare/contrast to the number of replicates at a given condition? Does Design-Expert® software have a methodology for determining how many replicates should be run at a given point to overcome the effect of normal process variation?"
Answer (from Stat-Ease consultant Pat Whitcomb):
"The graph in figure 2 shows how many runs are needed to have a high probability (about 80%) of seeing an effect whose size is of interest (the signal) divided by standard deviation of the process (the noise). If you want to find an effect of 10 units in size and normal process variation is 12.5 units then using figure 2 for a ratio of 0.8 (10/12.5) shows that about 50 runs are required. If you are planning a 2^3 full-factorial design that means you need about 6 replicates (48 total runs). If you are planning a 2^4 full factorial you can get by with 3 replicates (48 total runs).
Another question might be can I repeat the measurement rather than replicate the DOE run? The answer is yes, but in this case you enter the average of the repeated measures, not the individual results. Independent measurements will reduce the measurement system component of the total process variation. For example, let's say that the measurement system is contributing 75% of the total variation. Then repeating the measure would have the following effect:
Total variation = SqRt[(0.25*12.5^2) + ((0.75*12.5^2)/2)] = 9.9
The signal-to-noise ratio then becomes 10/9.9 or approximately 1. From figure 2 you can see that a ratio of 1 requires only about 35 runs; instead of the 48 first estimated.
Only with knowledge of the variance components and the costs of replicating the DOE run and/or repeating the measure can one decide which is the best option."
(Learn more about power and replication by attending the three-day computer-intensive workshop "Experiment Design Made Easy." See http://www.statease.com/clas_edme.html for a course description. Link from this page to the course outline and schedule. Then, if you like, enroll online.)
"When I combine components, is there anywhere I can look back and find out which components I combined? I lose track sometimes!"
Answer (from Stat-Ease consultant Pat Whitcomb):
Like real mixtures, such as adding vodka to orange juice, it's easy to combine components with Design-Expert but difficult to separate them again. Therefore I advise you save a backup of your file with a "before combo" suffix or the like and save it afterwards with the original name. Also, consider renaming your components to record what you combined.
(To learn more about combining components, attend our "Mixture Design for Optimal Formulations" workshop. For a description, see http://www.statease.com/clas_mix.html. Link from this page to the course outline and schedule. You can enroll online by linking to the Stat-Ease e-commerce page for workshops.)
Desktop Engineering's November issue of Elements of Analysis features an article by Pat Whitcomb and I titled "Response Surface Methods for Process Optimization." It details the application of optimal designs for nonorthogonal constrained spaces. Click on http://makeashorterlink.com/?T20812CA9 to view it, or go to http://www.deskeng.com/supplements/elements_of_analysis/ (update--3/07: these links have changed to http://www.deskeng.com/Previous-Elements-of-Analysis/Elements-of-Analysis-%11-November-2004/Response-Surface-Methods-for-Process-Optimization-20041101151.html) and follow the link to the article from there.
For an article that details application of response surface methodology (RSM) for biotech, link via http://www.babonline.org/bab/037/0225/bab0370225.htm (Update 3/07: this page requires subscription to view) "The Influence of Physico-Chemical and Process Conditions on the Physical Stability of Plasmid DNA Complexes using Response Surface Methodology." This April 2003 paper from Biotechnology and Applied Biochemistry (Vol. 37, pp. 225-234) introduces a new method of assessing the engineering effects of process and material factors on the colloidal properties of plasmid-DNA delivery systems based on RSM and experimental techniques.
(Learn more about RSM by attending the three-day computer-intensive workshop "Response Surface Methods for Process Optimization." See http://www.statease.com/clas_rsm.html for a complete description. Link from this page to the course outline and schedule. Then, if you like, enroll online.)
Click on http://www.statease.com/events.html for a list of appearances by Stat-Ease professionals. We hope to see you sometime in the near future!
Experiment Design Made Easy, our three-day computer-intensive workshop on the basics of DOE will be presented twice in California this Winter:
—December 7-9, 2004 in Anaheim
—January 25-27, 2005 in San Jose.
See http://www.statease.com/clas_pub.html for schedule and site information on all Stat-Ease workshops open to the public. To enroll, click the "register online" link on our web site or call Stat-Ease at 1.612.378.9449. If spots remain available, bring along several colleagues and take advantage of quantity discounts in tuition, or consider bringing in an expert from Stat-Ease to teach a private class at your site. Call us to get a quote.
Mark J. Anderson, PE, CQE
PS. Quotes for the month regarding political polls:
"Pollsters usually interview about 1000 registered voters and, thanks to the magic of statistical math, 95% of the time those 1000 accurately reflect the opinions of the entire country, give or take a margin of error of plus or minus 3%."
—From "The Top Line on Polls" by Mitch Frank, p.20, Time magazine, 11/1/04.
"Sampling error raises one of the thorniest problems in the presentation of poll results: For a horse-race poll, when is one candidate really ahead of the other?
Certainly, if the gap between the two candidates is less than the sampling error margin, you should not say that one candidate is ahead of the other. You can say the race is "close," the race is "roughly even," or there is "little difference between the candidates." But it should not be called a "dead heat" unless the
candidates are tied with the same percentages. And it certainly is not a statistical tie unless both candidates have the same exact percentages.
And just as certainly, when the gap between the two candidates is equal to or more than twice the error margin—6 percentage points in our example—and if there are only two candidates and no undecided voters, you can say with confidence that the poll says Candidate A is clearly leading Candidate B.
When the gap between the two candidates is more than the error margin but less than twice the error margin, you should say that Candidate A "is ahead," "has an advantage" or "holds an edge." The story should mention that there is a small possibility that Candidate B is ahead of Candidate A."
—From "20 Questions A Journalist Should Ask About Poll Results," Third Edition, Sheldon R. Gawiser, Ph.D. and G. Evans Witt, posted at http://www.ncpp.org/qajsa.htm (Update 3/07: link has changed to http://www.ncpp.org/?q=node/4) by the National Council on Public Polls (NCPP).
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