Stat-Ease | The DOE FAQ Alert Vol. 12 No. 3

1: Newsletter alert: The May issue of the Stat-Teaser features an educational experiment by a team of college students on germination of beans

Many of you have received, or soon will, a printed copy of the latest Stat-Teaser, but others, by choice or because you reside outside of North America, will get your only view of the May issue at this link. It features a report by me on results from an experiment done by a team of Auburn University students for their chemical engineering lab. See the results of their matchup of kidney versus lima beans subjected to varying conditions for germination. This is a good one to try at home with your budding scientists!
This Stat-Teaser also provides a fun and informative article by Consultant Brooks Henderson on “MONEY in BaseBALL”.* He applies tools in Design-Expert software to address this question: “Does More Money Equal More Wins?”

Thank you for reading our newsletter. If you get the hard copy, but find it just as convenient to read what we post to the Internet, consider contacting us to be taken off our mailing list, thus conserving resources. (Note: You will be notified via the DOE FAQ Alert on new newsletter posts.) In any case, we appreciate you passing along hard copies and/or the link to the posting of the Stat-Teaser to your colleagues.

*The capital letters pay homage to “Moneyball,” a book that touted the value of statistics for helping teams win at baseball. If Brad Pitt had played the part of the sabermetrician in the movie (not that nerdy-looking fellow), I’d have liked it better. ; )

2: FAQ: Power results provided in the design-building wizard do not appear in subsequent evaluation of the test matrix

Original Question:

From a Quality Assurance Consultant:
“When designing an un-replicated fractional-factorial experiment in your software I calculated power using the wizard. However, after completing the build, the Evaluation says that ‘power is not defined’ for my test matrix. Where did I go wrong? Also, how can the program estimate power when we don’t yet know the number of the insignificant effects that will be available to calculate error?”

Answer:

From Stat-Ease Consultant Wayne Adams:
“The reason power cannot be defined by the Evaluation is that it defaults to the designed-for factorial model, which, without replicates, uses up all the available degrees of freedom, in other words, nothing is left over to estimate error, thus no test for significance can be performed. As a general rule for screening experiments, one can expect about as many significant effects as there are factors—this is just a guess, but we must start somewhere a priori.

The power calculated during the design build can be reproduced in the evaluation afterwards by simply changing the model to main effects as shown below.

Changing Evaluation to Main Effects
Changing Order to Main Effects in Design Evaluation

In this case, the signal-to-noise ratio is one, so the relevant power is produced from default settings in Design-Expert—the middle column highlighted in the screen shot (a good result!).

Resulting power calculation

If you need to evaluate a different ratio, change the default via the Options provided prior to these Results under the Model setup screen. Contact Stat-Ease for further help on this if needed. We can be reached most readily via [email protected], or just give us a call and ask for assistance from a statistical consultant."

(Learn more about power by attending the two-day computer-intensive workshop Experiment Design Made Easy. Click on the title for a description of this class and link from this page to the course outline and schedule. Then, if you like, enroll online.)

3: Expert-FAQ: Finding an equivalency between simple sample-size equations and the power calculations done by Stat-Ease software for sizing experiment designs

From a Senior Mechanical Engineer:
“Often we need to calculate the suitable sample size for some measurement. For example, let’s say an engineer needs to estimate a plate thickness (t) within ±0.005 mm confidence interval at 95% confidence. Assume a standard deviation in thickness of 0.020 mm. In this case we must repeat our measure 62 times according to this standard sample-size equation:

The results match with output from our general statistical software, a standard package used in industry for quality assurance purposes. However, now I am using Design-Expert to experiment on things such as plate thickness. How do I connect sample-size calculations like that shown above to what your software does with its power calculator for factorial designs?”

From Stat-Ease Consultant Pat Whitcomb:
“As I will explain, the expected sample size should be four times larger for a given difference “d” when this is a difference between two means (as opposed to being the half-width of a confidence interval on a single mean). It helps to start with this picture showing what’s meant by ‘half-width’ (the segment labeled ‘d’):

The half-width of a confidence interval

The formula for a confidence interval is:

If you assume sigma is known without error then:

For your problem z equals 1.96 (for α = 0.05), σ equals 0.02 and d equals 0.005—resulting in your sample size of 62.

As pictured below, a difference in two means is another situation altogether:

Difference between two means

The formula for a t-test is:
Formula for t-test

where N is the total design size with half the runs at –1 and half at +1.

If you assume sigma is known without error then:
Formula if you assume sigma is known without error 2

Formula if you assume sigma is known without error 2

4: Webinar alert: (Encore) Overview of Robust Design, Propagation of Error, and Tolerance Analysis

Response Surface Methods (RSM) can lead you to the peak of process performance. In this advance-level webinar encore presented on Wednesday, July 11 at 10:30 AM CDT*, Stat-Ease Consultant Pat Whitcomb will present an advanced-level webinar on robust design, propagation of error, and tolerance analysis. Propagation of error (POE) accounts for variation transmitted from deviations in factor levels. It finds the flats—high plateaus or broad valleys of response, whichever direction one wants to go—maximum or minimum; respectively. Tolerance analysis drills down to the variation of individual units, thus facilitating improvement of process capability.

If you are working to make your system more robust, this webinar is for you! It will be especially valuable to those involved in Design for Six Sigma (DFSS).

Stat-Ease webinars vary somewhat in length depending on the presenter and the particular session—mainly due to breaks for questions: Plan for 45 minutes to 1.5 hours, with 1 hour being the target median. When developing these one-hour educational sessions, our presenters often draw valuable material from Stat-Ease DOE workshops.

Attendance may be limited, so sign up soon by contacting our Communications Specialist, Karen Dulski, via [email protected]. If you can be accommodated, she will provide immediate confirmation and, in timely fashion, the link with instructions from our web-conferencing vendor GotoWebinar.

*(To determine the time in your zone of the world, try using this link. We are based in Minneapolis, which appears on the city list that you must manipulate to calculate the time correctly. Evidently, correlating the clock on international communications is even more complicated than statistics! Good luck!)

5: Info alert: Primer on DOE for pharma QbD, case studies on pharma & biopharma, plus (for change of pace!) a new example on DOE for non-manufacturing processes

All of you who work in process industries (whether regulated or not), consider “Framing Your QbD Design Space with Tolerance Intervals to Verify Specifications” as I’ve detailed for the May print issue of PharmaQbD in the article posted here.

Pharmaceutical Manufacturing explains how “Design of Experiments Helps Boost Key Intermediate Yield by 18%” at Codexis Laboratories in Singapore. See the story with graphics produced by Design-Expert via this link.

A heads-up for biochemists and the like: The March 2012 Issue of BioProcess International promotes use of DOE enabled by Design-Expert in this article on “Fed-Batch Cell Culture Process Optimization.” See Figure 2 and read the supporting details on the optimization workflow for this project by researchers at Life Technologies.

The list of inspiring experiments at “Achieving Breakthroughs in Non-Manufacturing Processes via Design of Experiments (DOE)” now includes a great example from the US Bureau of Census showing how they improved their survey response via a factorial design. I heard about this from Professor Dan Rand of Winona State—a fellow speaker at the ASQ Hiawatha (MN) Section meeting earlier this year.)

6: Reader response: Further details on folding over a resolution IV fractional factorial

From Timothy M Michaelson, Senior Consultant, Manufacturing Excellence Group, International Paper:“I wrote my masters paper on fractional factorials so I can provide some interesting details regarding FAQ 1 on “Fold-over on resolution IV fractional two-level factorial did not de-alias interactions” in your DOE FAQ Alert, Volume 12, Number 2, Mar/Apr 2012. When you fold over an even resolution two-level fractional factorial, the resulting fraction remains the same even-resolution fraction (e.g., IV+IV=IV, VI+VI=VI). However, when you fold over an odd resolution two-level fractional factorial, the resulting fraction becomes a higher even-resolution fraction (e.g., III+III=IV, V+V=VI). Therefore, if you want to de-alias interactions by full fold-over, you need to start with an odd resolution fraction.”

7: Conference Alert: [Second Notice!] 4th European DOE Meeting June 26-28 in Vienna

You are invited to participate in our Fourth European Design of Experiments (DOE) User Meeting in Vienna, Austria. Find all the details here .

The meeting will focus on DOE, with a special emphasis on Design-Expert software. Both the theoretical and practical aspects of DOE will be addressed, including the latest developments in the field. The two meeting days will include lectures by DOE experts, case study presentations by DOE practitioners, and an opportunity to consult with the experts about your DOE applications. Optional pre-meeting workshops will be presented to sharpen your skills with these powerful statistical tools. Oh, and let’s not overlook the opportunity for breaking away to spend time in Vienna—a magnificent city of world culture.

Consultant Brooks Henderson carries the Stat-Ease torch forward to the Quality by Design India 2012 conference (one of a series in this rapidly-developing nation) with our “Overview of DOE for QbD” workshop in Hyderabad on July 27. See the agenda here.

I will attend the 2012 Joint Statistical Meetings in San Diego on July 28-August 2. Follow this link to the details on this annual event. If you make it, please stop by our booth to do some ‘networking’.

Consultant Pat Whitcomb will present a talk on “How to Design Experiments when Categoric Mixture Components Go to Zero” for the 12th annual conference of ENBIS (European Network for Business and Industrial Statistics) in Ljubljana, Slovenia on September 9-13. For details go here.

Click here for a list of upcoming appearances by Stat-Ease professionals. We hope to see you sometime in the near future!

PS. Do you need a speaker on DOE for a learning session within your company or technical society at regional, national, or even international levels? If so, contact me. It may not cost you anything if Stat-Ease has a consultant close by, or if a web conference will be suitable. However, for presentations involving travel, we appreciate reimbursement for travel expenses. In any case, it never hurts to ask Stat-Ease for a speaker on this topic.