A winning business strategy lays out a path with small steps that allows for changes in direction along the way. Our “SCO” flowchart for experimenters is a prime example of such a template for success. Its tried-and-true* core is screening (“S”), characterization (“C”) and optimization (“O”). However, we added one last, but perhaps most important, step: Confirmation. Let’s dive into the Stat-Ease strategy for experimenters and find out what makes it work so well.
Our starting point is the Screening design. Screening designs provide a broad, but shallow, search for previously unknown process factors. TIP – don’t bother screening factors that are already known to affect your responses! Newly discovered factors—the “vital few” carry forward into the next phase of experimentation, with the “trivial many” being cast aside. By using medium-resolution (Res IV) designs—color-coded yellow in the primary two-level factorial builder in Design-Expert® software (DX), you can screen for main effects even in the presence hidden interactions. If runs must be closely budgeted, take advantage of the unique Minimum-Run Screening designs in DX.
Moving ahead to Characterization with the vital-few screened factors plus the big one(s) you set aside, the identification of two-factor interactions becomes the goal. This necessitates a high-resolution design (Res V or better)—the green ones in DX’s main builder. To save runs, consider a Minimum-Run Characterization design. Either way, be sure to add center points at this stage so you can check curvature. If curvature is NOT significant, then your mission is nearly complete—all that remains is Confirmation!
If curvature does emerge as being significant and important, then move on to Optimization using response surface methods (RSM). The beauty of RSM is that, with the aid of DX and its modeling and graphics tool, you can see by contour and 3D maps where each response peaks. Also, via numerical tools, DX can pinpoint the setup of factors producing the most desirable outcome for multiple responses. Then it lays out a compelling visual of the sweet spot—the window where all specifications can be achieved.
Last, but not least, comes Confirmation, during which you do a number of runs to be sure you can reproduce the good results. Use the special tool for confirmation that DX provides to be confident of this.
In conclusion, DOE does not provide a single template that you can repeat over and over. You must apply a strategy, such as the one outlined here, that adapts at each stage of your journey to a new and improved process that saves money at an improved quality level. Why not go after it all!
*Strategy of experimentation: Break it into a series of smaller stages, Mark Anderson, StatsMadeEasy blog, 6/20/11.
Two-level factorial designs are highly effective for discovering active factors and interactions in a process, and are optimal for fitting linear models by simply comparing low vs high factor settings. Super-charge these classic designs by adding center points!
(Read to the end for a bonus video clip!)
There is an underlying assumption that the straight-line model also fits the interior of the design space, but there is no actual check on this assumption unless center points (the mid-level) are added to the design. Figure 1 illustrates how the addition of center points helps you detect non-linearity in the middle of the experimental space.
A center point is located at the exact mid-point of all factor settings. The example in Figure 2 shows a cookie baking experiment where the center point is replicated four times at the mid-point of 10 minutes and 350 degrees.
Multiple center points (replicates) should be randomized throughout the other experimental conditions to get an adequate assessment of whether the actual values measured at this point match what is predicted by the linear model. This is called a test for curvature. If the curvature test is significant, this is considered evidence that a quadratic or higher order model is required to model the relationship between the factors and the response. If the curvature test is not significant, then it is okay to assume that the linear model fits in the middle of the design space.
In Design-Expert® software, version 11, the curvature test is placed in front of the ANOVA when you have included center points in the design. This immediately shows you if the model is significant, and if the curvature is significant. As illustrated by the screen shot below (Figure 3), advice is provided to guide your next steps.
New to DX11, is the “Remove Curvature Term” button. If curvature is significant and you click on this button, then the regression modeling is done by using all the data, including the center points. Because the actual center points are not sitting in the middle of the design space, it is highly likely that the resulting model will be poorly fit and the lack of fit statistic will be significant. Then, click on “Add Curvature Term” to put the curvature effect back into the model, thus accounting for the information in the middle of the design space.
Ultimately, if curvature is significant, the recommendation is to augment the design to a response surface design to better model the relationship between the factors and the response. If curvature is NOT significant, then proceeding with the analysis is acceptable.
Bonus: Check out Mark’s 1-minute video on this topic: MiniTip 2 - Center points in factorials
Stat-Ease has moved approximately 1 mile north up to Broadway Place West. We are located on the top floor (foreground of photo). Our building is just off Hwy 36 and Industrial Blvd., east of downtown Minneapolis. Our new postal address is:
1300 Godward Street NE, Suite 6400
Minneapolis, Minnesota 55413-2561
Please make note and feel free to stop by and visit us!
Stat-Ease, Inc. and Ritme, scientific solutions hosted the 7th European DOE User Meeting & Workshop in Paris, France this past June. The DOE User Meeting was held at Le CNAM (the National Conservatory of Arts and Crafts) in the heart of Paris, close to the Louvre and Notre Dame. All agreed that this bi-annual event proved to be both informative and fun! The dinner cruise on the Seine was a highlight of the conference for all with gorgeous views of Paris landmarks and absolutely perfect weather. Vive la France!
Stat-Ease, Inc. and Ritme, scientific solutions invite you to attend the 7th European DOE User Meeting & Workshop in Paris, France this June 6–8. The DOE User Meeting will be held at Le CNAM (the National Conservatory of Arts and Crafts) in the heart of Paris, close to the Louvre and Notre Dame. This bi-annual event is always a favorite with attendees—both informative and fun! Besides the interesting presentations and learning opportunities, at this year's event in Paris you will have the opportunity to go on a dinner cruise on the River Seine in an all-glass boat, taking in the sights and sounds of this beautiful city!
The conference will include a pre-conference workshop on June 6, followed by the 2-day user meeting on June 7–8 with talks by DOE Experts, as well as practical case study applications by industry practitioners. We will explore the latest design of experiments (DOE) techniques, and demonstrate new features in Design-Expert software, version 11. In addition, you will have the opportunity to get help from DOE consultants on your own particular applications. Our expert trainers are offering a pre-meeting workshop on June 6th. Sign up for Practical DOE “Tricks of the Trade” and learn advanced DOE skills that you can take home and apply. This is your chance to network, increase your DOE knowledge, learn from others' successes and challenges—all while visiting the City of Lights!
You won't want to miss this fun and educational conference in Paris. For more details and to register for the 2-day meeting and/or workshop click here. We hope to see you in Paris!