Design of Experiments
Design of experiments (DOE) is one of the most powerful and influential engineering tools for product yield improvements, new products or processes development, or for problem solving. As mentioned in my last column, process problems led me to a career in printed circuits, and quickly solving those problems led me to a bonus stock award and a great life. Even though I knew nothing about printed circuit manufacturing processes, I was able to quickly find the root causes of all the problems and fix them. My secret? Total quality control (TQC), statistics, and DOE.
Experimentation is the manipulation of controllable factors at different values to see their effect on some desired result. An engineer can use three methods of experimentation:
- Trial and error
- One factor at a time
- Design of experiments
Trial and Error
Hopefully a trained engineer will not use this technique. But in the rush to fix the problem, one might think they know the true root cause and start changing parameters. In my case, I didn’t know the parameters so first I talked to the other engineers, line-workers and supervisors and created a pareto of possible causes. Then I called the chemical suppliers and asked them what they thought was important. Lastly, I went to the industry bible, the Printed Circuit Handbook by Clyde Coombs, and read what it had to say. From this list I got an inkling of what the possible causes could be.
One Factor at a Time
The objective of any experiment is to establish a probable cause-and-effect relationship. The common sense approach is to make trial changes of the most likely factors contributing to the observed problem, keeping all other contributor variables constant during the experiment, and then seeing if a significant correlation can be established between the suspected cause and the effect. If the experiment with the factor chosen gives no conclusive results, the next most likely factor is tried in the same way. Although this experimental strategy sounds logical, as you can see in Figure 1, it tests only a part of the process matrix and only what you know (variables X1, X2 and X3 and changing one at a time from -1 to +1 levels). Four steps are involved in this process:
- Observation: Study all phases of the situation in which the effect to be controlled occurs.
- Reflection: Try to think of all the causes which might influence this effect. Consult with others who have had experience with this or similar situations.
- Trial: Try the influence of the most likely factor; if not successful, try the next most likely one, and so on.
- Check: With a purported relationship established, attempt to turn the effect on and off, like a water faucet, by varying the suspected cause back and forth between its different levels.
The common sense approach is always recommended as a first try. It is fast and cheap when it works— as it often does for confirming single or independent factors whose presence can be logically suspected. However, when it has been tried several times on a problem with no clear cut solution emerging, a more sophisticated approach is called for—that of statistical experimentation.
This was the situation when asked to help the printed circuit plant. Months of tests and experimentation had not resulted in finding a cause for the problems and the solution.
Figure 1: Experimental methods: Can be trial and error or factorial design of experiments (DOE) that is much more comprehensive and effective than one-factor-at-a-time method. The DOE software can be found in The NIST/SEMETECH e-Handbook of Statistical Methods[1].
Design of Experiments
I guess I was lucky to be exposed to engineering statistics early in my college education. I never took a statistics course from the math department; if I had I might have thought it to be boring. Instead, it came as part of the chemical engineering basics. Since there is no “higher math” in most statistics, it is a good introductory course for engineers and essential to analyze lab and experimental results that will be part of the science and engineering education. My first design of experiment was done by long-hand; then, we did it by punched cards, and finally, with our slide rules (guess that dates me!). It wasn’t until the HP PCB problem solving that I wrote a basic program to conduct my DOEs on an HP 2116 computer.
Critical to DOE was the type of variables. In production, qualitative factors can be more significant than quantitative factors. Important quantitative factors (variables) are usually controlled, but qualitative variables can change without notice. Qualitative factors include: time of the year, day of the week, production shifts, production line, individual workers or machines, supplier sources, maintenance frequency, and even source of water. If you remember in my second column, and Figure 6 contained therein, for DOE with “factors not all being quantitative,” “screening experiments” are called for, such as described by Plackett-Berman[1] and in Fractional Factorial[2] (center boxes in Figure 1). Other application areas are comparative, modeling and optimizing.
Screening experiments (also called fractional factorial) are test plan used for an initial scan of problems having a large number—usually six or more—of presumed independent variables. The purpose of such plans is to determine which variables have the largest effects on the dependent variables. Results show only main or first-order effects (interactions), only the sensitivity of Y to a significant change in X1, X2 or X3, etc. Generally, interaction and second-order effects are not detected in screening plans.
Once the independent variables have been reduced to four or less, full factorial experiments can be conducted to understand all interactions and if the responses are non-linear and linear equations can be developed. Further experimentation can be conducted as ‘evolutionary operations’ to discover optimum settings and performances.
In the HP PCB problems, indeed the causes of the problems were an interaction of Monday vs. Friday, Day Shift vs. Graveyard Shift, process tank #1 vs. #4, and chemical supplier source. It was the qualitative variables that were at the Root Cause! A “one-at-a-time” experimentation couldn’t duplicate the root cause.
Some Examples
The next three figures show four different PCB process DOE results. The first, in Figure 2, is an experiment to minimize shifting of innerlayers during multilayer lamination. The variable and levels were a full factorial design of three variables at two levels:
1. Vented panel borders: with venting and without venting
2. Tooling methods for layup: ¼-inch holes and four 1/8-inch slots-centerline
3. Lamination pressure: 294 PSI & 344 PSI
The results are the image shift in microns. The lowest shift was 76 μm using vented borders, ¼-inch peripheral holes and the higher pressure. Analysis shows that the tooling method has the most positive effect on shifting and interacts with panel venting (V).
Figure 2: An example of factorial design of experiments (DOE) in printed circuit manufacturing to minimize innerlayer shifting during lamination.
The second experiment, in Figure 3, uses optimizing photoresist exposure, developing and etching to provide the highest production yield. The variable and levels were a full factorial design of three variables at three levels (center point):
1. Exposure energy in mjoules: 70, 50 & 30
2. Developer speed in inches per minute: 45, 40 & 35
3. Etcher speed in inches per minute: 45, 40 & 35.
The variables were chosen with the center point being the current production process: 50 mjoules, 40 in/min developer and 40 in/min etcher. The highest yield was 95% using slower developer speed, lower exposure intensity, and the slower etcher. Analysis shows that the developer speed has the greatest effect on yield and interacts with etcher speed.
Figure 3: An example of factorial design of experiments (DOE) in printed circuit manufacturing to optimize yield in exposure, developing and etch.
The third experiment, in Figure 4, serves to find the highest hole quality in a multilayer board. The variables and levels were a full factorial design of four variables at three levels:
1. Drill methods: (-) resharpened 4-8 times (0) resharpened
2. Drill diameter: (-) 0.008” (0) .014” (+) 0.020”
3. Infeed rate: (-) xx in. per min. (0) xx in. per min (+) xx in. per min
4. Construction: (-)Std. Foil-Lam (0) Thick-prepreg w/foil-Lam (+) Std. Core-Lam.
The results are the hole quality (rms roughness %) and max. innerlayer mushrooming in microns.
The best quality was 0 microns mushrooming and
The fourth experiment, shown in Figure 4, is to further find the highest hole quality and to look at drilling productivity. The variables and levels were a fractional factorial design of three variables at two levels:
1. Drill method: (-) new drills (+) resharpened 6 times
2. Stack height: (-) 1 high (+) 3 high
3. Panel venting dams: (-) no-flow dams (+) full venting dams
The results are the hole quality (rms roughness %) and max. innerlayer mushrooming in microns.
The best quality was < 4% rms hole-wall roughness using a plane of new drill bits for stacks of 1-high with any appropriate venting dams. Analysis shows that the old resharpened drills could be used with drill stacks 3-high and has a usable hole-wall roughness but it interacts with drill infeed rates.
Figure 4: Two more examples of DOE for hole quality in multilayer boards. Full factorial design on the left was conducted to optimize drilled hole quality. Fractional factorial DOE on the right further optimizes hole quality and production productivity.
Notice that this last experiment was a fractional factorial. The power of a scanning experiment using the fractional factorial methodology is that N number of variables can be reviewed with only N+2 experiments. This is useful to find main effects, but not interaction, while later experiments will provide examination of interactions and optimization.
More on DOE
If you are new to DOE and would like to read more, there are very good primers at Six Sigma Tools and Templates, MoreStream.com, and ASQ.com: What is Design of Experiments (DOE)? If you have downloaded the “Engineering Statistical Handbook” and software mentioned in my second column, then you can go to Sections 1.3.3.12 or 4.3.1 “What is design of experiments (DOE)?” and practice the case studies.
If you take advice from others, then the one thing you should do is to download the Engineering Statistics Handbook and software from NIST: http://www.itl.nist.gov/div898/handbook/stoc.htm.
I cannot guarantee that it will be available for long, so take advantage of it now. Next, read the Handbook and do the case studies to learn more about engineering statistics—the time will be well spent! Even if you have statistical software at work, your next job may not. Download DATAPLOT and you will have one at home. Additional articles and references are at the end of this column.
References and Further Reading
1. NIST/SEMATECH e-Handbook of Statistical Methods
2. Plackett, R.L., and Burman, J. P. “The Design and Optimum Multifactorial Experiments,” Biometrika, Vol. 33, pp 305–325 (1946).
3. Vandenbrande, Willy. Shainin: A Concept for Problem Solving, Shainin Conference, Amelior Hotel, Dec. 2009.
4. Murphy, Thomas, Jr. “Design and analysis of industrial experiments,” Chemical Engineering, June 6–1977, pp.168–182.
5. Feller, J. “Design experiments that control two or more variables at once,” Industrial Research & Development, July 1983, pp 94–95.
6. Geremia, J.O. “Test Less, Learn More,” Machine Design, Sept. 8, 1977, pp 110–115.
7. Anderson, L.B. “How to Apply Statistics In Design of Experiments,” Chemical Engineering, Aug.5, 1963, pp 113–116.
8. Anderson, L.B. “Factorial Design of Experiments,” Chemical Engineering, Sept. 2, 1963, pp 99–105.
Happy Holden has worked in printed circuit technology since 1970 with Hewlett-Packard, NanYa/Westwood, Merix, Foxconn and Gentex. Currently, he is the co-editor, with Clyde Coombs, of the Printed Circuit Handbook, 7th Ed. To contact Holden, click here.
