Demystifying Design of Experiments

I love Design of Experiments (DOE). Over the years I have done my fair share of them – everything from simple 2^2 full factorial designs to your more complicated Response Surface Methodology designs.

Tonight I want to start by explaining what DOE’s are and what they are not. I will build on this topic of DOE over the coming months (and years). I don’t want to attempt a 3 part series or anything like this since this topic is monstrous.

OFAT – What is it?

OFAT stands for “one factor at a time” and many people confuse this with DOE. OFAT problem solving occurs when someone changes one thing in a process to see what it does. Let’s use a real life example to explain. I experienced this exact situation when visiting a supplier of my former company about 5 years ago. The names of the guilty will be omitted for obvious reasons.

When touring this supplier I came across an engineer who wanted to show me how he determined the optimal settings for his injection molding machine. He didn’t know I had a Six Sigma background and I guess I forgot to mention it. I did later train this man on DOE during one of our “Supply Chain” green belt training classes so the story did end up nicely.

Anyhow, before his training on DOE, the nice engineer started off by showing how he tested “parameter 1” at the high, medium, and low setting. When he found the best one he set it in place and did not change it. Then he tested “parameter 2” at the high, medium, and low setting. Once he found the best one he set that parameter in place. So now he had the “best” settings for both parameter 1 and 2. He continued on until he had set all his parameters to the “optimal” settings. In the end, I will grant him, he had a good part. But he did tell me he had lots of variation in the process and that their scrap rates were too high.

This engineer was using your traditional OFAT problem solving approach. The problem with this technique is that you cannot determine how the various parameters interact with one another. It is this interaction understanding that makes DOE so powerful.

Full Factorial Designs

full_factorial_design.JPGA better approach to identifying the optimal parameters would be to design a simple full factorial experiment. Let’s assume a screening experiment (a topic for another day) had been completed and the engineer had determined that there were three key parameters he needed to optimize for this process. Let’s call them pressure, speed, and temperature for sake of simplicity. Let’s also assume he knows from process knowledge the realistic range each of these parameters operates at.

The picture is what this 2^3 (3 factors at 2 levels) full factorial designed experiment would look like. In this DOE all possible combinations are tested and thus any and all interactions would be seen. The output in this DOE may be something like the weight of the part. To be sure, much care must be taken in choosing the correct output. We also must be sure our measurement system is repeatable and reproducible or we are just wasting our time.

This full factorial approach is far more effective than the aforementioned OFAT approach. In many cases it is also quicker to complete!

In the future I will build on this DOE topic more explaining how to analyze them, etc. I have only begun to scratch the surface.

Tagged in:, ,

2 Comments

  1. robert

    March 20, 2007 - 7:02 am

    Ron – good luck with the posts on DoE. As you know its a massive topic. I came across a really interesting example of good experimental design over on Wikipedia.
    http://en.wikipedia.org/wiki/Design_of_experiments

    “In 1747, while serving as surgeon on HM Bark Salisbury, James Lind, the ship’s surgeon, carried out a controlled experiment to discover a cure for scurvy.” … “the main thing that is missing is randomized allocation of subjects to treatments”.

    Bizarre!

    Rob