What is a Designed Experiment?
Note: as some of you know, we can study more than two factors and two levels with more than one response. You can also study mixed levels for factors. But, the following examples introduce the fundamental concepts.
A designed experiment is a systematic approach to conducting experimental trials in order to determine the impact of two or more input variables on a response (or responses). The input variables are studied at two or more settings (levels) in order to obtain useful information about a process or technology.
In what follows we walk through the steps in conducting a simple Designed Experiment with a process for the creation of a Lego.
STEP ONE: Define process and key responses of interest. What are factors and levels to study? Is the process sufficiently stable or madly out of control? What are the questions we want to answer?
The Lego is an injection molding process part. In our simple conceptual example lets suppose we have a single cavity tool (making one part per injection molding cycle). In addition, suppose we have in place all of the elements of the process (molding machine settings, tooling, polymer, polymer lot, etc. and that none of these variables will be changed in our designed experiment. Additionally, suppose we want to conduct an experiment in which we study how to make relatively small changes in the overall length of the part. Additionally, we have conducted numerous trials and have determined that the process is sufficiently stable as we conducted repeated shots of the tool.
Continuing we use our knowledge of the technology to determine the key factors we wish to study. Suppose we believe that injection velocity will have a small proportion effect on the length of the part and hold pressure will have a larger proportional effect on part length. Frequency when reading books on DOE or simple DOE examples the factors and levels (settings to be studied) just appear! Selecting the right factors and levels are key to being successful with Designed Experiments. They require a knowledge of the technology or process being studied. For our example, we would first conduct a relative viscosity curve for the process, perhaps from this study we determine 2 and 4 inches per second would be appropriate. Regarding hold pressure we conduct a series of shots varying only the hold pressure to determine the points just before we shorted/flashed the part. Suppose from this effort we determine we want to study hold pressure at 4600 psi and 6500 psi. We want to create a mathematical model to hit an intermediate target value for our response of 57.284
STEP TWO: Select an orthogonal array
With two factors at just two levels the number of unique combinations is 2**2 = 4 trials in our simple designed experiment. In addition, we decided to conduct 4 replicate samples for each of the 4 trials, giving us 16 data points in our DOE.
STEP THREE: Conduct the experimental trials
We conduct the trials, and the data is as below (making sure that the only changes that are being made are called out in the design matrix, recording any weird stuff that might have happened during the conduct of the trials).