Misconceptions about Using Design of Experiments, Part 2

The last update you received discussed the first of the three misconceptions about using DOE. These are, the belief that DOE doesn't apply when all of the factors are discrete (categorical), thinking that responses are factors, and believing that factor constraints prevent the use of DOE. This update will discuss the second misconception. Sometimes it is hard to identify your factors. It isn't always clear, for instance, whether a variable is a factor or a response. Remember, you have direct control over factors and they influence your responses. Remember also that you do not have direct control over responses — you have to vary factor levels to change responses — but you have goals on your responses. Here is s simple example: you can vary time and temperature to bake a cake. You want the cake to be pleasing to the people who will eat it — let's call this “desirability.” You have direct control over time and temperature and they affect desirability, so time and temperature are factors. You do not have direct control over desirability, but you do have a goal for it, so desirability is a response. Identifying factors and responses becomes more difficult in certain situations. Here is an example: You want to choose the appropriate amount of a polymer and its optimal molecular weight to produce a solution in water with a particular viscosity. At first glance it appears that “amount of polymer” and “molecular weight of polymer” are factors and “viscosity” is the response. You do not have control over viscosity and you do have a goal for it, so viscosity really is a response. You do have direct control over “amount of polymer” and it does influence viscosity, so amount of polymer is a factor. While molecular weight does affect viscosity, you don't really have direct control over it. There is no “knob” you can turn to produce a polymer of a specific molecular weight. In order to produce a polymer with a specific molecular weight you will need to adjust the factors in the synthesis of the polymer, such as ratios of monomers, the amount of limiting reagent, the identity of the limiting reagent, etc. Molecular weight is a response to several other factors. If you tried to treat molecular weight as a factor you would run into the problem of providing polymer samples at the molecular weights specified in your experiment design. If you don't realize the root of this problem, it appears that DOE will not work. Here's another example: You have five chemicals that can treat cancer tumors and you have five different types of cancer tumor. You want to know the most effective combination of chemicals to destroy the five different types of tumor. This is tricky. It is clear that “effectiveness of the treatment” is not under your direct control and you do have a goal for it so this appears to be your response. You do have direct control over the chemicals used and the type of tumor, so these appear to be factors. “Chemical” is a process factor and “tumor type” is a discrete factor with 5 levels. This would require a minimum of 45 trial for a full quadratic model. But is this really correct? In order to understand this problem better we need to ask, “do we want to know the best possible outcome for treatment, including the mix of chemicals and the tumor type best treated, or do we need to know the best way to treat each type of tumor?” If the first scenario is correct we have set the experiment up correctly. If the second scenario is more correct — and it is in this case — then we need to make an important change to our set up. Since we we need to know the best way to treat each type of tumor, we really have five responses, namely treatment effectiveness for each type of tumor. We only have 5 factors in this case as well, namely the chemicals we can use for treatment. The minimum number of trials for this experiment is 21 for a full quadratic model (less than half as many as for scenario 1). Of course we now have 5 responses for each trial — the mix of chemicals will have to treat each tumor type to test for effectiveness. When you face a difficult decision about factors and response it isn't necessary for you to re-invent the wheel. It is likely that someone has already encountered a similar situation and learned how to deal with it. All Objective DOE students are welcome to contact me in these cases — I have seen many and may know how to solve your dilemma. If not, I may be able to help you find a way to solve it. Your knowledge of your field is your best tool for determining factors and responses, but sometimes a little experience with DOE can be of tremendous assistance to you. Next time let's look at how factor constraints can be accounted for in a designed experiment and the analysis of data. Objective Design of Experiments workshops will teach you to use DOE in your work. Design of Experiments is a fundamental technique for industrial experimentation. You will learn to apply DOE easily without excessive math and theory. We will help you be even more successful!