Hi All,
Hoping to get some feedback from experts and the collective mind regarding the above topics. I'll first describe the scenario and then go into the problem at hand.
SCENARIO: Our business is often in a situation where DOEs run by people in R&D suffer from an external nuisance factor -- and managing this in order to "save" the DOE is sometimes challenging. The R&D people will typically generate DOEs to test several factors at a time. In this process, there are normally multiples of 3 batches made, each batch has a different recipe in order to test the factors affecting the outcome(s). The factors going into the recipe are all continuous factors, and depending on the design are typically 2-level (low/high). Center points are often included to help estimate the variance. The R&D people typically make 3, 6, 9, etc. batches. The reason is because after the initial steps in the process, the batches need to be dried in an oven, and it's only possible to dry three batches at a time, hence batch quantities in multiples of 3. Batches are immediately taken to be dried after the first step. Directly after drying, the material is milled. Because of limited time within a day, there can only be a fixed number of runs performed each day, again this would be a multiple of 3, with no more than maybe 9 done in one day.
PROBLEM: Because of physical limitations of where the oven is located, the external ambient temperature and humidity (more often humidity) are nuisance factors. I call them nuisance in the sense that they are known, but uncontrollable. The ambient temp and humidity can be measured at the time a set of 3 batches are placed in the oven for drying, but there is no way to control these factors or to know what they will be ahead of time. It is known that the humidity can affect the material during (and/or shortly after) the drying step, and it's suspected the ambient temp might do so as well.
DISCUSSION: What I'd like to get a better understanding of is how to manage these nuisance factors in a DOE. Certainly, we can block by day and have a well-distributed, random set of runs within each block, thereby obtaining an estimate of the noise introduced by which day the batches were made and dried. We could also introduce it as a fixed effect (even though it's not really fixed), which would help to estimate the mean day-to-day differences in each block. We could even treat "day" as a "very hard" to change effect, to obtain a split plot design, which would help to see how that factor interacts with the other factors -- BUT -- we can't control the humidity and don't know what it will be before the experimental run is started. We could treat it as a covariate, which would require doing an ANCOVA analysis to remove the effect of the nuisance factor from the response. Or, we could simply introduce the nuisance factor as an uncontrolled factor.
Some discussion points:
- It would be nice, although not necessary to estimate the noise that is introduced because of the nuisance factors, which would suggest randomized blocking.
- It would also be nice to estimate the day-to-day variation caused by the nuisance factors, which would suggest fixed blocking.
- It would be nice too see if, or how, these nuisance factors are interacting with the other known main factors, suggesting including them as "very hard" to change factors, but indeed they are impossible to change factors as we have no control over them.
- Performing an ANCOVA might help to remove the nuisance factors in order to compare batches made on different days. However, it's my understanding that to do this in JMP, one can only have a single categorical factor combined with a continuous covariate factor in order to obtain the right kind of analysis. We certainly could change some of our main factors to categorical data types, but the problem is that we have several main factors that must be included in any model. When doing so, JMP no longer splits the data into the different lines of fit as you would expect for an ANCOVA. Although maybe I don't fully understand how JMP is performing the ANCOVA under situations where you have multiple factors in the model. The sample data and online help on this topic is very limited.
- Lastly, we could add it into a model as an uncontrolled variable, leaving the levels blank and fill in the data when the runs are executed. The analysis of the model later should show whether or not the uncontrolled variable has any impact on the response(s).
Some questions:
- In this kind of scenario where we typically have a fixed number of batches dried at a time, and all of them could be affected by the nuisance factors, is there a best approach in incorporating the nuisance factors into a model in order to understand what effect, if any, it has on the response?
- Would we use a singe approach or mixed approaches. For example, is it best to use only randomized (or fixed) blocking, or to use randomized blocking, but also include the nuisance factors as uncontrolled variables? Similarly, is it best to use Day as a very hard to change factor while also including humidity and air temp as uncontrolled factors?
- Is ANCOVA really the right kind of approach, or could this lead to wrong conclusions?
- Have you had to deal with a similar situation in your workplace, and if so, what methodology did you use to manage your nuisance factors?
Thanks for your help, and I look forward to reading the responses.
Thanks!,
DS
