Question on controlled factor in DOE

Question

Hi all, I am new to JMP and DOE, and here is the question:

If I have a factor (sample thickness) that is uncontrollable but can be measured at the time when measuring the run responses (i.e., when the run is finished). The sample thickness cannot be measured before the run, so I cannot record them beforehand and use them as covariate. This thickness uncontrollable factor varies statically in a normal distribution and it is independent from other variable because it relates to how I prepare the sample of each run. This uncontrollable factor has interactions with other controllable factors and together they affect the response reading.
In this situation, how do I investigate the effect of this uncontrollable factor? Could I define it as uncontrollable factor in the custom DOE and include its interactions in the "Model" section? And record the thickness values after each run, then run the model as usual?

Second question, To enhance the design, could I intentionally increase the "number of repeat run" -- but instead of actually repeating runs, can I just prepare multiple samples in each run and measure all of them (each sample will have different thickness but the rest stay the same), so that its impact on the response would be better elucidated by the model?

Thank you so much

statman · Answer

There really isn't enough information to provide specific advice, but here are some options.  There is always the question, are you trying to explain variation in the output or develop a causal understanding for predictive purposes?

Just curious, how do you know there is an interaction between the sample thickness and the other factors? Or is this hypothesis? Where did you get the data to support this?

Have you done any sampling? Perhaps use sampling of the preparation process to get an understanding of consistency and how much it varies.

Since you are "preparing the sample", can you experiment on how you prepare the sample, purposely varying the factors associated with preparation? If so, you can run an experiment on preparation as the whole plot (consider each sample from this experiment and split the sample) and subsequently run the experiment on the other factors in the sub-plot of a split-plot design.  This increases precision of the whole plot, the sub-plot and provides for interactions between the whole plot and sub-plot with increased precision.

Another option, as you imply, is to make one experimental unit for each treatment which consists of multiple samples. These samples are not independent of the treatments, but you can average those samples which will reduce the sample thickness effect and you can also take the variance of the samples and use this as a second response variable to see if your controllable factors effect the variation within treatment (mostly due to sample thickness and measurement error).

Also the option, if it is possible to sample to determine the two extremes of thicknesses, then grab enough of each to run replicates and confound this with the block (low thickness = Block -1, and high thickness = Block 1). You can then handle block as a fixed effect and add block and block-by-factor interactions into the model. This depends greatly on your confidence in knowing what is confounded with the block. If the block effect or block-by-factor interactions are significant, then there are options to disaggregate the block. Otherwise, you can treat block as a random effect and use it to be the basis of statistical tests.

There is nothing wrong with measuring the thickness and including the actual measure as a covariate unless the thickness changes due to the other factors. The measure doesn't necessarily have to be done before the experiment to use it as a covariate. The only potential issue I see with this, is you can only use one value for the covariate for each treatment. If there is variation within sample, then what value do you use? I suppose you could average the thickness measures...but this may not be useful.

There is no one right way to run the experiment. Many options exist, each with their relative plusses and minuses. My advice is to design multiple options, consider what the potential to learn is for each (e.g., model effects, restrictions, aliasing) and contrast/compare with the associated resource requirements and constraints.  Predict all possible outcomes and what the next possible iterations will be. Then pick one and prepare to iterate.

Victor_G · Answer

Hi @AttributedBurro,

Welcome in the Community !

Sorry that you didn't get an answer sooner.
You're right, if you have an uncontrollable factor like sample thickness, it may be best to consider and include it as uncontrolled factor in the design creation. This way, the uncontrolled factor is still part of the model.

Concerning your second question, I have a doubt: are you planning to add replicate runs in your design, or replicate your design entirely, but preparing and running the replicate runs randomly and independently ? Or do you want to prepare multiple samples of the same treatment and run them at the same time ?

* In the first option, you can easily add replicate runs in your Custom design or replicate entirely your design using Augment design platform.
* In the second option, you'll add a restriction of randomization in your design, by having "block of experiments" with the same factor levels. You could specify one or several of your factors used for the preparation of samples as "Hard-to-change" and the others as "Easy-to-change" to create this randomization restriction; you'll then have to specify the number of whole plots, meaning the number of time the "Hard-to-change" factors will vary in the design. Depending on the total number of runs (multiple of the number of whole plots), your design structure will be organized in p whole plots of k runs each, for a total of p*k=n runs in your design. This design structure is called a Split-Plot design. This design structure offers easier runs to perform (due to the randomization restriction), but at the cost of lower power for the Hard to Change factors and a slightly more complex model (adding the estimation of a random effect for the whole plot effect).

Hope this late answer may still help you,