How best to account for 2 nuisance factors in my DOE: 1 that's quantifiable (tank to tank variability), & 1 that simply accounts for monthly/time-series variation?

[#1]

If I want to do a (definitive?) screening design with 6 controllable factors in 17 runs (that DOE does not include tank to tank or monthly variation) - what would be the best way to capture the possible error due to those 2 potential nuisance factors?

My process involves trying to increase output in a batch reactor process, & I have 4 different reactor tanks & so we can complete 4 runs at a time (aka we run all 4 tanks at the same time in 1 batch). We then have to wait 10-14 days before we can run the next batch of experiments, again, 4 runs run in 4 different tanks, such that the 17 runs would take about~2 months to complete. 

What's the best way to capture the potential variation due to the 2 nuisance factors I describe? Split-plot design, covariates, etc..? We could potentially complete many as 21 runs, but any more than that might not be possible - so we'd have to eliminate some controllable variables to fit within our budget (which I'm okay with), but I really want to account for the possible nuisance factors either way. 

Separate question - what if we have a failed run? Do we just reassign it to the next tank and continue on like nothing happened? 

[#2]

First, there is no one best way to handle noise in an experiment.  Have you done any CoV/sampling of the within and between tank variation?  This would be quite useful for determining which components have the greatest leverage, assessing stability/time ordered effects and measurement variation at the same time. (this can be done in parallel with any experiments).

Have you rank ordered predicted model effects?  Do you really need to assess quadratic effects?  Could you run fractional factorials with center points? Are you suspicious of a large tank affect or tank by factor interactions (effects of the design factors dependent on tank)? You could treat tank as a block and run incomplete blocks.

My advice is always design multiple experiments (easy with JMP).  Consider each experiment for what effects can be estimated, what effects are confounded, what effects are not in the study.  Weigh this potential for knowledge gain vs. resource requirements.  Pick one and run it knowing you will have to iterate.

[#3]

Thank you for the response. 

I'm mostly looking for main effects + interactions, I was thinking of doing a DSD just to be efficient in case it collapses straight into an RSM if only a few factors are significant, but I don't really know if that's the case, so I suppose quadratic effects aren't really what I'm interested in. 

I'm not concerned with tank by factor interactions, mainly large tank effects as you say, but that is a bit of an educated guess. 

I'm not familiar with incomplete blocks - do you have any resources you'd recommend? What about the potential for time ordered effects? Are those likewise included in an incomplete block? 

[#4 · Accepted solution]

Incomplete blocks (aka BIB: Balanced Incomplete Blocks) are just like fractional factorials and are created by confounding (aliasing) a higher order effect with the block.  

https://www.jmp.com/support/help/en/19.0/?os=mac&source=application#page/jmp/balanced-incomplete-blo...

IMHO, time ordered effects are more efficiently studied with directed sampling /COV studies.

Sanders, D., Sanders, R., and Leitnaker, M. (1994) “The Analytic Examination of Time-Dependent Variance Components”, Quality Engineering

Now, if you have hypotheses about what factors are changing in time, then you may be able to manipulate those in a shorter time period.  In those cases, it is best to exaggerate those factor effects with bold level setting.

[#5]

Thanks. I will take a look. 

I don't have a great idea of which factors are changing in time - it could be environmental such as ambient temp and moisture having an impact, raw material lot changes etc..., so I'm sort of lumping everything in w/ this "time" nuisance factor. 

[#6]

Hi @MJZ82,

Welcome in the Community !

Considering the information and limited context you provided, as well as the helpful informations already provided by @statman, I will answer with a more practical approach.

I would use a blocking factor (with 4 runs per block) in the screening design, to account for the batch-to-batch variability, as well as a categorical 4-levels factor for the tank used. Using these blocking and categorical factors help allocate the experiments homogeneously across blocks and tanks, which can help detect any difference in time/batchs or between tanks. Using the block effect as a fixed effect in the analysis could inform you about the importance of this "batch factor" on the mean response (deviation of the mean response depending on time: bias), whereas using this block effect as a random effect could inform you about any change in the variance of the response. 

• With the blocking factor, you would be able to compare the batch variability, by comparing the average of the experiments for each block, since the experiments inside each block should be as similar as possible between blocks. Simple graphs and Xbar and R charts may help visualizing this variability.
• With the 4-levels categorical factor, the allocation of the levels of the 6 controllable factors would be homogeneous between tanks, and help compare the tanks variability (and any bias) by comparing the average and response range of the experiments for each tank across the blocks. 

For the analysis, it might be interesting to consider a two steps approach :

1. Identify important active effects of the 6 controllable factors thanks to The Fit Two Level Screening Platform
2. Fit a model using the effects identified previously, and adding categorical factor tank, as well as the random effect batch.

You will find attached an example of the design (created with Custom Design platform) and the two-steps approach on a simulated response.

If the topic of time-trend robust designs is interesting for you, I would recommend reading "Optimal Designs of Experiments : A Case Study Approach" (chapter 9) by Peter GOOS and Bradley JONES. You can also find a practical example of this methodology in this discussion Covariates in defined order in custom design

Hope this complementary answer may help you,