Offset "Center" Point in 2 level Full Factorial Design

ProtSci23

 

Hello,

 

I have a question regarding center points for a 2-level full factorial design with 3 continuous factors. As we are fairly resource constrained, we would be including 8 runs without repeats and then adding a center point (duplicated) to test for curvature and estimate the variability associated with our experiment.

 

The goal of our experiment is to evaluate the robustness of our process and we would like to use our standard process setpoint as the center point. However, for one factor our setpoint condition is not midway between the low and high levels for this particular factor. From my understanding center points are typically set at the mathematical center of each factor to maximize the probability of detecting curvature. Would there be other concerns/impacts with having a slightly offset center point condition in this design within JMP?

 

Thanks in advance,

 

statman

Some clarifications and questions:

1. You mean you will not be replicating the experiment?  This is different than repeats.

2. You will be replicating the center point?  How many replicates?

3. Center points are intended primarily to assess curvature inside the design space.  There are other possible reasons for center points.  If you run them randomly over the course of the experiment, and run enough of them, you could get some idea of stability over the design space.  In addition, you will be getting an estimate of mean square error inside the design space.  Theoretically this estimate is less biased from factor effects, so may be a reasonably good estimate of the process variance.

4. Evaluating the "robustness of your process has little to do with running center points.  I assume you mean robust to noise?  To evaluate the robustness of your process, you should either manipulate the noise during the experiment (e.g., blocks or split-plots) or ensure the noise varies randomly and sufficiently (representatively) over the design space (e.g., randomized replicates)

5. In the absence of resources to do any kind or replication, you might consider sampling post experimentation to assess robustness.

6. Regarding the center point not being at the center.  This does introduce a bias into your experiment.  Whether this bias will have much impact is situation dependent (e.g., slightly offset probably will not have much effect).  How far from center is it (geometrically)?  How bold are your factor levels? Why can't you put it at center? The purpose of putting the points in the center is to simplify the analysis while still detecting curvature.  Theoretically the surfaces can be quite complex.  We don't know á priori what the surface is, so we pick points that are balanced across the design space.  This, hopefully, provides a reasonable estimate of what the surface is.