General DOE argumentation: Replicates and center points

Question

Hi

I get from time to time questions like "why do you do not use replication or centerpoints, as in our guideline we should always add replicates and at least 2 centerpoints?". I guess you do as well.

How do you answer/argue on that? What is your experience on their reaction (do they just believe you?)? What would be situations where you would recommend replication/duplication/center points

Regarding center points, I say something like "if you have the quadratic effect entered as model effect the custom design will take care for it (of course as long as you have enough runs to get a fair estimate, which you can check with e.g. the power analysis). Additional center points will improve the error estimate.

Regarding replicated runs, it is almost the same plus talking about prediction variance.

Regarding duplicated runs, you will have less power and a higher prediction variance as if you would use replicated runs in the custom designer. But sometimes you want to have the same experimental unit measured at e.g. different time points and I often see this done then (though you would have to take care of that in the modeling.

I'd be happy to hear from your arguments/experiences both on the theoretic part as well on the customer believing/convincing part.

Thanks,
Martin

DonMcCormack · Accepted Answer

Martin,

I'd tell the customer that there is no general agreement as to whether you should use center points or add replicates and we leave it for them to decide. I'd explain the advantages/disadvantages for both cases. Personally, I like center points because they can be used to test for curvature without running a full RSM, can be used to check model misfit, and can be spaced out over the design to check for drift. A few disadvantages are they add runs but don't improve estimate of coefficient precision. Using a DSD may be a more effective way to deal with the possibility of curvature when you don't want to run a model with all ME, 2FI and quadratics. In short, they can be seen as an inefficient use of the extra runs. As for replicates, I'm not a big fan because I believe in most cases it's an inefficient use of runs. Many folks don't realize that for DOE, experimental error can be estimated by either replication or pseudoreplication (i.e., when an effect is removed from the model and the design space collapsed in some direction(s). For example if one factor is removed from a 3-factor full factorial you end up with a replicated 2-factor design). I see two disadvantage of not replicating. First, the power is low and replication is the best way to improve it (rather then adding non-replicated points). Second, as a way to account for not constant error variance across the design space. If this is the case, though, you have bigger problems.

Hope this helps. Be interested to hear what others think.

Dan_Obermiller · Accepted Answer

Great points made by Don. My executive summary: I used to be a big fan of center points, but not so much anymore. The only time that I advocate for them is if I want to have a control-type run and the center point is a spot where the scientist has good knowledge. In that situation the center point can serve as a check that all is going well before running the design. Now for the reasons I don't recommend them anymore.

I have no real objection to center points as it keeps a design balanced, can check for curvature, and provides mechanism for obtaining pure error. However, it is an OLD approach. There are newer techniques that JMP provides for most of these situations. So I don't have a problem if a customer uses them, but I do like to point out newer and different ways of thinking about design rather than relying on tradition.

Check for curvature. You can do this without center points. Add squared terms to the model window and check the estimability to be "if possible" (a Bayesian D-Optimal design). With enough runs you can now check for the curvature without center points. In fact, this would allow for the best placement of those "check points" for curvature. Again, as Don said, a DSD is often starting to win over the Bayesian  D-Optimal that JMP provides, but many people forget that DSD is for SCREENING! It is not always appropriate, especially if you expect most of your factors to be active. So having the Bayesian D-Optimal as an option is fantastic.

As a point for replication/pure error, as Don already said: center points are not very efficient for that. If you want to ensure you have pure error, you are better off providing the number of replicate runs you wish and letting JMP determine the best points to replicate. There is nothing magical about it needing to be the center. Yes, the center keeps it balanced (orthogonal), but small correlations are okay when your goal is model estimation and prediction. Let's get the best estimate and/or prediction from our model.

Increasing power by replication: Don is (of course) absolutely correct on what he says. The center point is not really very good at increasing the power. In fact, if your factors are continuous, you can also increase power by widening the factor range. This goes back to letting JMP choose the points to replicate.

Replication as a way of accounting for nonconstant error variance: center points will not do this because they are only in the center of the design space. As Don said, if this is the situation you have bigger things to worry about. This is the one spot where JMP does not offer that much help. Best you can do is to replicate the entire design. You could also put the variance in as a response and optimize your design for that, but JMP will not know that the response requires replication for estimation.