How do I Use Boolean Logic on Continuous Factor to Create a DoE

Question

Hello. Thank you in advance for your time to consider this problem.

I am trying to create a DoE with 2 continuous factors and a 2-Level discrete numeric factor.

I want to create a DoE in which if the discrete numeric factor value is 1, only range of values from the 1st continuous factor is experimented. And, if the discrete numeric factor value is 2, only range of values from the 2nd continuous factor is experimented.

How do I go about designing such experiment?

Thanks,

Charlie Roh

statman · Answer

Thanks for the explanation, Charlie.  I may be over simplifying or don't completely understand your situation, but it seems to me you have one factor as a predictor variable and multiple continuous response variables.  This one factor has multiple levels.  You could collect multiple measures of each Y (based on some rational subgrouping strategy. Answers to  these questions may help you decide how best to collect the data (e.g., your hypotheses): Why would flow rates vary? Do the diameters need to be cylindrical? Does surface finish matter?  Is there an exothermic reaction of the fluids?  How does ambient conditions affect the materials the pipes are made of? How is "possibly inconsistent input pressure" accounted for?  Measured?  These hypotheses can be used to create subgroups to estimate the range at each inner diameter and perform analysis using  Analyze>Fit Y by X .  This will allow you to estimate the model strength and its form (polynomial).

Now if you expand the number of hypotheses as to why there would be variation in the relationship between diameter and flow rate & pressure, etc. then you might want to design some sort of factorial design.  A lot depends on whether the factors you think might influence the variability in Y's is controllable or not (noise).

Nesting, also known as hierarchical, is a relationship between components of variation (or factors).

see here:

https://www.jmp.com/support/help/en/16.2/?os=mac&source=application&utm_source=helpmenu&utm_medium=application#page/jmp/twofactor-nested-random-effects-model.shtml

ExplanatoryLynx · Answer

Hi Statman,

I am afraid I can't go into much detail due to company policy.

I will try to come up with an example.

Let us say there are 2 pipes at a fixed inner diameter and a a male to male NPT connector that connects the 2 pipes together.

A compressible fluid goes through this fluid path.

The outer thread of the connector remains the same in order to connect the 2 pipes, but the inner diameter of the connector can vary (1/8, 1/4, 3/8 etc).

At different inner diameters of the connector, different ranges of flow rate are possible. The response would be pressure, velocity, Reynolds number in the connector and other values that characterize fluid flow. So the responses would not be nominal.

How do I relate the inner diameters of the connector to its range of flow rates?

Can you elaborate on the approach of nesting a continuous variable inside a discrete factor?

Thank you in advance for your time

-Charlie

statman · Answer

Charlie, welcome to the community.  It is very challenging when the situation is not understood from an engineering or scientific perspective.  What model are you looking to provide insight into?  Or, in other words, what effects are you trying to understand?  One approach would be to nest the continuous variables inside the discrete factor.  Apparently you are not interested in the interaction between the continuous variables.  You mat be able to use Custom Design to add the terms you are interested in.

Is the response a nominal value?