Using disallowed combinations to remove a factor from the DoE

[#1]

Hello!

I want to design an experiment to test the best setup in a machine where one of the factors define if I should test the other factors. Simplifying the problem, suppose the machine have a (A) water valve: on/off. If the water valve is on, then I want to test (B) hot/cold water and (C) flow rate between 5 and 7 mL/s. When the water valve is off, B and C does not make sense.

How should I design an experiment this way?

Summary

1) If A = on, then test B and C

2) If A = off, then don't test B and C

[#2 · Accepted solution]

Hi @PValueEnemy,

Your design constraint is very similar to previous post about this topic of disallowed combinations /nested factors.

You can read the following posts :

Disallowed Combinations not working 

Design of Experiment - Optional Mixture Additives 

Measurement plan (DoE) where factors can be present or absent. Interactions and concentrations are o... 

Nested DOE with continous factors? 

There may be several solutions/workarounds for your situation :

1. Simply use/add a 0 level for factors B and C (you don't need a factor A for valve). B can become a 3-levels categorical factor (no water/hot/cold) and C could be discrete numeric with values 0, 5 and 7. If factors B is different from "no water" and C is different from 0, it means the valve is on. Perhaps you will have to use disallowed combinations or a candidate set approach to avoid combinations with B different from "no water" and C = 0 OR B = "no water" and C different from 0.
   Example of such design with interaction and quadratic effect for C :
   
   

   Disallowed combinations/Constraint : 

   B == "No water" & C >= 0.1 | (B == "Hot" | B == "Cold") & C <= 0.1

   And script :

   DOE(
   	Custom Design,
   	{Add Response( Maximize, "Y", ., ., . ),
   	Add Factor( Categorical, {"No water", "Hot", "Cold"}, "B", 0 ),
   	Add Factor( Discrete Numeric, {0, 5, 7}, "C", 0 ), Set Random Seed( 1774495 ),
   	Number of Starts( 42311 ), Add Term( {1, 0} ), Add Term( {1, 1} ),
   	Add Term( {2, 1} ), Add Potential Term( {2, 2} ), Add Term( {1, 1}, {2, 1} ),
   	Set Sample Size( 18 ), Disallowed Combinations(
   		B == "No water" & C >= 0.1 | (B == "Hot" | B == "Cold") & C <= 0.1
   	), Simulate Responses( 0 ), Save X Matrix( 0 ), Make Design}
   )

   
   
   
2. Use a candidate set approach, by creating a table with all possible combinations, and then remove impossible ones (implying valve is off and B OR C is different from 0/"no water", or valve is on and B = "no water" AND C = 0). Use this candidate set in the Custom design to directly create a design based on these covariate runs. This enable to force complex constraints naturally in the design without having to specify them. A specific care should however be adressed to the model so that the constraints are well incorporated in the model.

Anyway, I think your factor A  may be redundant, as it is directly correlated to the values of factors B and C.

Hope this first response will give you some ideas,

[#3]

You are describing a nested deign.

Here is some information about nesting:

https://www.jmp.com/support/help/en/18.1/?os=mac&source=application#page/jmp/statistical-details-for...

and here:

https://pmc.ncbi.nlm.nih.gov/articles/PMC9098003/

Realize with nesting you do not get interactions, but you will get main effects.