cancel
Showing results for 
Show  only  | Search instead for 
Did you mean: 
The Discovery Summit 2025 Call for Content is open! Submit an abstract today to present at our premier analytics conference.
Choose Language Hide Translation Bar
View Original Published Thread

Using disallowed combinations to remove a factor from the DoE

PValueEnemy
Level II

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

1 ACCEPTED SOLUTION

Accepted Solutions
Victor_G
Super User


Re: Using disallowed combinations to remove a factor from the DoE

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 :
    Victor_G_0-1732205578752.png

    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,

Victor GUILLER

"It is not unusual for a well-designed experiment to analyze itself" (Box, Hunter and Hunter)

View solution in original post

2 REPLIES 2
Victor_G
Super User


Re: Using disallowed combinations to remove a factor from the DoE

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 :
    Victor_G_0-1732205578752.png

    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,

Victor GUILLER

"It is not unusual for a well-designed experiment to analyze itself" (Box, Hunter and Hunter)
statman
Super User


Re: Using disallowed combinations to remove a factor from the DoE

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.

"All models are wrong, some are useful" G.E.P. Box