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## DOE

Hello,

I am a new user of JMP and have a question concerning the design of experiments.

I want to design an experiment and thereby two continious factrors should have always together a sum of 100.

This to factors are chemical agents. So in my experiment they appear as continious factors and because I use different of these chemical agents also as catigorical factors.

I tried to realize it by defining factor constraints but Iit wasn`t possible for me.

I really appreciate every help.

5 REPLIES 5
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## Re: DOE

Suppose the two factors are called A and B. Then it sounds to me as though you really only have one factor here, not two, because whatever the value of A is, the value of B must be just 100% minus A. If so, this isn't the usual sort of experimental design problem for which you need assistance deciding what factor combinations to choose: all you really need to decide in this instance is how many different levels you want to investigate. For example, you might decide to look at just five levels of factor A, say 0%, 25%, 50%, 75% and 100%, in which case B will necessarily take values of 100%, 75%, 50%, 25% and 0% respectively. (Incidentally, if you had three chemical ingredients as opposed to just two, again with the sum totalling 100%, this would be a Mixture Design, which is one of the designs included in the DOE main menu.)

If you consider the above example as a categorical variable with five different levels, and replicate each level at least twice, you would be able to perform a one-way Analysis of Variance on your data to investigate which levels were different from which others. Your five different levels would be Level1={A=0%, B=100%}, Level2={A=25%, B=75%}, Level3={A=50%, B=50%}, Level4={A=25%, B=75%} and Level5={A=0%, B=100%}.

However, I think it would probably make more sense to consider the above simply as distinct levels (of either A or B - it doesn't matter which one you use) on a continuous scale between 0% and 100%, and then perform a regression analysis on the data instead. You should choose enough different levels to be able to (a) capture satisfactorily the expected shape of the response curve between the two extremes you choose and (b) allow you to check for any lack of fit of your curve to the data.

For example, if you were only interested in combinations of the chemicals between {A=30%, B=70%} and {A=60%, B=40%}, and you expected to see a quadratic relationship between A and response over that range, I'd suggest that you investigate at least four (and possibly five) equally-spaced different levels of A between those extremes (because three would only allow you to fit a quadratic, whereas you really should give yourself the option of testing for a more complex relationship than this, just in case your original assumption turns out to be wrong), and also to replicate every level at least twice. If so, testing A=30%, 40%, 50% and 60% in duplicate or triplicate would probably be a sensible choice of design.

As an aside, if you have to make up the chemicals sequentially, try to balance the design for any effects of time on the process. For example, if you wanted four replicates of each combination, but could only make up four solutions each day, rotate them so that each one is made up at a different time on each of the four days, giving you a Latin Square like this:

Mon: 30%, 50%, 40%, 60%

Tue: 40%, 30%, 60%, 50%

Wed: 60%, 40%, 50%, 30%

Thu: 50%, 60%, 30%, 40%

If there were to be such a time effect, DOE would be able to help you decide how to structure the experiment.

Is that of any help?

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## DOE

Firstly, Thank you for you answer. Whenn I created for the first time an experiment I did it as you mentioned. I just concentrate on the one factor A. That means, I entered that the factor A should be between 60 and 100 parts. At the same time I entered two categorical factors which describes which chemigal agents I use. So:

continious factor:

A: 60-100

Categorical factor:

B: chemical agent A; chemical agent B -> this factor belongs to the continious factor A

C: chemical agent C; chemical agent D -> this factor describes the addidtional added agents to form the sum of 100

but they are not mentioned as a continious factor

When I designet the experiment, I had experiments like that:

A        B                     C

1         60     Agent A         Agent C        -> I know that here I have to add 60 parts of chemical agent A and 40 parts of C

2        100    Agent B         Agent D        -> here I have to add 100 parts of B and nothing of D, but D is mentioned her.

Is this influencing the analysis?

Is that  what you meant ?Is this way of creating the experiment the right one?

One more time, thank you for your help.

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## DOE

Feels like you are dealing with a Mixture Design scenario. Is this a chemical formulation? If so then just add your 4 ingredients as Mixture factors and specify the ranges that you want to examine. A mixture design feature is that all of the components of the mixture will sum to 100%. See the Help>Books>DOE Guide>Mixture Designs

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## DOE

I think I can not use a mixture design, because i have addtional other continious and categorical factors in my DOE.

The factors that I wrote in my previous answer are just a part of my factors.

Can I do it like i described it in my previous answer?

Highlighted  louv
Staff (Retired)

## DOE

JMP will accomodate both Mixture factors and Process factors in the Custom Design platform.

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