Doe constraint on the blocking

Question

Helo everyone :)

I am quite new in the design of experiment using JMP and I have an issue with the blocks.

The situation :

I would like to perform a DoE with :

-> 4 parameters of 2 levels

- 1 parameter, let call it "A", with 3 levels (A1, A2 and A3).

I have some constraintes :

- this experiment will be perform by "blocks", i.e for each 6 experiment, I will change my starting material which is known to have an impact on my response.

- One of the parameters of 2 Levels is linked to my starting material, it means that this parameter will be fixed by my starting material.

- Another constraint is that we can only test 2 levels of "A" per blocs.

As I coud not put constrainte in the blocking, I tried :

- A as "discrete numeric"

- 3 paramaters continous

- The parameter linked to ma starting mat in "uncontrolled"

- my starting mat as "Categorical"

And I used the disallowed combinaitions to eclude one "A" per "Categorical".

It seems to work but if I do so, I will not follow the order of the experiments (as I will work by blocks and it is not said to JMP). In addition, this is not very elegant as the categorical should be use to evaluate the effect of my starting materials, which I do not really need.

Do someone have suggestion ?

Thank you very much for reading,

Have a nice day and stay safe.

KevinT · Answer

Dear statman,

Thank you very much for your time and your answer, I will try to reply below:

Welcome to the community!

Thank you very much :)

There are a number of questions/comments relating to your situation in addition to the ones already posed by Mark.  Here are some of my thoughts:

1. Is this a screening design or are you further down the knowledge continuum (is this the first experiment in a series or have you already run some experiments).  What questions are you trying to answer?  Have you predicted or anticipated the potential results of this experiment?  How will the information learned in this experiment added to your knowledge?  What will be your next set of work?  It is extremely difficult to give sound advice without understanding the situation better.

I will try to answer the best I can:

It is set of experiment which is based on previous knwoledge. The objective is to optimize 3 responses, all are continous. No I can not anticipate the potential results at the moment. I want to reach some threshold for my responses, once this threshold are reached, the higher it is, the best it is.

2. Blocking is a strategy to increase the inference space while either improving the precision of the design or at least not compromising the precision.  It accomplishes this by confounding noise (factors you are not willing to manage) with the block effect.  The noise within block remains constant (thereby having no effect and reducing the within block random errors due to noise, thus increasing the precision of the design and lowering the MSE) then that noise is purposely changed between blocks (so as to increase the inference space).  In addition, if you are able to assign the factors confounded with the block, you may be able to estimate block-by-design factor interactions to determine the robustness of your design factors to noise (absence of noise-by-factor interactions).  Is this what you intend to do?

If I have well understood, this is correct. Yes I am able to assign the factor confounded with the block but please note that this factor is not completly confounded. This factor is a 2 level categorical factor and I can have up to 6 or more blocs.

3. You have 5 design factors (4 with 2-levels and 1 with 3 levels)?  It appears you are fractionating the design or attempting some optimal design strategy and then considering the block.  This is likely an incomplete block (BIB).  There are alternatives...as Mark suggests, if the noise is measurable, you could trade the noise as a covariate.

Yes that's correct. I am not used to the use of covariate, I will have a look, thanks for the tips.

4. What is A?  Is A "nested" within material (different levels of A are used conditional on Material)?

A is a categorical factor with 2 levels (starting material is treated or untreated).

5. Why do you not want to quantify the effect of material? "the categorical should be use to evaluate the effect of my starting materials, which I do not really need."  Are you concerned about the potential interactions of the design factors with Material?

Yes that's true my factors might interact with my starting material. Unfortunatly my different starting materials are in fact the same "starting material" but with different batches. This batches are and will be very different from each other. My objective is to evaluate the effect of each parameters "independently" of my starting material.

I do not know if my answer is clear.

6. What are the response variables?  Are they continuous?  What is your predicted rank order of model effects?

3 responses, all continuous. I do not know the rank order of model effect, I would go for rank 1 but I might add the higher, it depends on the number of runs.

Thank you very much.

Have a nice day,

KevinT · Answer

Dear mark,

First, thank you very much for your time and your answer,

Are the four factors at two levels continuous or categorical? Are the levels of factor A really categorical (A1, A2, and A3)?

The 2-levels factor, are a mix between continuous and categorical, let say 2 categorical and 2 continous.

No A is not categorical in fact it is a "continue factor", but I can only set 2 levels of A per "bloc" (temperature of incubator and number of incubator limited), that is why I thought to use "discrete numeric", but I might be wrong.

Be careful, 'blocks' have a specific meaning in DOE. Let's check your meaning. Is the starting material used to provide 6 experimental units (samples)? If so, then blocking is correct.

Yes this is correct, my starting materials will provide 6 experiments unit. My starting material can be spread in 6, with this 6 "sub-starting material" I can set differents 6 experiment.

Can you measure the levels of the factor that is related to the starting material? If so, then record the measurements in a data table and enter the levels in your DOE as a Covariate factor. If you cannot measure the levels before the experiment, then enter the factor as Uncontrolled, then measure the levels during the run and update your data table.

Sorry I did not mention that, the factor related to my starting materrial in categorical : my starting material treated or untreated. I can know before the experiment weither it is treated or not BUT for a given starting material, this parameter will be fixed. It means that my 6 experiments that comes from a given donor will all have this parameter fixed to treated or untreated.

I do not want to know the effect of my starting material as I cannot and will not control it in the future but I would like to evaluate the impact of treated vs untreated.

Thanks again for the help,

Have a nice day

statman · Answer

Welcome to the community!  There are a number of questions/comments relating to your situation in addition to the ones already posed by Mark.  Here are some of my thoughts:

1. Is this a screening design or are you further down the knowledge continuum (is this the first experiment in a series or have you already run some experiments).  What questions are you trying to answer?  Have you predicted or anticipated the potential results of this experiment?  How will the information learned in this experiment added to your knowledge?  What will be your next set of work?  It is extremely difficult to give sound advice without understanding the situation better.

2. Blocking is a strategy to increase the inference space while either improving the precision of the design or at least not compromising the precision.  It accomplishes this by confounding noise (factors you are not willing to manage) with the block effect.  The noise within block remains constant (thereby having no effect and reducing the within block random errors due to noise, thus increasing the precision of the design and lowering the MSE) then that noise is purposely changed between blocks (so as to increase the inference space).  In addition, if you are able to assign the factors confounded with the block, you may be able to estimate block-by-design factor interactions to determine the robustness of your design factors to noise (absence of noise-by-factor interactions).  Is this what you intend to do?

3. You have 5 design factors (4 with 2-levels and 1 with 3 levels)?  It appears you are fractionating the design or attempting some optimal design strategy and then considering the block.  This is likely an incomplete block (BIB).  There are alternatives...as Mark suggests, if the noise is measurable, you could trade the noise as a covariate.

4. What is A?  Is A "nested" within material (different levels of A are used conditional on Material)?

5. Why do you not want to quantify the effect of material? "the categorical should be use to evaluate the effect of my starting materials, which I do not really need."  Are you concerned about the potential interactions of the design factors with Material?

6. What are the response variables?  Are they continuous?  What is your predicted rank order of model effects?