Custom Design Around Existing Data With Blocking Factor

[#1]

Hello,

I'm trying to optimize process parameters for a 3D printing task. I have 6 different "plants" that I'd like to treat as a blocking factor. In order to get an estimate of process variance, I collected 18 center-point samples for my factors, 3 samples per plant. I'd like to design an I-optimal experiment and I'd like to use these center-point samples in that study to reduce the number of new samples needed. Here's what I've tried:

1. Set all factor columns coding and design role. I have 4 numeric continuous factor, one numeric discrete factor, and one blocking factor.
2. Augment design
   1. I don't select the blocking factor, as I can't edit the "number of runs per block" in augment design 
   2. Set I-optimality criteria
   3. Add appropriate levels to factors (augment design treats my discrete numeric factor as continuous, but this seems ok because the levels are just 0, 1, 2 which works as a continuous variable with levels 0 and 2).
   4. Add 2FI and 2nd power effects to model where applicable
   5. Set number of runs to 78 (targeting 90 runs total with 12 repeats)
   6. Generate table
3. Custom design, here's where I'm getting stuck
   1. Add blocking factor to table
   2. Make sure blocking factor column design role is "blocking"
   3. Add 72 runs from table in last step as covariate factors including blocking factor
   4. Add same 2FI and 2nd power effects to model from last step
   5. Select "Include all selected covariate rows in the design" and "Allow covariate rows to be repeated"

A few problems I've ran into:

• It doesn't look like I can specify "12 repeats" when I am creating a custom design with covariate factors, I can only tell JMP the number of runs
• If I select the blocking factor as a covariate factor it isn't treated like a blocking factor, just a covariate factor. If I don't select the blocking factor when adding covariate factors and add it as a blocking factor in my custom design, the custom design has no way of knowing what blocks each of my 18 data points belongs to.
• All of the factors that I add as covariates appear in my factors table as "covariate" role. I'm not sure if this is a problem, but it means I can't distinguish blocking, numeric continuous, and numeric discrete
• I get the error "The selected terms in the model outline are linearly dependent on previous terms" whenever I have any effects other than my blocking factor and the interecept. When I tried just making a custom design with 90 total points, 18 center-points, and 12 repeats with all the same modeled effects that worked fine so I'm not sure why I'm getting this error here.

I feel like this workflow (get center-point data to estimate variance, then build a DOE around your already-collected center-point data) is pretty common so there must be a good way to do it. Any guidance would be greatly appreciated!

[#2 · Accepted solution]

Hi @TimCarrWPI,

Welcome in the Community !

From what I understand, you're able to augment your design, but you are facing problems to enforce the blocking factor correctly in the augmented design ? Concerning your factors, it seems the ironing pass factor is wrongly defined as continuous and not discrete numeric (you also have to change the modeling type to Ordinal).

What may be possible is to :

1. Augment your initial 18 center points into a RSM I-Optimal design, and specifying a total number of runs of 90. This option may however not provide exactly 12 replicate runs, so instead, you can use the Custom Design with the factors you have defined to create the design around the center points, and enforce the 12 replicate runs condition:
   
2. Once your design is created, you can concatenate your initial 18-runs dataset to this custom design to get to 90 runs.
3.  You finally have to sort the runs by the block number (Mandrel factor), and randomize the runs within each block, and you'll end up with the design you expected.

I recreated and added the script in the final design table to evaluate the design and launch the fit model platform. Please find attached the factors table I used to create the "Custom Design part", the Custom design, and the final design with your 18-runs dataset.

You might get interested in this closely related topic: Forcing center points to be equally distributed across blocks custom design 

I hope I have understood your situation and that this response will help you,

[#3]

Thank you for your help @Victor_G ! I believe you've presented two potential solutions, but I have a few questions/concerns about them:

Augment the design around my 18 center-points at 90 total samples. Here's what I am trying for this method: 

1. Start with "Augmented Design Input.jmp"
2. Select "Augment Design" an add all columns besides the response (adhesion strength) to X with adhesion strength in Y
3. Add levels to each non-blocking factor so they're not treated as constant

Here are the issue I'm having:

• I can't change "runs per block", so when I try to expand to 90 runs it adds a ton of levels to the blocking factor (mandrel)
• If I can't specify the number of repeats, does JMP intelligently choose repeats to ensure I have a good estimation of the error? Obviously I need some repeats to perform a lack of fit test.

Use a custom design at 72 runs and then concatenate my center-points. Here's my concerns with this method:

• JMP's custom design tool doesn't "know" that I've already collected 18 center-points, so I worry that the optimizer will choose a sub-optimal distribution of points as it tries to fill in near the center of the parameter space not knowing that I already have a bunch of points there.
• If I could force the custom design solver to put 3 center-points per block when it generates the design, then I could just fill in those points with my already-collected data, but based on the discussion you linked to it doesn't seem like that's possible.

TLDR:

• I need exactly 6 blocks and Augment design doesn't let me specify the runs per block
• If custom design doesn't "see" my previously-collected data then it won't generate an optimal design (I think)

[#4 · Accepted solution]

Hi @TimCarrWPI,

Yes, the direct design augmentation path may be difficult to handle regarding the blocking factor. One way to solve this is to augment your initial design without the blocking factor up to 90 runs, and then use the Custom Design platform to include all the runs of the augmented design as covariates, add a blocking factor with 15 runs per block : 

As you mention, during the augmentation you won't have full control over the number of replicate runs, but JMP will allocate replicate runs to reduce the prediction variance where it is the highest.

Regarding your concerns about the optimality of the design with the second option:

• Center points are primarily used for two reasons: estimate pure error for the lack-of-fit test and decrease variance prediction in the centre of the experimental space (see effect of centre points for more details). They are not helpful for model terms estimation, so I wouldn't worry much about any optimality loss of not considering them during design creation.
• By default, when you specify a RSM model, JMP is not proposing any center points, but instead some points where one factor is at the middle level, and the other factors levels are at min and max values. So even if you build the Custom design independantly before concatenating your center points dataset, you won't create new center points. One way to check this is to look at my final design file shared previously, you can select one row of your center points for the 5 factors columns and use Rows > Row Selection > Select Matching Cells. The center points highlighted in the table only comes from your initial dataset. 
  

I'm not aware of a way to enforce center points "homogeneously" across blocks, so that's why I linked the previous discussion relating the same issue.

Hope this answer will help you,

[#5]

Your explanation makes sense, thank you! I'll proceed using the custom design tool to create 72 runs and just concatenate the center-points in front of that data during analysis.

Cheers!