How do I create a fractional factorial DOE with replicates in JMP 16?

[#1]

Hello all,

I am trying to create a fractional factorial balanced DOE matrix with 11 3-level factors and 27 conditions and 4 replicates per condition (5 runs per condition). How do I go about doing this in JMP 16? I tried using a custom design and specifying "4 replicates" and "135 runs" but I am not getting a matrix with replicates. Instead, I am getting 135 different runs. Below is the DOE data table I want to generate with 5 runs for each of the 27 conditions.

[#2]

A couple of things regarding terminology. It sounds like you are creating a Custom Design, which will be an optimal design, not a fractional factorial. This type of design is not guaranteed to be a "balanced" design.

With that out of the way, here is how you create the design: DOE > Custom Design. Enter your 11 3-level factors. Choose your model (which is just main effects, apparently) and create the 27 run design. Note that there is an option to enter the number of replicate runs BEFORE you make the design. However, entering a number there has JMP search to add that number of replicates in an optimal fashion. It is not for replicating the entire design. Once the design is created, make the table. Now go back to the DOE menu and choose Augment Design. Specify the factors and responses. Then you can choose Replicate. JMP will ask for the number of times to perform each run, enter 5.

Since it appears that you already have a 27 run design, you can just use the Augment Design option on your existing 27 run design.

[#3]

Hi Dan, 

Thanks for the clarification. If I use the custom design option and create the 27 run design (which does not match my reference design shown above), can I change the values of the factors based on my reference matrix above and retain all the functionality of the built-in DOE model evaluation?

Thanks,

Sravya

[#4]

Hi @Sravya_J,

Looking at your coded matrix, it's hard to tell which type have the different factors (all continuous, or some categoricals ?), and so to give you advice for the design creation. Note that if you have the matrix in Excel file, you can simply import your file and then add manually properties to the different factors column (Coding, Design Role and Factor Changes for continuous factors) to make JMP understand this is a DoE (even if the model will not be pre-specified and will have to be specified in the analysis through the platform "Fit Model").

@Dan_Obermiller gives you the whole procedure to create a Custom optimal design and how to replicate, but there may be some details to consider :

• In case of only continuous factors and looking at your matrix, this design doesn't look like a typical fractional factorial design, as you seem to have three levels for all factors; "traditional" fractional factorial designs have 2 levels (one high, one low). Which design did you use ? What are the model terms ?
• Do you have constraints in your design (blocking factor or hard to change factor) ? It seems Cycle time (first factor of the DoE ?) has some constraints on randomization, so if it's the case, you can specify it during the Custom DoE creation (creating blocking Factors (jmp.com), Group runs into random blocks of size (Design Generation (jmp.com)), or setting some factor type as "Hard to change" to specify a constraint on randomization (exemple here : Example of the Factor Changes Column Property (jmp.com))

For Screening situations with a high number of factors (only continuous or 2-level categorical) and no constraints on randomization (no blocking or else), you could also use a Definitive Screening Designs (jmp.com), which creates experiments for continuous factors at 3 levels (low, medium and high).

• For 11 continuous factors, the DSD creates between 25 (minimum without extra runs) and 29 runs (4 extra runs, settings recommended and by default in the DSD platform), and you can then replicate the entire design by following the procedure explained by @Dan_Obermiller.
• If "Cycle time" is not a factor, the DSD requires for 10 factors between 21 and 25 runs.

If you can give a little more informations on number of factors, type, objective of the design and terms in the model, we can perhaps help you create other designs that may be well-suited for your needs. It might be very rewarding to create several designs with different platforms/options or terms in the model, and Compare the Designs (jmp.com) : the advantages and drawbacks of each design to make the best choice and have more confidence in the properties and performances of the chosen design.

Hope this complementary answer will help you,

[#5]

Hi Victor,

Thanks for the detailed explanation. All my factors are categorical with three levels and identical cycle times were put together for ease of conducting the experiments. I asked Dan as well, but when I do a custom design like Dan suggested, a matrix which is not the matrix I want is generated. Could I simply change the entries in the generated data table to match my desired matrix and have the built-in DOE evaluation script run accurately?

Best,

Sravya

[#6]

JMP will build the design you want. The design is available in one of the older DOE platforms. Select DOE > Classical > Two-Level Screening > Screening. Define your 11 factors as Discrete Numeric with 3 levels. Click Continue and select the first radio button (fractional factorial), which is the default choice.

See this documentation and read about Placket-Burman designs.

Please see the important advice offered here. A successful experiment is more than how the design is made.

Here is an example with 11 factors with 3 levels. It is a P-B L27 design. Use the DOE Dialog table script to start at the beginning of the design process.

[#7]

Here are my thoughts/questions/comments:

There are many questions before providing an appropriate response.  I apologize, I think it is appropriate to consider why you want the experiment you are planning rather than just say here is how you create it in JMP.  Feel free to ignore my thoughts if they are not useful.

It sounds like you have decided on 27 runs (treatment combinations)?  Is this a Taguchi L27 design you want?  Why?  You want to do a fractional factorial, but you are testing factors at 3 levels?  Why?  Are you trying to do a screening design? You will be confounding 2nd order linear effects with non-linear effects. This doesn't really follow hierarchy guidelines.  So this begs the question, what model are you trying to evaluate?  Do you want to understand causal structure or "pick a winner"?  Why 4 replicates?  Estimating quadratic and cubic effects of a replicate is non-sensical.  Can you get a reasonable estimate of noise using 2 replicates?  You want 5 repeats of each treatment, why?  Do you understand how you will use the repeats?

My advice is to think sequential experimentation.  First evaluate the relative importance of the 11 factors by exaggerating each of their effects equally.  Accomplish this by using 2-levels that are set boldly.  This creates a design space.  Determine if this space is appropriate.  If not, move the space (by changing factors or factor levels), if it is, augment the space (add levels, center points,  etc.).  replication and repetition are 2 excellent strategies to handle noise.  Repeats for short-term noise components (measurement, within sample, sample-to-sample) and replicates for long term noise components (raw materials, ambient conditions, etc.).  You might consider blocking as strategy for replication.  I would start with 2 extreme blocks.  Much depends on the noise you are trying to "evaluate" or whether you are trying to be robust to noise.