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Apr 1, 2009 8:09 AM
(1548 views)

Hi there!

I have a four step process whose process robustness I'm evaluating and I was hoping to do this with a DOE. Here's the basic process:

Input stream--->Step A--->output/input-->Step B-->output/input-->

Step C-->output/input-->Step D--> product!

Step B has three factors affecting the product purity and yield of its in-process output while steps C and D each have four factors affecting the product purity and yield of their in-process output. What I want to do now is correlate changes of these factors to the PRODUCT purity and yield. It seems to me that a fractional factorial DOE is the way to go. What are your thoughts? Also, is there a mechanism that could allow me to correlate analytical data from output/input of one step with the analytical data from the product? We have a debate going with some of our group arguing that the tolerance intervals of a given step output can serve as a predictor of the product quality. I argue that the remaining process steps aren't accounted for in those tolerance intervals and thus limit their ability to predict the final product quality. Your thoughts?

I have a four step process whose process robustness I'm evaluating and I was hoping to do this with a DOE. Here's the basic process:

Input stream--->Step A--->output/input-->Step B-->output/input-->

Step C-->output/input-->Step D--> product!

Step B has three factors affecting the product purity and yield of its in-process output while steps C and D each have four factors affecting the product purity and yield of their in-process output. What I want to do now is correlate changes of these factors to the PRODUCT purity and yield. It seems to me that a fractional factorial DOE is the way to go. What are your thoughts? Also, is there a mechanism that could allow me to correlate analytical data from output/input of one step with the analytical data from the product? We have a debate going with some of our group arguing that the tolerance intervals of a given step output can serve as a predictor of the product quality. I argue that the remaining process steps aren't accounted for in those tolerance intervals and thus limit their ability to predict the final product quality. Your thoughts?

10 REPLIES

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A fractional factorial is one of many experimental designs that *could *be used here. Since you don't specify whether or not you want to look for interactions (and what type of interactions), since you don't specify whether or not you want to look for curvature, and since you don't specify how many runs you can make of this four step process, and you don't specify other things that may or may not be important in an experiment, then all I can say is that you *could *use a fractional factorial design, but other designs might work better.

> Also, is there a mechanism that could allow me to correlate analytical data from

> output/input of one step with the analytical data from the product?

Let me make sure I understand ... we are no longer talking about a designed experiment, but simply analysis of data collected from this process, right?

In that case, correlation analysis should be able to do this.

> We have a debate going with some of our group arguing that the tolerance

> intervals of a given step output can serve as a predictor of the product quality.

Tolerance intervals are basically a function of the variance at a particular step. Therefore, you*could* use the variance rather than the tolerance intervals as a predictor. I have never seen tolerance intervals used as predictors.

> I argue that the remaining process steps aren't accounted for in those tolerance

> intervals and thus limit their ability to predict the final product quality.

Any single predictor from Steps A, B, C and D necessarily doesn't use information from later or earlier steps, and so their ability to predict may be limited. Or its ability to predict may not be limited. It depends on your process. But, if you know you have a multi-step process, you will be better off building a model that has all of the predictor variables in the model (plus interactions, curvature as appropriate) from all of the steps. You wouldn't normally model on a single predictor variable's effect on final product quality.

> Also, is there a mechanism that could allow me to correlate analytical data from

> output/input of one step with the analytical data from the product?

Let me make sure I understand ... we are no longer talking about a designed experiment, but simply analysis of data collected from this process, right?

In that case, correlation analysis should be able to do this.

> We have a debate going with some of our group arguing that the tolerance

> intervals of a given step output can serve as a predictor of the product quality.

Tolerance intervals are basically a function of the variance at a particular step. Therefore, you

> I argue that the remaining process steps aren't accounted for in those tolerance

> intervals and thus limit their ability to predict the final product quality.

Any single predictor from Steps A, B, C and D necessarily doesn't use information from later or earlier steps, and so their ability to predict may be limited. Or its ability to predict may not be limited. It depends on your process. But, if you know you have a multi-step process, you will be better off building a model that has all of the predictor variables in the model (plus interactions, curvature as appropriate) from all of the steps. You wouldn't normally model on a single predictor variable's effect on final product quality.

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Ack! Paige, you are quite right to point out what's missing in my request! Thanks so much! Let me elaborate:

1. Goal: determine how robust a process is within the normal operating ranges of its various steps

2. We're limited by time, so mostly interested in main effects with some two-way interactions welcome (aliasing is okay!). We can always go back and dig deeper if we see something important.

3. Curvature is useful. My initial plan was to simply include some centerpoints to get a very rough idea if there's any curvature there. Again, we can expand if something becomes apparent.

4. "Also, is there a mechanism that could allow me to correlate analytical data from output/input of one step with the analytical data from the product?" You know, I hadn't considered correlation analysis! DOH! Great idea, thanks!

5. "Tolerance intervals are basically a function of the variance at a particular step. Therefore, you could use the variance rather than the tolerance intervals as a predictor. I have never seen tolerance intervals used as predictors." Thanks!

6. Ditto on the remaining points!

Did I say thanks? ;-) Thanks! I look forward to paying it forward. *lol* Not to be redundant or repeat myself. *lol*

1. Goal: determine how robust a process is within the normal operating ranges of its various steps

2. We're limited by time, so mostly interested in main effects with some two-way interactions welcome (aliasing is okay!). We can always go back and dig deeper if we see something important.

3. Curvature is useful. My initial plan was to simply include some centerpoints to get a very rough idea if there's any curvature there. Again, we can expand if something becomes apparent.

4. "Also, is there a mechanism that could allow me to correlate analytical data from output/input of one step with the analytical data from the product?" You know, I hadn't considered correlation analysis! DOH! Great idea, thanks!

5. "Tolerance intervals are basically a function of the variance at a particular step. Therefore, you could use the variance rather than the tolerance intervals as a predictor. I have never seen tolerance intervals used as predictors." Thanks!

6. Ditto on the remaining points!

Did I say thanks? ;-) Thanks! I look forward to paying it forward. *lol* Not to be redundant or repeat myself. *lol*

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Process robustness usually requires curvature and some interactions.

You could do a fractional factorial with center points as a first experiment, and then follow up with a central composite design experiment using only the "active" factors found in the fractional factorial.

You could do a fractional factorial with center points as a first experiment, and then follow up with a central composite design experiment using only the "active" factors found in the fractional factorial.

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That's a really good idea! I'm in the process of drawing up my plans for this investigation and hadn't considered expaning beyond the fractional factorial. I like the idea of identifying "active" factors and then exploring their behavior in full. Thanks for the continuing dialog!

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One solution is to run a 12 or 24 runs plackett burrman. You may have 11 factors wit the 12 run. Thanks to projectivity if only 3 or 4 factors are active you will be able to detect interactions (I recommend to use partition to see that or stepwise regression)

I have had some very good experiences with those designs in similar cases.

Yves

I have had some very good experiences with those designs in similar cases.

Yves

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Yves, thanks for the thought. I may stuck, however, because one of my process steps may not have a sufficiently small scale-down model to enable me to complete even a modest fractional factorial. I totally appreciate your input!

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I have two questions that fit with this thread.

1) once I have determined the interactions and have created my process parameters can I have jmp help me design a study to check that those parameters can consistently produce good product.

2) What if my final test is just a pass/fail? How do I determine appropriate sample sizes using jmp.

1) once I have determined the interactions and have created my process parameters can I have jmp help me design a study to check that those parameters can consistently produce good product.

2) What if my final test is just a pass/fail? How do I determine appropriate sample sizes using jmp.

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> I have two questions that fit with this thread.

>

> 1) once I have determined the interactions and have

> created my process parameters can I have jmp help me

> design a study to check that those parameters can

> consistently produce good product.

>

> 2) What if my final test is just a pass/fail? How do

> I determine appropriate sample sizes using jmp.

1) JMP will design experiments for you, given the requirements that you provide it. It will also statistically analyze the experiments. By "consistently produce good product", I assume you mean you want to optimize the responses somehow, and if a condition exists that "consistently produce~~ good product", JMP should be able to find it.~~

2) I have an older version of JMP, and it will help you find sample sizes in the case of two sample proportions, which is about as close as it will come to finding sample sizes for pass/fail responses in a designed experiment. I don't know if newer versions of JMP will handle this situation exactly.

>

> 1) once I have determined the interactions and have

> created my process parameters can I have jmp help me

> design a study to check that those parameters can

> consistently produce good product.

>

> 2) What if my final test is just a pass/fail? How do

> I determine appropriate sample sizes using jmp.

1) JMP will design experiments for you, given the requirements that you provide it. It will also statistically analyze the experiments. By "consistently produce good product", I assume you mean you want to optimize the responses somehow, and if a condition exists that "consistently produce

2) I have an older version of JMP, and it will help you find sample sizes in the case of two sample proportions, which is about as close as it will come to finding sample sizes for pass/fail responses in a designed experiment. I don't know if newer versions of JMP will handle this situation exactly.

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You did not specify whether your factors are continuous or categorical. Assuming they are all two level categorical factors then I would recommend using the custom design capability in JMP to examine your factors and delineate the key main effects with the minimum number of experiments. It would be useful to have some replicates of the center point to give you a feel for lack of fit (curvature) as well as pure error. After completing the first set of runs thenI would use the augment feature in JMP to pick the additional terms to add to the model to delineate based upon the conclusions from the first set of experiments. As far as identifying the most robust operating conditions JMP allows you to use the prediction profiler along with the prediction formula from the model to include not only the response of interest but also the first derivative of the response to find the most robust settings. You can also use the simulation capability to examine Monte Carlo simulations of the model and see the effect of variable X levels on your output Y responses.