Assign values to factor level in a definitive screen design

[#1]

Hello all,

I have a seven continuous three-level factors for a DOE. Definitive Screen Desgin (DSD) seems better fit my purpose. For each factor, I have three phisical test samples to be assigned to the three levels. However, they don't represent the max and min values of the factor. How do I assign the physical values to each factor level in the design?

Thanks,

John

[#2]

What is your purpose for this experiment? A DSD is a better fit than what other designs? In what respect?

The DSD is likely to succeed, like any other screening design, when your case meets the screening assumptions. These assumptions are effect sparsity, effect hierarchy, and effect heredity. Otherwise, it probably won't succeed.

The answer to your specific question is two-fold:

1. You can manually change the levels of any factor in any design. The regression analysis might not be supported as well as it would be by the optimal design for the given model, but it will likely work. If the effects are large, then you should still find them.
2. You cannot change the levels of a DSD and expect it to perform like a DSD. You will introduce correlations and break the fold-over pair structure on which the new analysis depends. You can still use regression analysis but in an economical design like the DSD you don't have a lot of data to spare, so any changes of levels will have a more pronounced effect than in a large design.

Examine the impact of your level changes by selecting DOE > Design Diagnostics > Evaluate Design. Follow through the launch dialog and then look at the Design Diagnostics outline for details. Compare this information to that of the original DSD.

Also, you could simulate the response before and after you change the factor levels and compare the analyses from regression.

[#3]

Hi @Mark_Bailey

Thanks a lot for your answer. I want to optimize a mechanical system with say 7 control factors, and each factor can have three levels. In this early stage of the DOE, I want to achieve primarily screening, 2ndly characterization, and 3rdly some degree of optimization. I can afford to run about 30 tests in this phase.

I have test several designs as follows:

SSD (under Classical\Screen) using 3-level discreet numerical variables:
- Option 1: A L27 OA is given by JMP. Correlation between main factors and 2nd and 3rd order interaction were analyzed by JMP Color Map. I also was able to add 11 pair of 2nd order interactions.
- Option 2: I manually select 27 run of experiments test main factors and add 2nd order interactions (JMP allowed 19 pairs)

DSD using continuous variable
- JMP generate a 21-run design, and allowed me to add 9 pair of 2nd order of interactions.
- Based on you message, I assume I can replace each factor level with a test sample value. Right? What is efficient way to do this instead of manually change factor level one by one?
- Can the test run number be changed from 21 to 27 so as to compare with SSD?

Thanks,
John

[#4]

First of all, I want to address your general approach. We strongly advocate the principle of sequential experimentation first espoused by Box, Hunter, and Hunter. However, this strategy does not always apply. In particular, screening is not always necessary. Furthermore, screening designs are not capable if the assumptions of screening are not valid. Also, the method of sequential experimentation continues to evolve constantly. Today you have the powerful but inflexible DSD and the most powerful and most flexible custom design methods. That is, these newer methods change the tactics that you use within this strategy. Now on to your specific questions...

SSD

I don't know what you mean by "SSD" but I assume that it is a fractional factorial or Plackett-Burnam design.

Option 1:

• So you are using an orthogonal array? The L27 design is a P-B design, not an OA.
• These OA designs are specifically for main effects only models and systems. The presence of even a couple of interaction effects in your response will compromise your analysis significantly. Do not use the OA if you suspect that this is the case.
• If it is really a P-B design, then you have a good chance of estimating effects that are large. There is little confounding and the correlations of the estimates are usually small enough to allow estimation.
• What do you mean by "add 11 pair of 2nd order interactions?" You can't add terms during the design. If you mean that you added these terms later in the Fit Model dialog after clicking Make Table, how did you select these 11 terms out of the potential 21 two-factor interaction effects? Why add these terms to the initial analysis?

Option 2:

• I do not understand your explanation of this option at all.

DSD

• What do you mean you can add 9 interaction terms? Yes, you will have sufficient runs but this model will be saturated. How do you know which 9 out of 21 to select?
• Yes, you can change the factor levels. Such changes may significantly compromise the performance of the resulting design. The best way is to select the factor columns and then select Cols > Recode.
• You can change the number of runs in the design platform before you commit to the design by clicking Make Table. We strongly recommend adding at least 4 runs to the minimum. The minimum number of runs in the DSD when the number of factors is odd (7) is 2k+3 = 2(7)+3 = 17. The default number of extra runs is 4 so that is why your design is 21 runs.

Please take the time to carefully explain what you want to know, what you have done, and what you got for results. These quick, terse statements are cryptic and cause many exchanges for clarification and full disclosure before you get all the help that you need.

[#5]

Hi @Mark_Bailey,

Sorry for the confusions. Let me try to clarify them:

SSD

"I don't know what you mean by "SSD" but I assume that it is a fractional factorial or Plackett-Burnam design."
A: The term of SSD stands for standard screening design which is used by JMP 13 user guide. It is under DOE\Classical \Screening Design.

Option 1:
"So you are using an orthogonal array? The L27 design is a P-B design, not an OA."
A: I though the L27 here is a Taguchi L27 OA. I was wrong based on your description.

I do believe there are interactions here or there. So I should not use Taguchi L27 OA at this phase per your advice.

"What do you mean by "add 11 pair of 2nd order interactions?" You can't add terms during the design. If you mean that you added these terms later in the Fit Model dialog after clicking Make Table, how did you select these 11 terms out of the potential 21 two-factor interaction effects? Why add these terms to the initial analysis?"
A: Yes, I "added these terms later in the Fit Model dialog after clicking Make Table" and by clicking the Interaction command button. I didn't have the options of selecting which interaction to use. I want to study the effect of interactions, but I could not find a way to add them before clicking Make Table.

Option 2:
At DOE\Classical \Screening Design, after select factor level and type, JMP gives me two options: "Choose from a list of fractional factorial designs" or "Construct a main effects screening design". I used the latter option, and specified I want to conduct 27 runs of test. After clicking Make Table, I added interaction.

DSD

"What do you mean you can add 9 interaction terms? Yes, you will have sufficient runs but this model will be saturated. How do you know which 9 out of 21 to select?"
A: Again, I click interaction after clicking Make Table, and I couldn't select which interaction to use.
Yes, I just found I could change the number of runs, and there is a upper limit.

"Yes, you can change the factor levels. Such changes may significantly compromise the performance of the resulting design. The best way is to select the factor columns and then select Cols > Recode."
A: DSD takes 3-level continuous variables. I can specify low and high values for each factor before Make Design. After that, JMP fit the average value as the mid automatically. If the mid value of my physical sample is different, I will have to manually change it after I click Make Table. Is this going to be problem?

Yes, Custom Design is very versatile. I can add 2nd order interactions and quadratic terms. However, it seems to me that adding terms besides main factors is not supported by JMP screening design (either SSD or DSD). Please clarify and explain why.

Thanks,
John

[#6]

We have multiple topics going in this discussion. I will try to answer them in a coherent way.

Orthogonal Array

No, you were right. The Taguchi designs use an 'orthognal array' for the inner and for outer arrays of the design. These are often fractional factorial designs but they can also be P-B designs. They are generally limited to two levels. Taguchi are not used for screening, per se. The Taguchi method of experimentation is not sequential. It simultaneously screens by spanning the design space with two-level combinations and optimizes by 'pick the winner' based on a S/N ratio derived from the mean and standard deviation of the observed response (not modeling). Your previous explanations never made me think of Taguchi.

The P-B designs produce orthogonal factor columns for the experiment and, therefore, the estimates of the main effects are also orthogonal. The higher-order terms are not necessarily orthogonal, though.

There is a new design method that is also called 'orthogonal arrays.' These designs generally perform better than 'regular fractional factorial' designs in the absence of many two-factor interactions.

So the confusion comes from the different uses of the same term in different contexts.

I think that you could use the P-B L27 design for screening if the screening assumptions are valid in your case. P-B designs handle interaction effects (i.e., better chance of estimation) than the regular fractional factorial designs. I would not use the newer OA, though, if you suspect active interaction effects.

Add Interaction Terms

There is no "Interaction command button" in the Fit Model dialog.

You definitely have the choice of all the terms in the model using the Fit Model dialog. See Help > Books > Fitting Linear Models.

You cannot add terms for interaction effects before clicking Make Table in the Screening Design platform. These designs assume main effects only.

Construct a Main Effects Screening Design

The second option produces the newer OA designs, not the P-B designs. (The P-B designs are available along with the regular fractional factorial designs using the first option.)

Change DSD Factor Levels

Yes, you can change the factor levels after you make the DSD. These changes will compromise the performance and benefits of using a DSD, though. The DSD is a special case of the an alias optimal custom design. It is based on a defined structure composed of a fold-over pair of runs for each factor in which the given factor is set to the middle value and the other factors are set to either their low or high value. Center points are also added. The claims for a DSD are based on this structure. Changing factor levels after the design is constructed will destroy this structure so you should not expect the resulting modified design to be a DSD or perform like a DSD. It isn't a DSD anymore.

But changing the levels is perfectly legal and the resulting design will likely support some analysis and modeling but not in the same way or to the same extent as the original DSD. This is not the intention of the DSD method. The DSD is rigid. It does not handle every case in which screening is warranted and valid. (Hard to change factors, for example.) Have you read Brad's blog posts about the proper and improper use of DSD?

Adding Terms for Screening Designs

The JMP interface for the design of experiments is divided across many platforms that are specialized for a given method of design. You selected the Screening Design platform. It implements the regular fractional factorial method of Box and the irregular fractional factorial method of P-B. Neither of these methods address interaction effects directly with terms in the model. The regular fractional factorial design method allows you to change the generating words in order to change the aliasing of the model estimation columns by changing the factor design columns. You can't change the aliasing in the P-B design. You also selected the DSD platform. This method is even more restrictive. You can add two-level blocking and additional runs above the minimum number but that is all. In return, the unchanged DSD will allow you to estimate the main effects for up to about half of the factors in your design (effect sparsity) and some interaction and quadratic effects (assuming effect heredity).

So you are correct that the Screening Design and Definitive Screening Design platforms do not allow you to add terms to the model because that action is not part of the methods on which they are based. Those methods are design-oriented. Your idea of starting with the potentially active effects is the opposite: model-oriented design. That way is custom design.

Why don't you use custom design?

We offer two JMP training courses that you might find helpful. The first course is our introduction to DOE and it is based entirely on custom design: Custom Design of Experiments. The other course is devoted to the special situation of screening: Modern Screening Designs. (Note that the second course is advanced and assumes that you have attended a class for the first course.)

Of course the JMP guide for design of experiments is also very helpful (Help > Books).

[#7]

Hi @Mark_Bailey,

It took me a while to digest all your inputs. Let me try to summarize my understanding with questions below:

About Screen methods:
- Design oriented
- "These designs assume main effects only." So they are not designed to study interactions or quadratic terms?
- "P-B designs handle interaction effects (i.e., better chance of estimation) than the regular fractional factorial designs." This means P-B designs can handle experiments with main factor interactions, but it does NOT mean we can include the interaction terms in the model, right?
- DSD: "unchanged DSD will allow you to estimate the main effects for up to about half of the factors in your design (effect sparsity) and some interaction and quadratic effects (assuming effect heredity)." Say I have seven factors, DSD can estimate the effects of three to four factors, but not all the seven? DSD can estimate some interaction and quadratic effects, but does NOT include interaction and quadratic terms in the model, right?

Taguchi Method
- It can be fractional factorial or P-B based
- Assumptions include addictiveness (orthogonal) between factors, thus interaction will cause problem
- Not sequential, thus not for screening purpose
- "It simultaneously screens by spanning the design space with two-level combinations and optimizes by 'pick the winner' based on a S/N ratio derived from the mean and standard deviation of the observed response (not modeling)."
- Question: Taguchi Method actually encourages the usage of three level factors so as to catch the nonlinear effect. Why you said the factors area mostly two-levels?

For my condition and goal:
1. I have 7 continuous 3-level factors
2. There will be interactions between factors, but don't know exactly which ones
3. The goal: optimize the system performance (by studying factor effects)

Model-oriented: If I know what (main, interaction and quadratic terms) I want to study, custom design is effective. In addition, if additive condition is met, Taguchi Method can be efficient. 

Design-oriented: If I don't know much about effect of main, interaction and quadratic terms, sequential approach with screening design is effective. 

Please comment/answer on my understandings/questions.

Thanks,

John

[#8]

First of all, I am sorry for the delay in responding.

It is clear from your questions that you need an education in the design of experiments. It is difficult to educate anyone in short exchanges within a discussion on a forum like this. I want to point you to some books that will help.

1. In JMP, select Help > Books > Design of Experiments.
2. Obtain a copy of "Optimal Design of Experiments" by Goos and Jones.

We also offer training about design of experiments. Assuming that you are already familiar with JMP and the analysis methods of ANOVA and regression, you would benefit from attending a class for:

• JMP Software: Custom Design of Experiments (introduction to DOE)
• JMP Software: Modern Screening Designs (advanced course specifically about screening)

As to your specific questions:

• P-B designs do not address interactions or non-linear effects directly. The sparsity of effects and projection principles might help obtain information about interaction effects if they hold.
• The DSD for 7 factors might work if you ultimately have 2-3 active factors.
  • The higher order terms are not included.
  • They are discovered after the main effects have been selected assuming that the hierarchy and heredity principles hold.
  • Alternatively, you can use the new Fit DSD approach if you have not changed the levels.
• The Taguchi approach may include three levels for your factors.
  • It does not overtly estimate model parameters. There are no interaction or non-linear effects per se.
  • It is a 'pick the winner' methodology among the existing set of inner array runs based on an appropriate S/N ratio over the outer array levels.
  • There is no modeling and, hence, no prediction (interpolation or extrapolation).
  • The Taguchi designs might lead to sub-optimal results if there are non-additive effects.
• The model-oriented method is custom design.
  • Taguchi method is definitely not model-oriented.
  • Taguchi method fails except in the simple case of only main effects.
  • Taguchi designs are not the most economical designs.
• Design-oriented methods simply means methods that are focused on the method of design (e.g., factorial design) and the model is a result (full factorial terms). Model-oriented methods, like custom design, focus on the model and the design is a result.