Design of Experiments (5 factors with 3 levels) - How to proceed with Minitab?

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Don S.

Hello Quality Professionals,

I have very little experience with DOE's and I was wondering if I could get some much needed advice. I have been involved with a team to improve a process to find the optimum settings to ensure the process produces a product within specifications. The team has arrived at 5 factors with 3 levels for 3 of the factors and 2 levels for the other 2 factors. I find Minitab a little intimidating as I have not used that software for this purpose before. I was wondering if anyone could offer some advice with how to proceed with this experiment.

Thanks,

Don
 

Miner

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Re: Design of Experiments

I have been involved with a team to improve a process to find the optimum settings to ensure the process produces a product within specifications. The team has arrived at 5 factors with 3 levels for 3 of the factors and 2 levels for the other 2 factors.

First question: Do you know for a fact that all 5 factors have a significant effect on the process? If not, start with a fractional factorial of the 5 factors at 2 levels. Keep the resolution of the design at IV or greater to identify main effects and 2-way interactions. This is called a screening design. It is used to reduce the number of factors to those that are significant.

Once the number of factors has been reduced, the next step is to run the modeling and optimization experiment. The best approach is to run a response surface design on the remaining factors.

Another possibility depending on your process is EVOP (Evolutionary Optimization of Process). This involves making small incremental changes and tweaking the process along the path of steepest ascent.
 
K

kaikai

There are many kinds of Experimental designs.
So, the suitable design is determined by considering various situations as mentioned by Miner.

If you explain more clearly about the problem you faced, someone can help you. (Sorry, I can't use minitab. I'm a JMP user.)
 
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D

Don S.

Hello,

Thanks for the responses. Here is my challenge: the team needs to design the optimum setting for a "flow coat process". The flow coat is applied to a product in a wet state and proceeds through an oven process and comes out in a "fired thickness" state. A dimensional change to the product being flow coated has resulted in the flow coat being too thick and out of specifications using the current settings. Therefore the team believes there is 4-5 factors contributing to the process. Some factors would be considered to have 3 levels, however we need to start with 2 levels for each factor. The factors in question are pressure; pump time; spin time; spin speed and maybe dwell time. I have reference material but this is the first DOE I have attempted and obviously a very large and potential complex one. We don't have the time or resources to conduct a full factorial design so would a fractional factorial design work? I know Miner mentioned to keep the resolution of the design at IV or greater and I am not 100% sure what this refers to. We are firstly going to collect data at the current settings of the process and go from there however I am looking for some much appreciated direction.

Thanks,

Don
 

Tim Folkerts

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Here is one definition of "resolution" from the NIST handbook http://www.itl.nist.gov/div898/handbook/index.htm (This handbook is a very handy source of info on industrial statistics)
Resolution: A term which describes the degree to which estimated main effects are aliased (or confounded) with estimated 2-level interactions, 3-level interactions, etc. In general, the resolution of a design is one more than the smallest order interaction that some main effect is confounded (aliased) with. If some main effects are confounded with some 2-level interactions, the resolution is 3. Note: Full factorial designs have no confounding and are said to have resolution "infinity". For most practical purposes, a resolution 5 design is excellent and a resolution 4 design may be adequate. Resolution 3 designs are useful as economical screening designs.
 

Miner

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Tim gave a good explanation of resolution.

There are three classical experimental designs available in Minitab for 5 factors. These are:

  • 2^5 = 32 run full factorial
  • 2^5-1 = 16 run half fraction factorial of resolution IV
  • 2^5-2 = 8 run quarter fraction factorial of resolution III
I recommend the 16 run half fraction. This will allow you to screen out any unimportant factors and identify potential interactions. The purpose of this first experiment is only to reduce the potential number of factors, not to optimize.

All of your factors appear to be continuous, so a response surface design is probably the best type of design to follow-up and optimize the levels of the important factors.
 
D

Don S.

Hello,

The team has decided to explore the three factors with three levels. I am using Minitab to perform the calculations however I am having some difficulty and I hope I can get some help. I have followed the steps as per the tutorial procedure: General full factorial design with 1 replicate for a matrix of 27 runs. I have used the random generator of 9. I enter my results in the last column. When I get to step 7 which is "screening the design-fit a model" I enter the response box and click graphs I do not get the option to select the "normal" and "pareto" graphs as in the tutorial when a 2 factor DoE is performed. I then proceed to the next step and the General Linear Model statistics do not give a "p" value thus I cannot tell which factors are deemed significant. It states at the bottom of the stat table the the "denominator of F-test is zero" and also a note stating "could not graph the specified residual type because MSE=0 or the degrees of freedom for error =0. I do not have a lot of experience using Minitab in this application.

Could someone please help explain what I am doing wrong with this software?

Thank you,

Don
 

Miner

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I am trying to go by memory on this because I am at home and do not have access to Minitab at the moment to verify what I am about to say next.

The General Full Factorial analysis does not perform the standard ANOVA as is done for the 2-level designs. Instead, it uses the General Linear Model, which is a form of regression analysis. This adds the flexibility needed to handle the variety of levels, but does not provide some of the graphical output to which you may be accustomed. Note: the Taguchi option provides output that differs even more, so use with extreme caution.

Now for your other question, the answer is straight forward. The reason that you do not get a p-value is that your model is fully saturated (0 df left for the error term). You can handle this two ways. Best way: Add a replicate. Alternate way: Find the term with the smallest mean square value, and remove it from the model. This will move the df to the error term and allow the calculation of p-values.
 
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Don S.

Thanks for the reply.

Is it possible to add another replicate without having to perform more runs in the experiment? Due to time and scheduling factors we cannot perform any more than 27 runs.

Don
 

Miner

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Admin
Unfortunately, no. Replicates are independent runs, so adding a replicate would double the number of runs in your experiment.

Do not confuse this with repeats, which are multiple measurements for a single experimental run. Repeats allow you to analyze means and standard deviations in order to optimize both, but do not add additional degrees of freedom.

Since you cannot add runs, use my alternate recommendation, which is removing terms from the model to free up degrees of freedom. Start removing the highest level interactions first (3 - way and higher). Make sure that the mean squares for these terms are low compared to the other terms.
 
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