F and P-value in L9 Taguchi Design

[javadaria61]

Dear Miner

Thanks again.

This book is very old and only in hard cover, and can not access to it. Is there any other book to cover this problem? Moreover, I have Qualitek and design expert software. can you tell me what's the tittle that I search it in google.

Thanks
Javad

 

[Miner]

See section 4.3 Trend comparisons of this paper for an example.

 

[Miner]

Another paper on this topic. And one on Orthogonal Polynomial Coefficients.

 

[javadaria61]

Thanks for all of your help to me. But I have only work with software. And I don't have any basic information about experimental design. So, although you introduce very good resource for me, but I don't used them.

Thanks again for your patient and very kindly attention to me.

Javad

 

[Performer]

Hi, I came through this post while googling for the same thing. Taguchi design L9 is a saturated model, if you did only 9 experiments. In that case, you can eliminate one or two less significant terms from the model. It is called 'pooling'. When you did one set of repetitions you will have 9 more equations for estimating statistics. DOF of error/residual will be 9. With that you can calculate F and P values. Refer the following book. It's simple and easy to understand.

Design of Experiments Using The Taguchi Approach: 16 Steps to Product and Process Improvement

 

[mutbaby]

Dear Colleagues,

I have experiencing a similar situation that has been highlighted in this forum. I used L9 array for my experiment via Taguchi DOE. I tried to analyse the result but the p-value and f-value come out as *. I really need these values to explain the result of my analysis.

I have 4 factors at three levels. There are 2 responses (i.e. Response 1 and 2). Response is to be evaluated at "smaller the better" and Response 2 at "Larger the better". I have attached a spreadsheet containing the DOE with the response values.

I would be glad if you could help me out with this. It is very urgent.

 

[Miner]

You do have the same problem. The L9 array has only four columns. When you use all of the columns as you have, you have a fully saturated model with no remaining degrees of freedom for the error term, which is required to calculate the F ratio and the p-value.

As with the previous poster, you only have two options:

1. Pool one term with the smallest effect (remove from model)
2. Look up the book that I referenced near the beginning of this thread and remove the quadratic terms leaving the linear terms.

 

[mutbaby]

Thank you very much for the response to my question. I really appreciate. However, I could not get the book you referred to in your reply. I would be glad if you could attach the book for me to see the how to deal with the problem via the second approach as highlighted.

In my case, if i decided to remove one of the terms (which I tried doing and the factor removed was very important factor in my model development) it might not be able to explain the model i am intended to develop. Do you have any suggestion. Thank you.

 

[Miner]

Thank you very much for the response to my question. I really appreciate. However, I could not get the book you referred to in your reply. I would be glad if you could attach the book for me to see the how to deal with the problem via the second approach as highlighted.

There is a link for the book in an earlier post. I will not attach copyrighted materials.

In my case, if i decided to remove one of the terms (which I tried doing and the factor removed was very important factor in my model development) it might not be able to explain the model i am intended to develop. Do you have any suggestion. Thank you.

So the factor with the smallest effect size is that important?

The only other approach I can think of is for you to replicate the experiment and analyze the complete experiment using GLM (General Linear Model).

 

[mutbaby]

Thank you very much.

In fact when I realized this problem, I quickly repeated each of the runs. The ANOVA results showed a good outcome. However, because I have already stated in my experiments that I used L9, the new GLM results showed 17 total degree of freedom instead of 8 which I am quite skeptical to report in my research results.
FYI: I have seen the link for the book.

What do you suggest in this case? Should I just go ahead to report it as it is shown in the ANOVA table?

This is the out of the ANOVA after repeating each of the runs

Var DoF) SS MS F-value P-value (%)

A 2 1335.90 667.95 1471.30 0.00 63.40
B 2 305.74 152.87 336.73 0.00 14.51
C 2 448.89 224.44 494.38 0.00 21.30
D 2 12.40 6.20 13.65 0.01 0.59
Error 9 4.09 0.45 0.19
Total 17 2107.01