Full factorial design- results interpretation 1

[hubihubi2]

Hello,

I conduct an engineering research and use Design of Experiments method. One of techniques that I employed is full factorial design (3^3=27 runs per 1 series of experiments) in order to identify potential interactions between 3 parameters. I have processed the results using MiniTab programme and received plots representing the interactions. Please refer to the picture attached. I also enclose the plot showing the individual influence of the examined parameters on the system, achieved from Taguchi L9 (3 parameters, 3 levels, 9 runs).
My interpretation of the interaction plot is that:
- there is no interaction between the parameters as the lines in the plot do not cross and they are parallel,
- if the line would cross that would indicate very strong interaction,
- if some lines would not be parallel (but they would not cross), then I would assume that there is an interaction and perhaps another factorial design with higher number of levels would be recommended.

Links to the pictures:
- interaction: [

http://files.engineering.com/getfil...0-412a-8574-5431ab337f1a&file=interaction.JPG

]

- individual: [

http://files.engineering.com/getfil...3c-43e2-b57d-efc28d0d882c&file=individual.JPG

]


As I understand well, the results from individual analysis of the parameters already indicate (in the plot attached) that influence of 'plate thickness' on the system is absolutely dominant, and that perhaps no interactions can be expected. However, the interaction between parameters had to be checked, as some parameter may have small influence on the system but it may also have strong impact on the system along with another changing factor.

I post this message with kind two inquiries:
1. do anyone has any ideas about possible another or additional interpretation of the results shown in the plot,
2. my second inquiry would be about possible 'ABC' type of interactions. There is an option in MiniTab to present results for this type of interaction but the only plot that I achieve, is this one that I enclosed to this message.
I would be very appreciated for any comments or help.

Best regards,

Robert

 

[magoo2]

I think you have extracted all the usful results from the data.

The main effects plot clearly shows that thickness is the dominant characteristic followed by width and length.

Your interaction plots (torsion 135) have no intersecting lines, so there is no interaction. The characteristics are all parallel.

On your question about the ABC interactions, wouldn't you expect to see some non-parallel lines on your interaction plot to guide you in this? Not seeing any, why do you believe they exist?

 

[hubihubi2]

magoo2,

Thank you for your reply. I am very appreciated for your answer.
I was interested in ABC only from the point of view, how to do it with MINITAB. I agree tha AB, AC ,BC analyses showed that there was no interaction between the parameters.

Please allow me to ask one more question.
When I was calculating the individual influence of the parameters on the system, then I was using logarithmically transformed values of the stresses (output value) measured after each run in the construct (according to formula -10*log(sigma^2), where sigma denotes the stress in the system induced after particular run. This gives the advantage of allowing factor effects to be added in unbiased manner.
However, for the interaction analysis, I used the values of the output (stress in the construct) not logarithmically transformed. I would like to ask you very kindly whether you would have any suggestions that I should use logarithmically transormed or not transformed output values for the interaction analysis.
I would be very appreciated for any comments or advice.

Best regards,

Robert

 

[magoo2]

I think, if you don't get interactions between AB, BC or AC, you shouldn't expect to get any ABC interactions. I think you can do this in MiniTab. Set up a regression for torsion using t, w and l. Include t*w, t*l and w*l. The p values for the products should all be fairly high meaning they are not significant. Repeat with t*w*l. Again I'd expect the p value to be higher still.

I'm guessing you chose the log of because it gave something that looked more normal in the distribution. I believe if you should also use the log of the stress and the inputs in the interaction plot. Once you see if there are any interactions, you can work back with inverse log to see the range of interest.

It's been a while since I messed with this aspect of MiniTab, but if you post the data, I can see if what I suggested makes sense or not.

 

[hubihubi2]

magoo2,

Thank you for your email and your advice regarding to the interaction analysis.

Please find below the link to the file, which shows set of data for which I am going to do interaction analysis.
You will find there values of three varying parameters measured after each run (plate thickness, plate width, plate length), value of the stress measured in the system after each run as well as the transformed stress which I have used in analysis of the individual influence of the parameters on the system.
I am very appreciated for your help.

link: [

http://files.engineering.com/getfil...-b76c-c6c44abf8b44&file=axial_L9_135_6810.xls

]

Best regards,

Robert