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Difference between softwares in choosing correct Taguchi designs

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christianos

#1
Dear All,

I've met a strange problem. I use Minitab 15. I've created Taguchi L36 design (2 factors on two levels, and 2 factors on 3 levels)
Level 1 2 3
Level 2 20 40
Level 3 25 30 35
Level 4 0.1 0.2 0.3

Everything looks nice, however, when I used DOE++ software (from Reliasoft) just to compare my matrices it did NOT give me the same arrangement. Those mixes of factors are in some cases different and don't occur in matrix from Minitab. I thought it is because of the difference between "run order" and "standard order", however, when I created those matrices in the same order there was still a difference.

For example, Minitab produce runs like:
2 20 25 0.2
2 20 25 0.3, I could not find these runs in other DOE++ software.

Do you know what are the rules (science behind) that these softwares are picking up different examples of runs?

If you need more explanation, please let me know.

Thanks,

Krystian
 
A

Allattar

#2
I dont know how DOE++ works but in Minitab you can pick from the designs either where to put the factors, or the interactions you want to estimate.
Look in where it says factors inside create factorial design and you can choose the column position for each factor. Compare that to a taguchi plot to identify what you want where.

It is probably easier, to use the more automatic feature to allow it to select interactions. That way Minitab will place factors into the columns such that you can identify that interaction. Although for your design you cannot specify any interactions, eg: you cant see them from this design.

Taguchi designs are not typically randomised either. The suggestion being you put hard to change factors in as column A then B etc... Which means you have to be careful of time dependant effects, or be sure you have none.

Out of interest why are you using the Taguchi design, instead of say a 2 level factorial design.

A 2 level factorial with 4 factors is 16 runs and can see interactions. Replicate twice for a high power and its 32 runs. If you need to check for curvature 2 or more centre points may be added. Unless there is a specific reason for the Taguchi, the factorial is more efficient in number of runs here.

Also how many noise factors are you using in the outer array? eg how many times are you re running the design with different settings on the outer array?
 
C

christianos

#3
It has been told me that Taguchi will work fine as different people in that company use it. I might be wrong with that approach.

I thought that when I type some parameters in Minitab it will do a work for me. I mean software will locate my parameters in correct columns. How do I know where and in which order I should put these parameters?

I need to find out what is between 25 and 35. It means that Taguchi and 3 level design is better because in that case I can check, either my response (measured item) is decreasing in the whole range or first is going down and after that increases.

25,
30, Level 1
45

and

0.1
0.2 Level 2
0.3

might be, let say, my cutting conditions.

Level 3 it can be an angle (e.g. chisel angle in drill, whatever)
Level 4 – might be a type of the tool. (tool 1, tool 2)

In that case I want to find an interaction between type of the tool and chisel angle. Using cutting conditions (Level 1 and Level 2) I will run some trials to get these results. Do you think it might be a good approach?

Regarding noise factors, there is a small problem as I assume there is no any big noise. Using the example, I will run my experiment in the same temperature, humidity of ait etc. I will run it randomly. I am not sure what I could treat as a noise in that case.

I though I can treat outer array as a table for my results (but it might be a wrong thinking – I am not the best in Minitab and I think I need more practice with it)
I would like to run my L36 design just once.

Would it be possible to create an example of correct design with those Levels in Minitab, maybe if I visualize it will help me to understand it?
 
A

Allattar

#4
I think Taguhi is the wrong approach here. I tend to find Taguchi is used incorrectly and people think they are using it right.

Someone correct me if I am wrong, but if you do not have the outer array of noise factors then you are missing a crucial piece of the taguchi design.

For your example lets say you have environment noise factors of ambient temperature and ambient pressure. You would want to run all 36 runs where the ambient temperature and ambient pressure are expected to reduce the response. Then run another set of 36 where the ambient temperature and pressure are expected to increase the response.

By comparing the results of the runs at the different noise levels you can discover combinations of inputs that minimise the variation introduced by noise on the environment.

That is the situation where I would use Taguchi, if it isn't being used there that way then you can get a more optimum design with the factorial designs.

You have several choices, if the factors with more than 2 levels are numeric, continous factors then I would use a 2 level factorial design. You do assume a linear model on the response. This is where entering centre points can be used to see if there is curvature.

If the factors with more than 2 levels are categorical you could use a general full factorial. This will let you set the numbers of levels on each factor.

Is this design a screening design or do you want to see all interactions?
Using a 2-level factorial design, a full design that see's all interactions needs 16 runs. If you want to check for curvature add 2 centre points. These will be replicated for each categorical factor, so if you have 1 categorical factor you get 4 centre points. Replicating the whole design increases the power of the design.

If this is a screening design consider the half fraction 2 level factorial, it needs 8 runs, but will confound the 2 way interactions with each other. It is resolution IV.

If you need 3 levels on a categorical factor, then a general full factorial will need 36 runs in total. 2*2*3*3, This design will allow you to see all interactions, but will be saturated without replicates, and you can probably just remove all the 3 and 4 way interactions to start with to get an error estimate. Unless you expect 3 way interactions to be present.
Now if you are only interested in a few interactions, and you know certain ones cannot exist you can use the D-optimal design tool to specify which interactions you want to see. You do need to calculate how many degrees of freedom you are using, but this is the number of levels on each factor -1 for the main effects.
eg: A has 2 levels, D has 3 levels, A needs 1 DF and D needs 2 DF
The interaction df are just multiplying the main effects df together so A*D would need 2 DF.
Count up the number of df you need, so A (2L) =1DF, B(2L) = 1DF, C(3L) = 2DF, D(3L) = 2DF. These need 6df, then look at interactions and lets say you want to see AB and CD. AB = 1df, CD = 4df. In total then you need 11df.

That would be 12 runs, if you left no runs to find an error with. Then you can ask how many runs you can add to find an error, as many as possible is better but you may get away with 3. So total is 15 runs to find a model of A B C D AB and CD.

This is just given as an example of how it can be used, and the designs you can pick. Compare the above to the L36 you are proposing, which doesn't see any interactions.
A 36 run design that really should be run at 2 different noise levels, giving 72 runs total.
This is why I always question the use of taguchi designs.
Each DOE has a particular are of use, so it would be interesting to know if there is a good reason why your company is using taguchi or wants you to use taguchi over the other options above.

Where I am talking about position of factors in the design I really need a link to some tables or diagrams. The taguchi designs are all generated in a specific structure, you can put factors into different positions of the table. I find them a bit confusing but the idea is that it is supposed to represent which positions are confounded, and you can choose where to put items to make interactions visible, or confound them with another factor.

For instance the diagram may show a line where it starts
Position 1 - - - - Position 3 - - - - position 2
If you put A in 1 and B in 2, position 3 would be your interaction AB. but if you put factor C in position 3 it is confounded with AB.
Does anyone have a good link for these diagrams? and a better explanation of them?
 
C

christianos

#5
I was wondering how close as possible I should explain my experiment. I think that the table below will explain everything. I will use the same comparison as in my previous post.

First, I will answer your questions. My design is NOT a screening test and I would like to see all interactions (or at least between chisel angle and numbers of cutting edges).

Taguchi design was only advised as a good one; however, I have a free hand to change it.

Factor 1 (3 Levels)
(cutting condition 1) 25; 30; 40

Factor 2 (3 levels)
(cutting condition 2) 0.1; 0.2; 0.3

Factor 3 (2 levels) chisel angle 100; chisel angle 130

Factor 4 (2 levels) 2 cutting edges; 3 cutting edges


As you advised factorial design, I found 16 runs, 4 factors on 2-Levels as a good one because I can repeat it twice and obtain good results running 32 runs in total. However, I am not familiarized with those “central points” and I am not sure how to use it. Because of the technical problems, I cannot run more than 50 runs including one repetition, so max 25 runs for a design.

Could you ask me a question? If I have factors as seen in the table above which has 3 levels, and on the other hand would like to create a design only for 4 factors with 2 levels and add some central points, in which case I can get more reliable results?

Using 2 levels factors I can get small designs. When using 3 levels factors will create a huge design e.g. 72 runs.

My aims are:
- Create small design like L12, L16, L18 etc. and repeat it twice – maximum runs for a whole test is 50

- I need a design which give me a good understanding what is between (any curvatures) 25 and 45, and between 0.1 and 0.3. For two levels factors I cannot easily say if lines on the graph are straight or curved (for the results). I would not like to miss anything inside these boundaries.

- I would like to see interactions between chisel angle and numbers of cutting edges. If it is possible to see others, it is even better.


Thank you in advance for any help. So far, we agreed that Taguchi is not good approach in my case.
 
A

Allattar

#6
Well I will try and highlight some choices of design.
Factor 1, this looks like it is continous. Can you set any value for cutting condition? If you can use 25 and 40 as high, the midpoint will be 32.5.

Factor 2, looks continous.
Factor 3, Looks like it could be continous again, is it possible to set a midpoint for this factor as well? If not you can set it as a text factor under the design section of create factorial design.
Factor 4, Again you want to set this as a text factor in the design section when creating the design.

The Taguchi design that Minitab will give you cannot find interactions on the L36. I dont know how the DOE++ software is choosing the design so I will rule out Taguchi in Minitab becuase you want the interaction.

Choice 1 for a design. 1/2 fraction design, with 8 runs. Use 2 centre points. If both Factor C and D are text then centre points are duplicated for each level of C and D. A centre point is just that a measurement in the design centre. You will get a point at 32.5 for factor 1 and .2 for factor 2 at each level of C and D.
With 2 centre points the 1/2 fraction design has 16 runs. The full design has 24 runs. Becuase of the centre point duplication at levels of categorical factors.
If you use 1 centre point you get 12 runs on the 1/2 fraction design, or 20 on the complete design.

The 1/2 fraction design will confound the 2 way interactions, AB +CD, AC + BD, and AD + BC. The confounding means those pairs of 2 way interactions cannot be identified as seperate effects. eg if you see an effect of AB it could be CD instead. This can be fine to use if you plan on further doe to seperate out effects, or if you know that one of that pair is not an interaction that should occur.

The full design is unconfounded, so all interactions can be seen.

Replicating the design adds better power, you do not replicate centre points when replicating, only corner points.
1 replicate, 1/2 fraction 1 centre point = 12 runs
1 replicate, 1/2 fraction 2 centre points = 16 runs
1 replicate, full design 1 centre point = 20 runs
1 replicate, full design 2 centre points = 24 runs
2 replicate, 1/2 fraction 1 centre point = 20 runs
2 replicate, 1/2 fraction 2 centre points = 24 runs
2 replicate, full design 1 centre point = 36 runs
2 replicate, full design 2 centre points = 40 runs

All of these come within your limit of 50 runs.
Your next question needs to be what size of effect is important to identify? Then you can find how powerful the design is at seeing that effect. This can help pick which of the designs is best suited for you.
 

Miner

Forum Moderator
Staff member
Admin
#7
The 1/2 fraction design will confound the 2 way interactions, AB +CD, AC + BD, and AD + BC. The confounding means those pairs of 2 way interactions cannot be identified as seperate effects. eg if you see an effect of AB it could be CD instead. This can be fine to use if you plan on further doe to seperate out effects, or if you know that one of that pair is not an interaction that should occur.

The full design is unconfounded, so all interactions can be seen.
Everything Allattar stated above is correct, but don't be scared off by the confounding of the 2-way interactions. Typically you will be saved by something called hidden replication.

It is very rare for all of your factors to be significant main effects. Therefore, when you remove one factor from the model, your half-fraction experiment suddenly becomes a full-factorial with zero confounding. Remove another factor and you have a replicated full-factorial.

While this does not happen 100% of the time, it does happen with high regularity. If you experience one occasion where it does not, you can always run the other half fraction. This is where the center points become even more valuable, because you can then use them to tell whether there is a difference between the two blocks ( first and second half-fraction).
 
C

christianos

#8
Well I will try and highlight some choices of design.
Factor 1, this looks like it is continous. Can you set any value for cutting condition? If you can use 25 and 40 as high, the midpoint will be 32.5.

Factor 2, looks continous.
Factor 3, Looks like it could be continous again, is it possible to set a midpoint for this factor as well? If not you can set it as a text factor under the design section of create factorial design.
Factor 4, Again you want to set this as a text factor in the design section when creating the design.

The Taguchi design that Minitab will give you cannot find interactions on the L36. I dont know how the DOE++ software is choosing the design so I will rule out Taguchi in Minitab becuase you want the interaction.

Choice 1 for a design. 1/2 fraction design, with 8 runs. Use 2 centre points. If both Factor C and D are text then centre points are duplicated for each level of C and D. A centre point is just that a measurement in the design centre. You will get a point at 32.5 for factor 1 and .2 for factor 2 at each level of C and D.
With 2 centre points the 1/2 fraction design has 16 runs. The full design has 24 runs. Becuase of the centre point duplication at levels of categorical factors.
If you use 1 centre point you get 12 runs on the 1/2 fraction design, or 20 on the complete design.

The 1/2 fraction design will confound the 2 way interactions, AB +CD, AC + BD, and AD + BC. The confounding means those pairs of 2 way interactions cannot be identified as seperate effects. eg if you see an effect of AB it could be CD instead. This can be fine to use if you plan on further doe to seperate out effects, or if you know that one of that pair is not an interaction that should occur.

The full design is unconfounded, so all interactions can be seen.

Replicating the design adds better power, you do not replicate centre points when replicating, only corner points.
1 replicate, 1/2 fraction 1 centre point = 12 runs
1 replicate, 1/2 fraction 2 centre points = 16 runs
1 replicate, full design 1 centre point = 20 runs
1 replicate, full design 2 centre points = 24 runs
2 replicate, 1/2 fraction 1 centre point = 20 runs
2 replicate, 1/2 fraction 2 centre points = 24 runs
2 replicate, full design 1 centre point = 36 runs
2 replicate, full design 2 centre points = 40 runs

All of these come within your limit of 50 runs.
Your next question needs to be what size of effect is important to identify? Then you can find how powerful the design is at seeing that effect. This can help pick which of the designs is best suited for you.

These values are just an example. However, in the real test there are continuous, let say 25, 35, 45 m/min, and regarding values 0.1, 0.2, 0.3 mm/revolution, they are also continuous). Factor 3 I can treat as a continuous and as a text factor. I think it might be better to treat it as a continuous to see the results for a different angle (midpoint).

I am not sure what do you mean by saying :what size of effect is important to identify? The most important effect for me is a link between chisel angle and numbers of cutting edges.

Now I see that Taguchi approach was a wrong one. It is more clear for me now. I would need to think if I want those confounded the 2-way interaction. I would need to read about it more.

Thank you for your help. I will try to create a design in Minitab. I will be back with it in my next post tomorrow just to see if it does make sense.

Thank you,
 
A

Allattar

#9
Bear in Mind Miners point about hidden replications :) Also if you have 50 runs to use, and you start with a smaller set of runs say 20, then you still have another 30 left over for additional tests to improve on the knowledge of the first.

By size of effect that you need to see,
I mean that you want to consider the response(s) and ask how small a change in the response is of practical significance, or what difference in response you would need to identify.
 
C

christianos

#10
I managed to create a 2 replicate, full design, 2 centre points = 40 runs.
However, I have a couple of questions:

1)Do I need to specify generators for my design or leave it as a default? I think it is better to leave it as default. However, I do know the profits for that kind of move.


2)What does it mean to fold a design? Is it better to fold it? What are the profits?



3)Is that a useful thing to use blocks? I think that I understand the idea of blocks. In case if I would like to use 2 blocks (design = 48 runs) I can divide my experiment into 2 days. I mean to run a 1st block in the first day and a second block day after. Does it have any measurable advantages?

4)Is it better in “Content of Alias Table” to leave as:
a)default interactions, or

b)Interactions up through order: from 1 to 4 ?
What does it mean?

5)Is it better to run for example a test, let say 24 runs (1/2 fraction), and if results are not as accurate as we would like to have, run another test of 24 runs ( like a second replication to increase a power of design). Or is it better to run 40 trials straight away? Does it have any serious impact on the accuracy of the results? I think that Miner explain partially this problem in his previous post. I will be grateful for any "deep" explanation.


Regarding confounded interactions and hidden replications, I decided to run my first test as a full factorial. It might be better for me to understand the process and after that “play” and try ½ fraction design if my experience in this field will be better.

I am aware of the values of the responses; therefore, I think it might be relatively easy to find the significance of particular ones. Let say, that I would like to measure cutting forces as my response. I assume that for different cutting conditions I will have dramatically different values.

I am worried only about the interactions between chisel angle and number of cutting edges. I believe to see any interaction between these two. This is the aim of that experiment, to see if Factor C has an impact on Factor D and measure it. Unfortunately, I cannot put any midpoint for these categorical factors. Do you think that in case of this full factorial (or even 1/2 fractional) design, I would be able to see the interactions between these two above?


Thank you Allattar and Miner for all your help so far. I learned more practical knowledge from you than from books.


Please see attached Excel files. I attached these to show a difference between 1 block and 2 blocks design.


Please let me know if I am wrong in something.
 

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