Dear Aliyu,

A DOE is always associated to a model. So, you must first determine what model you want to estimate. And this model depends on the nature of your factors. If they are quantitative, the highest level of usual models is degree 2. In such a case, only 3 levels are necessary. If they are qualitative, of curse, all levels must be tested.

For 5 quantitative factors, you can perform a central composite design with about 32 experiments to test a full quadratic model.

With a specific model, you can calculate a optimal design.

If you need more information, I can give more explanations in some days.

Pierre

Stat > DOE > Taguchi > Create Taguchi Design > Taguchi Design: Available Designs Mixed 3 - 6 level use L18 > ok  

The 4 level factor will be placed in the column of the 6 level factor in the design. 

i appreciate your contributions. Thank you to all

I hope we helped. Please don't hesitate to ask anything.

@ Vaggelis.

I have tried today to see the point you are making in your previous answer. But after constructing the array, I found that levels 5 and 6 are there in the first column which does not exist in that factor. Are you saying that I should delete rows 13 to 18 so that I have L12?

Find the constructed array attached.

If your factors are qualitative, a perfect solution has 36 experiments if you don't need to estimate interaction effects (in this case, you would need all combinations: 4x3x3x3x3=324 runs).

One can calculate an optimal design (with MINITAB, it's not very simple). I did the exercise with SAS, and I put the results in the EXCEL file joined.

If you cannot do many experiments, the solution with 13(+2 repetitions) is not so bad. From my point of view, the solution with 24 (+2) experiment seems very good, even if not the best (36 + 2).

Of course, runs must be done in a random order.

@Pierre,

Thanks a lot for your reply. My factors are quantitative. I do not intend to consider interaction

Then, as your factors are quantitative, you could use a central composite design (32 runs and 5 level for each factor). With this DOE, you'll can estimate a full quadratic model (main effects, 2 factors interaction effects and quadratic effects.

My question is why 4 and 3 level? is it a technical constrain?

"My question is why 4 and 3 level? is it a technical constrain?"

This has to do with a research that was previously done without the use of DOE. in order to compare the benefit of doing DOE, similar factors and levels are intended. this is why I asked.

So can it be concluded that Taguchi method is not flexible to accommodate some combination of levels and factors 

A agree with you, with Taguchi  method, quite often people adapt their problem to a given table. from my point of view, one must do the opposite. So in your case, one can calculate an optimal design for the full quadratic model, and a good solution has 33 runs:

Obs A B C D E

1 -3 -1 -1 -1 1

2 -3 -1 -1 1 -1

3 -3 -1 1 -1 -1

4 -3 -1 1 0 1

5 -3 -1 1 1 0

6 -3 0 -1 0 0

7 -3 0 0 -1 1

8 -3 1 -1 -1 -1

9 -3 1 -1 1 1

10 -3 1 0 1 -1

11 -3 1 1 -1 1

12 -3 1 1 0 -1

13 -3 1 1 1 1

14 -1 -1 -1 -1 -1

15 -1 -1 -1 1 1

16 -1 0 1 1 -1

17 -1 1 0 -1 0

18 1 -1 1 -1 1

19 1 1 -1 0 1

20 3 -1 -1 -1 1

21 3 -1 -1 1 0

22 3 -1 0 0 -1

23 3 -1 1 -1 0

24 3 -1 1 1 -1

25 3 -1 1 1 1

26 3 0 -1 -1 -1

27 3 0 -1 1 1

28 3 1 -1 -1 1

29 3 1 -1 1 -1

30 3 1 0 1 1

31 3 1 1 -1 -1

32 3 1 1 -1 1

33 3 1 1 1 0

You can add 3 repetitions (-1 0 0 0 0) for exemple.

@Pierre.

Thanks for the reply. But please which method of DOE did you use to generate these array. is this orthogonal array too?

Ismaila,

This is an optimal design build for a full quadratic model. It is not perfectly orthogonal, but multicolinearity is very low as shown by VIF :

Term   VIF

a     1.05

b     1.09

c     1.08

d     1.05

e     1.03

a*a   1.28

b*b   1.39

c*c   1.46

d*d   1.37

e*e   1.31

a*b   1.05

a*c   1.06

a*d   1.05

a*e   1.05

b*c   1.04

b*d   1.05

b*e   1.04

c*d   1.03

c*e   1.05

d*e   1.06

I built this DOE with a SAS macro. It's possible with MINITAB, but it's fastidious.

You can be confident with this DOE to estimate a full quadratic model.

Thanks

Dear Ismaila,

Sorry for not answering earlier.... 

You can not delete rows of a matrix. You can use fewer columns if you want. I am proposing to substitute levels 5 & 6 with levels 1-4. 

Now in my previous post, I am proposing to substitute levels 5 & 6 with levels 1-4. 

As an example substitute level 5 with level 1 and level 6 with level 3. Usually, we use the levels that are easier (more convenient) or cheaper to our experiment.

Dear Vaggelis,

Thanks for your awaited response. I understand your point and tried it. it is straightforward. thank for such an idea. i would like to ask u, what is the implication of the additional rows created by replacement of 5 and 6  with two of 1 to 4? does it help the analysis to be more accurate since it looks to me as a sort of repetition.

You are right about the repetitions. Unfortunately, it is not more accurate. The repetition of levels allows you to use a smaller table. It allows you to execute fewer tests than other tables. 

Thanks you very much