# Orthogonal Arrays (Taguchi)

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• #42981

Jack Kules
Participant

When looking at orthogonal arrays, somethinig simple like three factors at two levels, the first condition is all 1s (lowest level) and the remaing three conditions are mixes of 1s and 2s. Whay is there no condition that is all 2s (highest level)?  There has to be an explanation, but I can not see it.

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#135974

Robert Butler
Participant

A full factorial of 3 factors at two levels will have everything at the high level.  For a fractional factorial (which is what you are describing) you may or may not depending on which half of the replicate you choose.
A  B   C  ABC
-1 -1 -1    -1
1 -1 -1      1
-1  1 -1      1
1  1 -1     -1
-1 -1  1      1
1 -1  1     -1
-1  1  1     -1
1  1  1       1
Choose the half fraction where ABC = 1 and your 4 experiments become
1 -1 -1
-1  1 -1
-1 -1  1
1   1  1
and you have all three at the high level but you don’t have all three at the low level.
The other half fraction (with ABC = -1) gives you everyone at the low but not everyone at the high level.
-1 -1 -1
1  1 -1
1 -1  1
-1  1  1

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#135975

Jack Kules
Participant

Thanks, Robert.  I figured there was a simple answer, but my mind come not come up with it.  This makes sense now.

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#135976

BTDT
Participant

Jack:When you have a sparsely populated orthogonal matrix, there are a number of different combinations of factor settings that satisfy your requirements of orthogonality. By coincidence, some may contain runs where all settings are low without a run where all settings are high. You may choose a different set (foldover) if you wish. This is true in an L4 design, but if it really bugs you, then go with an L8 design or higher.Cheers, BTDT

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#135977

BTDT
Participant

RB:Once again, I see that I type slower than you do.Cheers, BTDT

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#136043

Manee
Participant

The real advantage of Orthogonal Arrays appears when the factors have more than three levels.
Jane

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#136715

murat sanyilmaz
Participant

I m preparing a thesis abouth taguchi method. I need that “how is constitute of orthogonal arrays?”. if anybody have a sources about it, please reply to me!!! its very important.
thanks

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#136745

Robert Butler
Participant

While they are given different names in the Taguchi literature, orthogonal arrays are nothing more than factorial designs.  Almost any good book on experimental design should have a chapter devoted to their logic and construction.

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