Talk:Orthogonal array
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Factorial design application
 | The contents of Hyper-Graeco-Latin square design was merged into Orthogonal array on August 2012. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. For the discussion at that location, see its talk page. |
Notation; mixed-level arrays
There are two problems with this article.
- It ignores so-called mixed-level orthogonal arrays, where different factors can have different numbers of symbols. These arise naturally as fractional factorial designs.
- The notation t-(v,k,λ) is problematic. It is very unusual for orthogonal arrays, and it can’t be used for mixed-level arrays. (The more common notation is OA(N,k,v,t) where N is the number of runs, and this notation is easily generalized to denote mixed-level arrays.)
- More problematic, the same t-notation is used for combinatorial designs known as t-designs, where the parameters k and λ have very different meanings from those used here. Such designs are unrelated to orthogonal arrays. This is very confusing.
It would not be hard to fix the first problem, by simply adding a section on mixed-level arrays and making small modifications/additions elsewhere. The second issue is trickier. One option is to mention the OA(N,k,v,t) notation as an alternative at the beginning, so that it can be used for mixed-level arrays when suitably modified. But this means that the article would contain two distinct systems of notation.
A cleaner alternative is simply to replace all instances of the t-notation with the OA notation. This would be time-consuming but not difficult, but I don’t know what the editorial policy is on this. (I assume the original author is Douglas Stinson, whose book uses the t-notation for orthogonal arrays. That book is cited numerous times in the article.)
It would be worth having a brief section on notation, since there are yet other notations for orthogonal arrays. For example, the notation LN is used in many industrial applications, probably due to Taguchi. There are others.
I would be happy to make all the modifications I've suggested.
(I note, incidentally, that the Combinatorial_design article doesn’t seem to define t-designs, although it indicates when such designs are quasi-symmetric.) Johsebb (talk) 18:14, 16 February 2023 (UTC)