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Variants of Taguchi Orthogonal Arrays 261
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Table 17.5 Taguchi textbook L 9 (3 ) design.
I x 1 x 2 x 3 x 4
1 1 1 1 1
2 1 2 2 2
3 1 3 3 3
4 2 1 2 3
5 2 2 3 1
6 2 3 1 2
7 3 1 3 2
8 3 2 1 3
9 3 3 2 1

textbook. Users of Taguchi methods in industry who do not possess the necessary
background in statistics may not be aware of the fact that Taguchi orthogonal arrays
3
are by no means unique; thus an alternative L 4 (2 ) array is possible with the use of a
7
3 =−12 generator, and many more possibilities exist for the construction of an L 8 (2 )
4
array with the use of negative generators. The L 9 (3 ) array is similarly nonunique;
there is no reason why one should be confined to the particular design, shown in
Table 17.5, offered in all Taguchi methods publications. If, for example, in a product
development study, the (1, 1, 1, 1) combination is deemed undesirable or difficult to
implement, whereas there are existing prototypes featuring (2, 2, 2, 2), then one can
redesign an orthogonal array such as that shown in Table 17.6 where these exclusion
and inclusion requirements are satisfied.
To fully exploit and benefit from such flexibility in experimental design, it is highly
recommended that experimental designers be familiar with the construction of Latin
squares (and hence Greco-Latin and higher structures). The technique involved is in
fact rather simple: in a balanced design, every level of every factor is associated with every
level of every other factor. With this basic principle, a project in design of experiments
would truly begin with a design exercise, entailing the development of a matrix which
can accommodate requirements and meet constraints to the extent allowed by the
principle.

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Table 17.6 Alternative L 9 (3 ) design.
I x 1 x 2 x 3 x 4
1 1 1 3 2
2 1 2 1 3
3 1 3 2 1
4 2 1 1 1
5 2 2 2 2
6 2 3 3 3
7 3 1 2 3
8 3 2 3 1
9 3 3 1 2