21.4.3.13. Bose’s Orthogonal Design

Even though the level-balanced descriptive design is efficient, it gives an aliased result in the effect analysis. As explained in Level Balanced Descriptive Design, it is the limitation of the strength-I orthogonal design. For higher level design, AutoDesign provides the Bose’s orthogonal design that is a strength-II design. This design gives a \({{q}^{2}}\) design for the \(q+1\) factors and \(q\) levels that must be a prime number. Table 21.11 lists the number of trials for available factors.

Table 21.11 Experimental runs of Bose’s orthogonal design

Trials	Level	Factors
4	2	2-3
9	3	2-4
25	5	2-6
49	7	2-8
121	11	2-12
169	13	2-14

In the above table, the trial number 25 is well known as Taguchi’s \({{L}_{25}}\) design.

Reference

Hedayat, A.S., Sloane, N.J.A. and Stufken, J., Orthogonal Arrays: Theory and Applications, Springer, Newyork, 1999.