Definition
A t-(v,k,λ) orthogonal array (t ≤ k) is a λvt × k array whose entries are chosen from a set X with v points such that in every subset of t columns of the array, every t-tuple of points of X appears in exactly λ rows.
In this formal definition, provision is made for repetition of the t-tuples (λ is the number of repeats) and the number of rows is determined by the other parameters.
In many applications these parameters are given the following names:
- v is the number of levels,
- k is the number of factors,
- λvt is the number of experimental runs,
- t is the strength, and
- λ is the index.
An orthogonal array is simple if it does not contain any repeated rows.
An orthogonal array is linear if X is a finite field of order q, Fq (q a prime power) and the rows of the array form a subspace of the vector space (Fq)k.
Every linear orthogonal array is simple.
Read more about this topic: Hyper-Graeco-Latin Square Design
Famous quotes containing the word definition:
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)