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Taguchi proposed extending each experiment with an "outer array" (possibly an orthogonal array); the "outer array" should simulate the random environment in which the product would function. This is an example of judgmental sampling. Many quality specialists have been using "outer arrays".
In mathematics, an orthogonal array (more specifically, a fixed-level orthogonal array) is a "table" (array) whose entries come from a fixed finite set of symbols (for example, {1,2,...,v}), arranged in such a way that there is an integer t so that for every selection of t columns of the table, all ordered t-tuples of the symbols, formed by taking the entries in each row restricted to these ...
Genichi Taguchi (田口 玄一, Taguchi Gen'ichi, January 1, 1924 – June 2, 2012) was an engineer and statistician. [1] From the 1950s on, Taguchi developed a methodology for applying statistics to improve the quality of manufactured goods.
An alternate representation of a Latin square is given by an orthogonal array. For a Latin square of order n this is an n 2 × 3 matrix with columns labeled r, c and s and whose rows correspond to a single position of the Latin square, namely, the row of the position, the column of the position and the symbol in the position. Thus for the order ...
An orthogonal array, OA(k,n), of strength two and index one is an n 2 × k array A (k ≥ 2 and n ≥ 1, integers) with entries from a set of size n such that within any two columns of A (strength), every ordered pair of symbols appears in exactly one row of A (index). [33] An OA(s + 2, n) is equivalent to s MOLS(n). [33]
Orthogonal array testing is a systematic and statistically-driven black-box testing technique employed in the field of software testing. [ 1 ] [ 2 ] This method is particularly valuable in scenarios where the number of inputs to a system is substantial enough to make exhaustive testing impractical.
The definition of a Latin square can be written in terms of orthogonal arrays: A Latin square is a set of n 2 triples ( r , c , s ), where 1 ≤ r , c , s ≤ n , such that all ordered pairs ( r , c ) are distinct, all ordered pairs ( r , s ) are distinct, and all ordered pairs ( c , s ) are distinct.
In statistics, a central composite design is an experimental design, useful in response surface methodology, for building a second order (quadratic) model for the response variable without needing to use a complete three-level factorial experiment.