Outer Arrays

In Taguchi experimental design methodology, the repeated measurements of the response variable are often taken in a systematic fashion, with the goal to manipulate noise factors. The levels of those factors are then arranged in a so-called outer array, i.e., an (orthogonal) experimental design. However, usually the repeated measurements are placed in separate columns in the data spreadsheet (i.e., each is a different variable); thus, the index i (in the formulas for smaller-the-better, larger-the-better, and signed target) runs across the columns or variables in the data spreadsheet, or the levels of the factors in the outer array.

See Taguchi Methods - Robust Design Experiments - Overview for more details regarding these three signal-to-noise ratios.