Optimal blocked orthogonal arrays

•We constructed a mathematical framework using the count function.•We developed a comprehensive methodology, which allows experimenters to select various optimal blocked orthogonal arrays.•Most existing approaches are special cases of our methodology.

Blocking is an important technique to reduce the noises introduced from uncontrollable variables. Many optimal blocking schemes have been proposed in the literature but there is no single approach that can be applied to various blocked designs. In this paper, we construct a mathematical framework using the count function (or the so-called indicator function) and develop a comprehensive methodology which allows us to select various optimal blocked orthogonal arrays: regular or non-regular designs with qualitative, quantitative or mixed-type factors of two, three, higher or mixed levels. Under this framework, most existing approaches are special cases of our methodology.