Level: Advanced
Hyper design is a versatile and analytical design based on hyper structure functions. In order to further expand its versatility and improve its analyticity, two extensions have been made. One is an excerpt hyper design, which uses only the necessary parts of the function, and the other is a hybrid robust design that combines a multi-headed robust design with an assignment function (a function in which the value of the hyper factor is substituted into the hyper structure function) as a column-wise function.
A superstructure function is a function with a double estimation structure that treats data from a direct product experiment as a polynomial of a superfactor (specially specified design factor). Using this enables highly analytical design that utilizes the extreme values (maximum and minimum values) and inflection points of the function. However, if the approximation of the function is not high enough, there is a risk to the design. In this case, by extracting the areas near the required extreme values and inflection points and combining these superstructure functions, it becomes possible to design with a sufficiently high degree of approximation. This is extractive hyperdesign.
Even when the degree of approximation of the hyper-structure function is high, trade-off problems arise in optimization when there are a large number of parameters. For example, in the case of robust design, it is not possible to make all parameters robust at the same time, and when a goal (target value, goal function) is given, it is not possible to bring all parameters close to the goal at the same time. Even more difficult is the case of a design that takes into account both robustness and approaching the goal, which results in multiple trade-off problems. This study proposes the theory of hybrid hyper-design to solve these problems and its applications.
