Graphical evaluation of prediction capability when the number of noise variable increases in robust parameter design

The goal of robust parameter design is to identify settings of the control variables that are robust or insensitive to variability transmitted from the noise variables. By developing a model containing both the noise and the control variables, a combination of control variable settings can be determined, so that the response is robust to changes in the noise variables. As a result, robust parameter design entails designing the system to achieve robustness or insensitivity to the inevitable changes in the noise variables. From this viewpoint, we consider the cases where the control factor in robust parameter designs has a large number of noise factors. In this article, it is of interest in establishing a graphical evaluation for assessing prediction capability by extending the scaled prediction variance concerning the increased number of noise variables for representative robust parameter designs such as a modified central composite design, a modified small composite design, and a composite mixed resolution design. Additionally, we identify which design is highly performative or desirable concerning the variability in the noise variables themselves and the variability transmitted by these noise variables in the three designs.