Introduction of a robustness coefficient in optimization procedures:Implementation in mixture design problems: Part I: Theory

A robustness coefficient is introduced which is designed to deal with the sensitivity of an optimised response towards small variations in the design variables. This robustness coefficient takes account of the variance with which the design variables can be set to a value. A particular problem arises, especially in the area of optimization of mixture experiments. The variance / covariance structure of the error with which the design variables can be set to a predefined value varies over the design space. The robustness coefficient is capable of dealing with this phenomenon.