Reallocation of testing resources in validating optimal designs using local domains

We have recently proposed a new method for integrating design optimization with model validation by means of a sequential approach that uses variable-size local domains of the design space and statistical bootstrap techniques. Our work was motivated by the fact that global model validation may be neither affordable nor necessary. The method proceeds iteratively by obtaining test data at a design point, constructing around it a local domain in which the model is considered valid, and optimizing the design within this local domain. Due to test variability, it is important to know how many tests are needed to size each local domain of the sequential optimization process. Conducting an unnecessarily large number of tests may be inefficient, while a small number of tests may be insufficient to achieve the desired validity level. In this paper, we introduce a technique to determine the number of tests required to account for their variability by sizing the local domains accordingly. The goal is to achieve a desired level of model validity in each domain using the correlation between model data at the center and any other point in the local domain. To make the method more cost-effective we avoid generating some testsby statistically predicting a set of local domains along the optimization process. The proposed technique is illustrated with a piston design example.