Batch sequential NOAB designs by way of simultaneous construction and augmentation

Space-filling designs help experimenters to represent simulation outputs efficiently when entire input spaces cannot be exhaustively explored. Batch sequential designs allow for intermediate analyses to occur as later batches of experimental design points are being tested, given the ability to change later design points based on the outputs observed, and stop the experiment when the current observations are deemed sufficient to reduce experimental cost. Nearly orthogonal-and-balanced (NOAB) designs have good space-filling properties and can accommodate design spaces with continuous, discrete, and categorical factors. In this paper, mixed-integer linear programming (MILP) formulations used to find NOAB resolutions III, IV, and V designs are extended to construct batch sequential NOAB designs, where design stages can use different NOAB approaches. A case study is presented where a simultaneous construction approach results in overall more desirable designs than when using design augmentation, yet requires a predefined number of points for each design stage.