二水準因子試驗與區集試驗的新探

This project focuses on two-level second-order designs. Instead of estimating only the main e?ects of design factors, the estimations of some two-factor interactions are also of interest. We study two di?erent cases, one is completely randomized two-level designs and the other is when the experiments are run with randomisation restriction. Unlike the traditional approach of generalized minimum aberration criterion, we will use a general Q B -criterion to the selection of regular/nonregular factorial designs under model uncertainty. This criterion allows designs to be chosen to have good estimation properties across a large range of possible models, and allowing for prior probabilities of di?erent factorial e?ects being in the best model. We will extend this criterion to blocked regular/nonregular factorial designs under model uncertainty. In the ?rst part of the project, we will study the Q B -optimal two-level second-order designs for (1) the selection of the best subset of columns from the existing designs, (2) the study of a wider range of Q B -optimal two-level second-order designs without the level-balance and orthogonality requirements, and (3) the development of some e?cient exchange algorithms or natural inspired algorithms for the construction of Q B -optimal second-order designs. The second part of the project is the study of optimal regular/nonregular two-level designs with restricted randomization. We will extend the de?nition of Q B -criterion to designs with blocks and study its relationship with the extension of minimum aberration criteria for blocks. We will apply the new Q B -criterion to the problems for (1) the best blocking scheme for the selection of subset of columns from the existing designs, (2) the generation of a wider range of Q B -optimal blocked two-level second-order designs if the requirement of level-balance and orthogonality can be dropped, and (3) to develop e?cient computational algorithms for the construction of Q B -optimal block regular/nonregular factorial designs designs.