On some optimal design problems for response surface model with correlated errors

• Main Authors: Tzu-Lun Yuan, 袁子倫
• Other Authors: Mong-Na Lo Huang
• Format: Others
• Language: en_US
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/handle/7tntkf

博士 === 國立中山大學 === 應用數學系研究所 === 107 === Experiments performed with good designs on the settings of controllable factors are essential collecting useful information efficiently and may provide the precise estimation of statistical modeling and corresponding inferences. In the first part of this dissertation, our main interest is to investigate the design problems for first- and second- order response surface models (RSMs) with correlated errors and related applications. Under the first- and second- order RSMs with fixed effects and correlated errors, we investigate the D-optimal designs for estimation of the unknown parameters in the RSMs, for two explanatory variables. The design region is considered to be within a circle and the correlation between two observations depends on the distance of the two design points. We present analytical minimally supported D-optimal design results, and numerical D-optimal designs for circular design region with spatially correlated error structure. On the other hand, the main idea of RSM is to use certain experimental procedures to search for control variables of an optimal response sequentially in an experiment. Based on such an idea, we would like to find designs optimal for estimation and prediction on the nonlinear models, used to describe the behaviors of signals obtained from various differential pad placement designs of a capacitive coupling based stacked die package. In the second part of this dissertation, we provide parametric models under different pad sizes to exhibit the patterns of the SNR values versus the frequencies for various die placement designs with given pitch distance and overlapping percentage. In the end, we use an approach analogous to the response surface methodology to find the optimal design configuration for each pad size with an optimal response.