Development of robust analysis methods for experimental and observational data with emphasis on functional response analysis and kriging

Abstract

In order to evaluate and improve the performance of a certain system, it is necessary to analyze relevant experimental or observational data. In many practical cases, various types of errors, such as measurement error, experimental error, and modeling error, are present in experimental and observational data, and thus it is important either to eliminate those errors or to introduce robust statistics or models. Scientific experiments can be divided into physical and computer experiments. Taguchi’s robust design, which is usually based on physical experiments, is one of the most popular methods for reducing the effects of errors on the system performance. Traditionally, robust design problems are broadly classified into static and dynamic ones depending on the type of responses. However, with the rapid growth of measurement techniques, the functional response is emerging as a new type of response creating a new type of robust design problems. In Chapter II of this thesis, new distance measures are developed for a robust design problem with a functional response by using functional principal component analysis (FPCA) and modified Hausdorff distance (HD), and then based on those distance measures, new performance measures (location and dispersion measures) are developed. The effectiveness of the proposed performance measures are verified through simulation experiments. Due to the advent of modern computers and the advancement of computer simulation technologies, computer experiments have become a potential alternative to physical experiments. Since computer experiments are based on a deterministic model, kriging is regarded as one of the best choices for analyzing computer experiments data. However, outliers are frequently present in the data due to discretization errors and computer round-off errors, which reduce the predictability and stability of the kriging model. To attenuate the effects of outliers, a robust kriging model is developed in Chapter III by subst...