In industrial quality improvement and design studies, an important aim is to improve the product or process quality by determining factor levels that would result in satisfactory quality results. In these studies, quality characteristics that are qualitative are often encountered. Although there are many effective methods proposed for parameter optimization (robust design) with continuous responses, the methods available for qualitative responses are limited. In this study, a parameter optimization method for solving binary response robust design problems is proposed. The proposed method uses Mahalanobis Taguchi System to form a classification model that provides a distance function to separate the two response classes. Then, it finds the product/process variable settings that minimize the distance from the desired response class using quadratic programming. The proposed method is applied on two cases previously studied using Logistic Regression. The classification models are formed and the parameter optimization is conducted using the formed MTS models. The results are compared with those of the Logistic Regression. Conclusions and suggestions for future work are given.

Classification approaches are used in many areas in order to identify or estimate classes, which different observations belong to. The classification approach, Mahalanobis Taguchi System (MTS) is analyzed and further improved for multi-class classification problems under the scope of this thesis study. MTS tries to explore significant variables and classify a new observation based on its Mahalanobis distance (MD). In this study, first, sample size problems, which are encountered mostly in small data sets, and multicollinearity problems, which constitute some limitations of MTS, are analyzed and a re-sampling approach is explored as a solution. Our re-sampling approach, which only works for data sets with two classes, is a combination of over-sampling and under-sampling. Over-sampling is based on SMOTE, which generates the synthetic observations between the nearest neighbors of observations in the minority class. In addition, MTS models are used to test the performance of several re-sampling parameters, for which the most appropriate values are sought specific to each case. In the second part, multi-class classification methods with MTS are developed. An algorithm, namely Feature Weighted Multi-class MTS-I (FWMMTS-I), is inspired by the descent feature weighted MD. It relaxes adding up of the MDs for variables equally. This provides representations of noisy variables with weights close to zero so that they do not mask the other variables. As a second multi-class classification algorithm, the original MTS method is extended to multi-class problems, which is called Multi-class MTS (MMTS). In addition, a comparable approach to that of Su and Hsiao (2009), which also considers weights of variables, is studied with a modification in MD calculation. It is named as Feature Weighted Multi-class MTS-II (FWMMTS-II). The methods are compared on eight different multi-class data sets using a 5-fold stratified cross validation approach. Results show that FWMMTS-I is as accurate as MMTS, and they are better than FWMMTS-II. Interestingly, the Mahalanobis Distance Classifier (MDC) using all the variables directly in the classification model has performed equally well on the studied data sets.

由績效觀點，品質(適質)與成本(適量)，在概念上是完全一致的。因此，績效的管理，應以品質與成本作為其目標達成與否的衡量標準。本研究以績效觀點來解決公司面臨到品質與成本的兩難的問題。隨著電子產品的功能多樣化，發熱問題卻接踵而來，發熱密度的不斷提昇，對於散熱設計的需求也越來越受到重視。本研究以電源轉換器為對象，其目前已設計完成且已通過美國UL安規認證，但因為其溫升及其變異很大，因此降低電源轉換器的溫升及其變異是一急需解決的問題，以期能找出穩健於不可控因子，使產品變異小且各零件溫升與損失均能降至最低的最適外部零件組合。透過了田口與實驗設計的方法規劃及進行實驗並收集數據。引用加權SN比(multi-response S/N ratio)的方法，分別透過(1)管制圖法及(2)資料包絡法的CCR保證領域法(指CCR-AR模型)來決定加權SN比的權數，以決定可控因子及其水準值。對矩陣實驗的數據利用MTS ( M a h a l o n o b I s － Taguchi System)來篩選研究問題中較重要的特性變數，再針對篩選結果中較重要的特性變數的數據分別利用(1)倒傳遞類神經網路結合資料包絡法及(2)資料包絡法結合主成份分析法兩種分析方法，得到外殼鑽孔形狀與矽膠片大小的最佳因子組合。由改善後的確認實驗結果得知，雖然平均溫升下降的程度不大，然而大部份量測點的溫升標準差都顯著變小了，因此本研究在降低該電源轉換器溫升變異的效果顯著。