利用Tobit模型與QD方法估計實驗計畫中型I截斷資料

Abstract

工業界常應用實驗設計(Design of Experiments, DOE)或田口方法(Taguchi Methods)研發新產品或是改善產品品質，藉由規劃實驗及分析實驗數據，找出最佳因子水準組合，當在實驗時遇上突發狀況，如：當機或斷電，或是因時間或成本有限導致部分資料無法觀察或量測到而以未知數表示時，這些資料稱為截斷資料(Truncated data)，有關於實驗計畫中含有截斷資料的相關文獻並不多，這些文獻大都是先以受限點替代截斷資料，配適出一個模型來預估截斷值，並找出顯著因子，然後透過迭代的方法繼續估計截斷值及找出新的顯著因子，直到截斷值和顯著因子穩定後，才進行分析實驗結果。上述方法相當冗長且計算繁雜，因此本研究針對含有截斷資料之實驗設計(Design of Experiments)及田口實驗(Taguchi methods)資料提出一個利用Tobit模型與Quick and Dirty(QD)方法來估計截斷值的程序，然後找出最佳因子水準組合。本研究最後利用實例來說明如何使用本研究所提出之實驗計畫中截斷資料之估計程序，並與其他截斷資料估計方法及原始資料所得之結果進行比較，證實了本研究方法確實有效可信。

Design of Experiments (DOE) or Taguchi methods are often employed in industry to develop new products or improve product quality. Through the use of designed experiments and analyzing of experimental data, the best combination of factor levels of products can be obtained. When encountering some unexpected situations, such as: machine breakdown, power down, or limited time or costs, cause some of the experimental data cannot be observed, these data are called truncated data. Studies on the truncated data collected from experiments are rare. Some studies from the literature suggested to replace the truncated data by the censored point, then fit a prediction model to estimate the truncated data and identify the significant factors. Continue to estimate the truncated data and identify new significant factor through the iterative approach until the truncated data and significant factors are stable. Finally analyze the experimental data with the estimated truncated data. The develop method is quite lengthy and complex to calculate. Therefore this study proposed a procedure for estimating the truncated data using Tobit model and Quick and Dirty(QD) method for estimating the truncated data, then the best combination of factor-level can be obtained. Finally, this study uses some examples to illustrate how to use the estimating procedure proposed by this study to estimate truncated data in the experiment, and compared the result with other estimating methods and the raw data. This study confirms the method really effective and credible.