應用灰色系統理論於重複性實驗計畫中遺失資料之分析

Abstract

實驗計畫法是工業界最常用來研發或改善產品的一項品質改善技術，然而在蒐集實驗資料時，可能由於儀器設備發生故障、資料取得不易或人為的疏失等原因而無法收集到完整的實驗數據，這些無法收集到的實驗數據又稱遺失資料（missing data），會導致所設計的實驗不再具有平衡性、直交性以及對稱性，因此將無法以傳統的變異數分析法（Analysis of Variance）來分析實驗數據。目前中外文獻中提出了許多解決遺失資料的方法，如：直接刪除遺失資料、以現有實驗數據之平均值代替遺失資料值或是利用統計方法來建構模式以估計遺失資料之值。然而這些方法皆有缺失，譬如：以平均值代替遺失值或是忽略遺失值不計，有時會產生不合理的分析結果；而以迴歸法或最大概似估計法（Maximum Likelihood Estimation, MLE）等統計方法則需要嚴謹的統計假設與繁雜的運算，使得不具統計背景的人士運用困難。此外，也有學者提出利用不需統計假設的類神經網路方法來估計遺失資料，但其網路參數需要以試誤法來決定，使得分析過程繁瑣，實務應用亦不易。因此本研究針對重複性實驗數據，利用不需統計假設且計算過程簡單的灰色系統理論發展出一套估計每一因子水準組合下遺失資料的方法，最後並以傳統實驗設計與田口實驗之實例來說明本研究之遺失資料分析法的有效性及可行性。

Design of experiment methods are widely used for product/process improvement in industry. Sometimes missing data observations occurred in the experiments due to mechanical breakdowns, collecting data falsely, etc. Consequently, experiment results with missing data cannot be analyzed with conventional analysis of variance（ANOVA）methods. Since the experimental data are no longer balanced. Various methods for coping with the missing observations were developed. These methods include eliminating missing data, replacing the missing observations by mean, estimating the values of missing data using statistic/neural networks model. However, these approaches require complicated computations or complex statistical assumptions. Although some methods like mean plugging are convenient to perform, these are unreasonable. This study proposes a procedure to deal with missing data from repetitious experiments by employing grey system theory. The proposed procedure is simple and requires no assumptions. Two cases, one traditional experiment and one Taguchi experiment, are illustrated to demonstrate the effectiveness of the proposed procedure.