重覆性實驗計畫中型II受限資料分析方法

Abstract

一般分析工業受限資料方面的文獻, 主要是針對型I受限資料, 其共通的 特點是以受限資料來適配出一個模式, 再藉此模式來估計受限部份的資 料, 進而分析實驗的結果. 至於在分析型II受限資料方面, 截至目前為止 尚無特別的處理方式, 一般均是將型II受限數據當成型I受限數據來處理. 如此的處理方式有兩點可議之處: (1)以本來就不完整的受限資料去適配 出一個模式, 這模式的可信程度令人懷疑; (2)模式適配的複雜度相當高, 這不只是一般的計算複雜而已. 在型II受限的重覆性實驗計畫中, 當每一 因子水準組合的重覆樣本沒有完全受限時, 受限資料的分析可避免以建構 模式的方式來分析. 本研究乃依此針對重覆性實驗計畫的型II受限資料提 出一套分析程序, 利用最佳線性不偏估計法求出每一因子水準組合的參數 估計值, 再應用Torres所提出的非重複性因子分析法來設定最佳因子水準 組合. 對於型II受限的重覆性田口實驗, 本研究也提出一套處理程序, 使 受限資料依舊能以SN比的方式來判定最佳因子水準組合. 本研究最後並以 兩個實例來說明如何應用本研究所發展之受限資料分析程序, 分析結果並 與田口博士的精密累積分析法做一比較, 以證實本研究的可行性. The general methods of analyzing censored data from industrial experiments are usually focused on type I censoring. A common point of these methods is to use the censored data to fit a model. Then, based upon this model, the excepted failure time for censored observation can be estimated. However, there are two drawbacks of handling censored data by the above methods: 1. using the incomplete data to fit a model may not result in an accurate estimate of the censored data; 2. the model fitting is complicated for a practioner who has only limited statistical training. As for the type II censoring, the censored data is transformed to type I censored data. In a type II censoring experiment with at least two uncensored observations for each treatment combination, the censored data may be analyzed without constructing the complicated model. This thesis propose a method to analyze the censored data by using the best linear unbiased estimation(BLUE) and Torres's analysis of unreplicated factorials with possible abnormalities. Furthermore, this thesis also propose an effective method to analysis the Taguchi's parameter design with censored. Finally a comparison between the proposed methods and the conventional ways of analyzing censored data is made to verified the effectiveness of the proposed methods.