Abstract
本篇論文主題為田口玄一博士所提的實驗計劃法中有關品質工程的改進間題。田口博士提出有關的實驗資料在分析時, 可以經由所謂的信號噪音比統計量進行標準的變異數分析; 該統計量目前於工業界對於品質工程的改進有相當卓越的貢獻。本篇論文主要目的是提供該統計量的理論架構, 並肯定該統計量於標準的變異數分析中確實相當有效。為了達到上述的目的, 本篇論文中將引入一種新的非線性高維度的轉換法, 並且利用此種方法解出信號噪音比統計量的各種基本的分配特性; 尤其當母群體為指分配時,該統計量的抽樣分配, 文中給予相當詳細的皂討論與分析。文中證明與分析有利用到皮爾森與契達茜克兩位教授文獻。本文的方法可以推廣到各式的母群體裡, 文內亦有詳細說明。基於對該統計量的瞭解, 筆者的指導教授黃提源博士與筆者提出一項新的改良分析方法。此種分析方法為合Box─Cox與田口博士的方法, 稱為BCT轉換。在某種意義下,BCT轉換法可以得到某些最佳的特性, 尤其當母體為服從伽瑪分配且樣本數為小樣本(n=2, 3, 4和5), 文中有詳細討論與分析。此種方法可以延伸推廣到母群體為服從歌西、偉伯、邏輯、拉卜拉斯、帕拉多等各種分配。///////ABSTRACTOne of the most important ideas of Professor Genichi Taguchi is thatexperimental data should be analyzed in terms of quantity called signal tonoise ratio SN★=10 log★(Y★/S★)★. The quantity based on standardanalysis seems have been recognized optimal in the industry of would, andthe object of this thesis is to validate the use of this criterion basedon standard analysis of variance such as the analysis of variance.In order to achieve this object, a non-linear transformation will bepresented and applied to obtain the various distributional properties ofsgnal to noise ratio SN★; especially the sampling distribution of SN★under the exponential parent distribution is discussed in detail. theproofs of our results are partially based on a paper of Pearson andChandra Sekar. In addition, methods are outlined for extension to variousparent distributions.We also combine the method of Box-Cox with Taguchi`s SN★ to obtain apowerful family of transformations for a positive random samples, which isdenoted by BCT transformations. The optimality (in some sense) of BCTtransformations is investigated under the gamma parent distribution forsmall sample sizes n=2,3,4 and 5. The method can extended to cover otherparent distributions such as Cauchy,Weibull,Logistic,Laplace,Paretodistributions,etc..