線性迴歸模式之雙邊良質率的區間估計

Abstract

良質率一般被用來評估品質好壞的一種統計工具，例如：農業管理及產品評估、環境監測、工業製程上的可靠度分析、產品品質的控管以及製藥效益等等。良質率被定義為我們感興趣的品質特徵落在給定的範圍內之機率。本研究主要針對線性迴歸模式下，來建構雙邊良質率的信賴區間，提出兩個近似的估計方法，這兩種方法的建構過程分別是以廣義樞紐量 (generalized pivotal quantity) 的想法以及 Wang 和 Lam (1996) 所提出的方法來進行，並透過統計模擬來比較其區間的覆蓋率以及區間的期望長度，模擬的結果顯示出以廣義樞紐量為基準的方法擁有良好的覆蓋率以及合理的區間期望長度，可被建議用來解決一般實際的問題，雖然 Wang 和 Lam (1996) 的方法並沒有比較好的表現，但是其計算過程簡單，亦不失為一種可被建議用來解決一般實際問題的方法。本論文將以實際的例子來說明雙邊良質率之區間估計的應用與可行性。

Conformance proportion is commonly used in agriculture management and product evaluation, industrial product quality control or process improvement, environmental monitoring or assessment, pharmaceutical effectiveness evaluation, etc. The bilateral conformance proportion is defined as the probability of a quality characteristic that falls within a specification interval, which can be denoted by , where Y is the quality characteristic of interest and [A,B] is the specification interval. In this study, we focused on constructing confidence limits for the bilateral conformance proportion under the linear regression model. Two construction approaches are proposed. One is based on the concepts of a generalized pivotal quantity, and the other is adopted from the method by Wang and Lam (1996). Detailed simulation studies are conducted to evaluate the performance of these two methods, by comparing their empirical coverage probabilities and expected lengths. The simulation results reveal that the generalized pivotal quantity based method appears to have better coverage probabilities and reasonable expected lengths, which can be suggested in solving generally practical problems. Although the performance of the Wang-Lam method is slightly inferior, it can still be implemented in practical use, due to its computational ease. In addition, some examples are given to illustrate the proposed methods.