容許區間之研究

Abstract

統計區間被廣泛的應用於各個領域。相對於信賴區間是用於包含母體的一個未知參數，容許區間希望能在給定的信心水準下，至少涵蓋母體的一定比例。容許區間的應用廣泛見於各種產業，包括製藥工業、品質管制、臨床試驗和工業與環境衛生。由於運用廣泛，過去已有文獻探討並建構了許多分配的容許區間。在這一篇論文裡，我們專注於為不同資料型態或是特定的分配建立容許區間。這篇論文主要包含了兩個主題。第一個是討論如何建立混合常態分配的容許區間，第二個則是討論如何用群集資料 (aggregate data) 建立常態分配的容許區間。我們也討論不受分配限制的容許區間與其內插法的性質，並透過模擬與我們在本篇論文所提出的方法做比較。

Statistical intervals have wide applicability in many fields. As opposed to a confidence interval for estimating an unknown parameter of a distribution, a tolerance interval is expected to capture a certain proportion or more of the population with a given confidence level. The applications of tolerance intervals are widely-used in industries, including pharmaceutical industry, quality control, clinical trials, industrial hygiene and environmental health. Due to these wide applications, tolerance intervals for many distributions have been constructed in the literature. In this dissertation, we focus on constructing tolerance intervals for different types of data or specific distributions. There are two topics in this dissertation. The first one is to construct tolerance intervals for the mixture normal distribution; the second one is to discuss tolerance intervals for normal distribution based on the aggregated data. We also discuss the properties of the distribution-free tolerance interval and interpolated distribution-free method. Simulation studies are conducted to compare these proposed tolerance intervals and the existing intervals.