利用設限比例方法建構設限資料之容忍區間

Abstract

在工業、臨床試驗及藥理學的應用上，容忍區間是個能分析資料特徵 之有用工具之一。在實際應用上，尤其是可靠度分析及臨床試驗，在 蒐集資料時常難免會碰到資料遺失或不完整之情形。在現行的研究 中，有不少關於容忍區間之建構方法在特定分配上。但較少有一般性 的方法來建構設限資料之容忍區間。故在此篇研究，我們會探討如何 建構設限資料之容忍區間。並利用設限比例方法去估計資料未知之參 數。且將常態分配及一般性分配分別提供演算法步驟。最後在將設限 方法應用在實際案例上。

Tolerance intervals are useful tools to capture characteristics of the un- derlying distribution of collected data in industrial, clinical trials and phar- maceutical applications. In real applications, especially in reliability test- ing and clinical trial, it is common that the collected data with censored outcomes. Although there are existing methods for constructing tolerance interval for speci?c distributions or models, there lacks a uni?ed approach for constructing tolerance intervals with censored data for any distribution. In this study, we consider the problem of constructing tolerance intervals for parametric distributions with censored data. A censored rate approach is proposed to estimate the parameters. Algorithms based on the estimation to construct tolerance intervals for the normal and other distributions are provided in this study. A simulation study and a real data example study show the superiority of the proposed methods.