利用設限比例方法建構設限資料之容忍區間

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。

關鍵字

區間設限；設限資料；覆蓋率；設限比例方法

並列摘要

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 specic distributions or models, there lacks a unied 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.

並列關鍵字

Tolerance Interval ； censored data ； coverage probability ； censored rate

參考文獻

[12] Krishnamoorthy, K and Mathew, T and Mukherjee, S (2008). Normal-Based

[1] Cai, T. and Wang, H. (2009). Tolerance Intervals for Discrete Distributions

[2] Coles, Stuart (2001). An introduction to Statistical modeling of Extreme Values.

for insurance and finance. Springer,Berlin.

scale Regression Models in the Presence of Censoring, Technometrics,

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利用設限比例方法建構設限資料之容忍區間

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