容許區間判別與樣本數選取之演算法

Abstract

容許區間為一個被廣泛運用的統計工具，不僅是藥物製程檢驗時經常使用的工具，也是工業製程中估計良率的一種方法。在工業與製藥業公司中，製程檢驗時所需的樣本數一直是個公司所關注的議題，其中不僅僅是良率的保證，也是各公司所注重的成本的考量。此篇論文提供一套演算法，首先利用文獻上所提供的一些檢定，找出資料的分配為何，再根據分配依照文獻的方法找出適當的容許區間，且找出對於資料最適當的容許區間樣本數，最後利用各種分配假設下進行統計模擬以驗證此演算法。此論文提供一套樣本數選取的方法，可適用於不同的分配，對於各公司在製程檢驗時所抽取的樣本數決策時，相信可以發揮不少助力。

Tolerance interval is a widely used statistical tool in many industrial applications ranging from engineering to the pharmaceutical industry. The determination of the sample size of a tolerance interval has been one of important issues for the study of the tolerance interval. In this study, we develop an algorithm to find the tolerance interval of a sample and then calculate the sample size satisfying some conditions. The required sample sizes for different cases are provided in this study. To evaluate the algorithm, we conduct a simulation study to investigate its performance. In addition, the algorithm is applied to a real data example. The method proposed in this study can help companies choose the adequate sample size for quality control.