容忍區間

Abstract

針對生產者的需求，我們定義了可容許性容忍區間的概念。 由此一觀念，一般藉由Wilks (1941) 所定義的容忍區間可能是 不具可容許性的容忍區間。因此，我們證明出最常用於常態分配 的Eisenhart et al. (1947) 容忍區間是不具可容許性的。我們 證明出一個隨機區間是具有可容許性的性質，若且為若它是一個 由覆蓋區間所建立的信賴區間。我們更進一步地評估一些已存在 的容忍區間它們的可容許性程度。最後，我們推導出某些分配的 最短可容許性容忍區間。

For tolerance interval, we define a concept of admissibility that is desired for manufacturer. This leads to a problem that the general concept of tolerance intervals defined by Wilks (1941) may provide in-admissible tolerance intervals. For this, we show that the most popular normal tolerance interval of Eisenhart et al. (1947) is not admissible. A theory showing that a random interval is an admissible tolerance interval if and only if a confidence interval of a coverage interval is established. We further evaluate some existed tolerance intervals for their admissibility and also derive the shortest admissible tolerance intervals for some distributions.