眾數型態全距之統計推論及其應用

Abstract

在這一篇論文裡，我們提議了一個新的全距，叫做「眾數型態全距」。對於這個新的全距，我們對它做一些統計推論，包括點估計、區間估計及假設檢定。同時，我們亦會介紹如何用它來表示已知分配的四分位差及標準差。更進一步的，我們會利用它來建構一個新的製程能力指標。

We propose a new range, called the mode range, as an alternative scale parameter. Statistical inferences including point and interval estimations and hypothesis testing are discussed. Applications of this scale parameter to construct standard deviation and interquartile range of parametric distributions are introduced. Moreover, using this range, we also propose a new process capability index for quality improvement in manufacturing process. Examples for analyzing the proposed techniques are provided.