固定長度眾數區間及其在品質管制上的應用

Abstract

通用的Shewhart 管制圖是利用一個統計量T的平均數加減3倍標準差來做為管制上下限。這套方式應用於所有的分配，不管是對稱或不對稱，以及連續或不連續。我們把Huang (2003)的眾數區間概念應用於固定長度，但具有最大覆蓋機率的管制圖。對此一區間我們討論了有母數及無母數估計並且做了資料分析。

The popular used Shewhart control chart is choosing a statistic T and setting its upper and lower control limits as T's mean plusing and minusing 3 times of T's standard deviation. This rule has been applied for variables with distributions continuous or discrete and symmetric or asymmetric. We extend the mode interval of Huang (2003) to define the fixed width mode interval which is one having largest coverage probability among the intervals with the same width. Estimation of this new chart has been discussed in parametric and nonparametric techniques. Moreover, a real data analysis has also been provided.