管制圖作為一種覆蓋區間之研究

Control Chart as a Coverage Interval

黃婉婷(Wan-Ting Huang)

指導教授 ： 陳鄰安

國立交通大學/理學院/統計學研究所/碩士(2018年)

摘要

管制圖為常用的品質管理方法。管制圖可以看作一種有固定機率涵蓋我們有興趣的統計量的覆蓋區間。本文以統計觀點重新敘述管制圖，並且將管制圖分為母體型態與樣本型態，審視常態分配、指數分配下的 X − S 管制圖，和常態分配下的個別值管制圖。除此之外也建立管制圖的信賴區間，模擬新製程資料的生成，並計算其涵蓋覆蓋區間的機率。傳統上，檢定製程是否在管制中其實是檢驗管制圖的母體平均是否改變;而本文建立管制圖的區間估計，將檢定母體平均擴展成檢定管制區間。

關鍵字

管制圖 ； 覆蓋區間 ； 信賴區間 ； 品質管制 ； 個別值管制圖 ； 管制圖的區間估計 ； 假設檢定

並列摘要

Control chart is a common tool of quality control. Control chart can be viewed as a coverage interval, with a certain coverage probability. In this article, we reconstruct control chart from statistical point of view, and categorize them into population-type control chart and sample-type control chart. We study on X − S chart under normal distribution and exponential distribution, and also on individuals control charts under normal distribution. In addition, we construct confidence intervals of control charts and compute their coverage probability. Traditional process control actually tests if the process mean of a control chart is changed. The confidence interval of a control chart expands this hypothesis testing to test if the control chart interval is changed.

並列關鍵字

quality control ； control chart ； coverage interval ； confidence interval ； hypothesis testing ； individuals control chart ； interval estimation of a control chart

參考文獻

[1] ISO 3534-1 1993 Statistics–vocabulary and symbols–part1: basic statistical term and concepts(Geneva: International Organization for Standardization)

[2] ISO 3534-2 1993 Statistics–vocabulary and symbols–part2: statistical quality control (Geneva: International Organization for Standardization)

[3] Huang, J.-Y., Chen, L.-A. and Welsh, A. H.(2010),“A note on reference limits”.

IMS Collections Vol. 7, 84-94

[4] Chen, L.-A., Huang J.-Y., Chen, H.-C.(2007), “parametric coverage interval”.