在科技發達的現代，為了使產品有良好的品質，監控其壽命變化是一項重
要的議題。現今工業界常以韋伯分佈來描述產品的壽命，因此如何同時監控韋
伯分佈的形狀參數和尺度參數成為了研究的重點。在既有的文獻中較多在監控
韋伯分佈完整資料的形狀參數改變，而在本文中我們利用兩個現有的舒華特管
制圖的監控統計量，在考慮樣本資料為型二設限的條件上建構出能同時監控韋
伯分佈雙參數的EWMA 固定抽樣區間管制圖。接著我們引入變動抽樣區間的
想法來改進監控效率，建構兩種變動抽樣區間EWMA 管制圖並與文獻上現有
的監控方法來進行比較。此外，我們找出修正的管制界限來改善以參數估計值
建構EWMA 固定抽樣區間管制圖所帶來的缺點。最後我們將提出的監控方法
應用於一組碳纖維拉扯強度資料來說明所提出的管制圖在實務上的運用和表現。

As technology continuously advances, to make products with good quality, it is an important issue to monitor their lifetime during the manufacturing period. The production industry often uses Weibull distribution to represent the lifetime of products. Therefore, this paper focuses on how to simultaneously monitor the
shape and scale parameters of the Weibull distribution. There are a lot of studies on monitoring the shape parameter of Weibull distribution for complete data. In this article, for type-II censored data we use two existing Shewhart-type charting statistics to develop the EWMA and AEWMA FSI control charts for monitoring the shape and scale parameters of the Weibull distribution simultaneously. Further, we apply the concept of variable sampling intervals to construct two kinds of EWMA VSI control charts and compare them with the existing monitoring methods in literature. Additionally, we propose a modified control limit to improve the disadvantages of the EWMA FSI control chart developed with the estimated parameters. Finally, we apply the proposed monitoring methods to a breaking strength example from a carbon fiber process to demonstrate the applicability and performance of the proposed control schemes.

摘要
目錄
第一章 緒論------------------------------1
1.1 管制圖的簡介-------------------------1
1.2 研究動機與目的-----------------------2
第二章 監控韋伯分佈的雙參數--------------4
2.1 文獻回顧-----------------------------4
2.2 固定抽樣區間管制圖-------------------5
2.3 變動抽樣區間管制圖-------------------7
2.4 調適的EWMA變動抽樣區間管制圖---------9
第三章 管制圖的比較---------------------14
3.1 管制界限----------------------------14
3.2 警戒界限----------------------------18
3.3 管制圖的ARL1比較--------------------20
3.4 管制圖的ATS1比較--------------------26
第四章 修正的管制界限-------------------30
4.1 未修正管制界限的缺點----------------30
4.2 修正管制界限------------------------32
4.3 修正管制界限的真實ARL0值------------34
第五章 實例分析-------------------------37
第六章 結論與後續研究-------------------41
附錄----------------------------------- 43
參考文獻--------------------------------45
附表---------------------------------- -48
附圖-----------------------------------107

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