產品的可靠度會反映出製程的技術與產品設計的優劣進而影響品牌地位，因此如何即時監控產品可靠度是工廠製造極為關注的議題。在可靠度分析中經常使用韋伯分佈來描述產品的失效時間，因此監控韋伯分佈的雙參數相當於監控產品的可靠度。在本文中提出舒華特與EWMA類型的聯合管制圖來監控韋伯分佈的雙參數，透過統計模擬的結果說明了我們所提出的舒華特管制圖大幅改善了現存舒華特管制圖監控韋伯分佈雙參數的偏差問題。所提出的EWMA管制圖不但對雙參數微小的變動有較好的監控效率，我們還可以利用估計改變點以及參數改變的診斷來幫助監控者找出製程問題的根源。最後我們利用碳纖維拉扯強度資料來詳細說明實務上如何應用所提出的舒華特和EWMA聯合管制圖來監控韋伯分佈的雙參數。

The reliability of products reflect the skills of the manufacturing process and also affect the brand reputation. Therefore, how to monitor the reliability of products in real time is an important topic in factory manufacturing. The Weibull distribution is often used to describe the product's failure time in reliability analysis. As a result, monitoring the two parameters of Weibull distribution is equivalent to monitoring the reliability of the products. In this paper, joint control charts of Shewhart and EWMA types are proposed to monitor the two parameters of Weibull distribution. The results of statistical simulation show that the proposed Shewhart control chart has greatly improved the biased phenomenon of the existing Shewhart control charts. Also, the proposed EWMA control chart has better efficiency for monitoring small shifts of the two parameters of Weibull distribution. Furthermore, we also provide the method for estimating the change point and diagnosing the shifts of the two parameters of Weibull distribution. Finally, we use an example of the breaking strength of carbon fibers to show how to apply the proposed Shewhart and EWMA joint control charts to monitor the two parameters of Weibull distribution.

第一章 緒論 1
1.1 管制圖簡介 . . . . . . . . . 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 監控韋伯分佈雙參數的管制圖 . . . . 5
------2.2.1 舒華特管制圖 . . . . . . 6
------2.2.2 指數加權移動平均管制圖 . . . 8
2.3 改變點的估計 . . . . . . . . . 9
2.4 參數診斷 . . . . . . . . . . 10

第三章 統計模擬 13
3.1 管制圖的管制界限 . . . . . . . 13
------3.1.1 舒華特管制圖的管制界限 . . . 13
------3.1.2 指數加權移動平均管制圖的管制界限 14
3.2 管制圖的比較 . . . . . . . . . 16
------3.2.1 管制圖效率比較 . . . . . .16
------3.2.2 改變點的估計 . . . . . . 17
------3.2.3 參數改變的診斷 . . . . . .18

第四章 實例分析 20

第五章 結論與未來研究 23

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