在可靠度分析中，我們常使用韋伯分佈來描述產品的失效時間，而在本文中使用的韋伯迴歸模型即是將韋伯分佈的雙參數表示成共變數的迴歸式，這常用於加速壽命實驗上。本文是利用多變量符號指數加權移動平均管制圖來監控韋伯迴歸模型的製程。我們將透過統計模擬來評估多變量符號指數加權移動平均管制圖用於監控韋伯迴歸模型時的監控效率，以及改變點的估計與參數診斷的優劣。同時我們也探討在第一階段樣本組數不足時，多變量符號指數加權移動平均管制圖真正的平均連串長度是否可以達到名義的平均連串長度。最後我們透過一筆聚酯樹脂-聚氨酯絕緣材料的壽命資料，說明如何使用此管制圖來監控韋伯迴歸模型。

In the reliability analysis, we often use the Weibull distribution to describe products' failure times. The Weibull regression model is to express the two parameters in terms of the covariates, which is often used in accelerated lifetime testing. In this article, we monitor the Weibull regression model process by multivariate sign EWMA control chart to ensure that products' lifetimes are stable. We use statistical simulations to evaluate monitoring efficiency, change point estimation and parameter diagnosis of the multivariate sign EWMA control chart which is used to monitor the Weibull regression model process. We also discuss whether the true ARL$_0$ of the multivariate sign EWMA control chart can achieve the nominal ARL$_0$ or not, when the number of Phase I samples is not large enough. Finally, we use mylar-polyurethane insulation lifetime data to illustrate how to apply the multivariate sign EWMA control chart to monitor the Weibull regression model process.

第一章緒論 1
1.1 管制圖簡介 1
1.2 研究動機與目的 2
第二章監控韋伯迴歸模型 3
2.1 文獻回顧 4
2.2 製程改變點的估計 7
2.3 參數診斷 8
第三章統計模擬 10
3.1 MSEWMA 的管制界限 10
3.2 管制圖的比較 12
3.3 改變點的估計與參數診斷 14
3.4 第一階段樣本組數對管制圖的影響 16
第四章實例分析 18
第五章結論與未來研究 22
參考文獻 24
附表 26
附圖 59

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