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研究生:張凱鈞
研究生(外文):Chang, Kai Chun
論文名稱:預燒程序在window size為1及2下之績效比較分析
論文名稱(外文):Performances of Optimal Burn-in Policies when the Window Size is One or Two
指導教授:曾勝滄曾勝滄引用關係
指導教授(外文):Tseng, Sheng Tsaing
學位類別:碩士
校院名稱:國立清華大學
系所名稱:統計學研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:中文
論文頁數:68
中文關鍵詞:預燒程序衰變路徑Wiener過程window size
外文關鍵詞:burn-in policydegradation pathWiener processwindow size
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任何產品在製造過程中,必然會生產出少部分的瑕疵品,如何在出貨前能夠有效地篩選出潛在的不良品,將是生產者或廠商相當關注的一部份。執行一預燒試驗 (burn-in procedure) 將可達到篩選不良品之目的,但高可靠度產品,其壽命動輒上千小時,使用傳統預燒試驗,很難在有限的測試時間內篩選出潛在的不良品。若產品存在一具代表性之品質特徵值 (quality characteristic, QC) ,利用衰變試驗 (degradation test) 進行篩選分類將會是一實際可行的方法。近年來預燒試驗之相關文獻大多以衰變試驗為研究主軸,其中Tseng and Tang (2001) 與Tseng, Tang, and Ku (2003) 分別在window size為1及 (s + 1) 下,引入混合型Wiener過程,來描述高可靠度產品的品質特徵值之衰變模型,並皆以成本觀點建構一套篩選試驗執行程序。唯上述兩種篩選方法之績效表現,在文獻上並未深入分析,因此本研究將針對上述兩篩選方法進行優劣比較,且限定後者之window size為2。本研究發現衰變模型之結構在某些條件限制下,兩篩選方法之績效表現是相同的。更進一步利用數值方法探討一般化衰變模型之參數設定,其績效表現之差異則利用圖形呈現之,發現使用Tseng, Tang, and Ku (2003) 之準則比Tseng and Tang (2001) 更能有效篩選出早夭產品。然而因為前者沒有完整的理論架構且需要繁雜之數值計算,所以當兩篩選方法之績效表現差異不顯著時,其定義為兩分類準則造成之錯誤分類機率差異少於0.005,建議使用後者進行篩選試驗。在本研究的搜尋範圍當中,約10% 之參數設定適合使用window size為2之分類準則進行篩選試驗。而這些成果,對工程師規劃欲燒篩選試驗將有實質助益。
Today’s free market is very competitive. In order to compete with others, it is a great challenge for the manufactures to design an optimal burn-in policy to eliminate failure or weak components before their products are shipped to the market. Without removing these defective products, the warranty and replacement costs will increase substantially. The burn-in policy is conventionally based on the formulation of a mixture of two lifetime distributions. For highly-reliable products, it is not easy to obtain their lifetime distributions within a short time of life-testing. Instead, if there exists a quality characteristic whose degradation over time can be closely related with the product’s lifetime, then we can construct optimal burn-in policy based on suitable degradation models. Recently, Tseng and Tang (2001) and Tseng, Tang, and Ku (2003) proposed two optimal burn-in policies (which are essentially based on the choices of the different window size) to screen out the defective products. However, there is no suitable literature to compare the performance of these two burn-in policies. Focusing on the setting of window size 2, this study demonstrates that these two approaches are essentially the same under some specific conditions. Furthermore, under more general parameter settings, we use numerical computations and graphical approach to compare the performance of these approaches. The results demonstrate that the policy proposed by Tseng, Tang, and Ku (2003) is always better than that of Tseng and Tang (2001). More specifically, among all the parameter settings in this study, the ability of reducing total misclassification probabilities up to 0.5% is around 10%. Note that the former one, however, requires a complex computational effort to obtain its screening procedure. Therefore, we recommend to using the later one if these two policies did not have significant differences in their screening performance.
目錄
第一章 緒論 1
1.1 研究動機與目的 1
1.2 文獻探討 2
1.3 研究範圍與限制 5
1.4 研究架構 6
第二章 高可靠度篩選試驗之相關參考文獻探討 8
2.1 衰變模型 8
2.2 篩選方法 10
2.2.1 分類準則一之最佳分類點 10
2.2.2 分類準則二之最佳分類點 12
2.2.3 最佳預燒時間 14
2.3 動機例子與問題描述 15
第三章 兩篩選試驗之績效比較 22
3.1 分類準則二 之 window size為2 22
3.1.1 當κ(t) = τ(t) 之情形 25
3.1.2 當κ(t) ≠ τ(t) 之情形 26
3.2 參數空間縮減 28
3.2.1 以產品壽命區分兩群產品之限制 29
3.2.2 以混合衰變模型之形狀及變異限制 32
3.3 兩分類準則之優劣比較 36
3.3.1 對於錯誤分類機率之差異 37
3.3.2 對於錯誤分類成本之差異 39
第四章 數值分析結果 42
第五章 研究結論 49
附錄 51
附錄一 定理一證明 51
附錄二 定理二證明 59
附錄三 數值解方法 62
A 數值解一 非線性方程組 62
B 數值解二 二維度常態分配之機率 63
參考文獻 66

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