失效率函數與可靠度呈等差或等比及混合型關係之探討

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劉偉彥(Wei-yen Liu) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

失效率函數與可靠度呈等差或等比及混合型關係之探討

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摘要(中)

隨著科技進步發展，高品質與高可靠度之產品已成為工程設計上所追求的目標。而可靠度較佳之產品在市場上將有較高之競爭力。本研究以失效率函數為出發點，根據失效率函數與可靠度之間，分別呈現等差、等比、與混合型關係而發展出不同的模型，分析比較各模型之性質，並使用真實與模擬數據分別驗證模型的適用性，以求能夠利用各模型中參數描述系統或產品之退化行為，進一步將模型應用於預測產品之壽命。
可靠度理論是以機率與統計為工具，來處理工程設計中各類問題。本研究同時也利用失效率函數與機率密度函數間之關聯性，比較各模型機率密度分佈之趨勢，並建立特性指標以區分不同種類的機率密度分佈之集中性與對稱性。

摘要(英)

Along with the advancement of the scientific technology, the goal of engineering design has already become designing products with high quality and high reliability. Products with higher reliability show better possibility to seek a competitive advantage over competitors.
This study, based on hazard rate function, used the mathematical relationship between hazard rate function and reliability to create three different kinds of models. The characteristics of these models were then compared and analyzed by verifying the applicability of the models using different failure data. The parameters of the models were used to describe the degeneration behavior of the products or systems. Furthermore, the life of the products was expected to predict by using these reliability models.
Reliability theorem is relying on probability and statistics as a tool set to solve all kinds of engineering related problems. This study used the correlation between failure rate function and probability density function to compare the performance of different probability distribution models. New indexes about centricity and symmetry were established to distinguish different models.

關鍵字(中)

★ 機率分佈
★ 失效率函數
★ 可靠度

關鍵字(英)

★ probability distribution
★ hazard rate function
★ reliability

論文目次

摘要.............................................................................................................................. I
Abstract ......................................................................................................................... II
誌謝............................................................................................................................ III
目錄............................................................................................................................ IV
圖目錄...................................................................................................................... VI
表目錄................................................................................................................... VIII
符號說明................................................................................................................. X
第一章緒論.................................................................................................................. 1
1.1 研究動機......................................................................................................... 1
1.2 文獻回顧......................................................................................................... 2
1.3 研究範圍......................................................................................................... 3
第二章可靠度分析概要.............................................................................................. 4
2.1 可靠度概要..................................................................................................... 4
2.2 可靠度函數與失效率函數............................................................................. 5
2.2.1 可靠度函數.......................................................................................... 5
2.2.2 浴缸曲線.............................................................................................. 7
2.3 可靠度退化模型............................................................................................. 8
2.3.1 韋伯可靠度退化模型.......................................................................... 8
2.3.2 累積失效模型...................................................................................... 9
第三章可靠度模型之建立........................................................................................ 14
3.1 失效率與可靠度間呈現等差或等比關係................................................... 14
3.1.1 以使用時間觀點探討失效模式......................................................... 14
3.1.2 以失效時間觀點探討失效模式......................................................... 15
3.1.3 失效率函數與可靠度間呈等差關係或等比關係............................. 16
3.2. 失效率函數與可靠度呈等比關係之模型.................................................. 18
3.2.1 (A0 , b)模型的建立 ............................................................................. 18
3.2.2 (A0 , b)模型之性質分析 ..................................................................... 19
3.3 失效率與可靠度呈等差且等比之混合型模型I ........................................ 21
3.3.1 (A0 , A1 , b)模型的建立 ...................................................................... 21
3.3.2 (A0 , A1 , b)模型之性質分析 .............................................................. 22
3.4 失效率與可靠度呈等差且等比之混合型模型II ....................................... 24
3.4.1 (A0 , A1 , b*)模型的建立 ..................................................................... 24
3.4.2 (A0 , A1 , b*)模型之性質分析 ............................................................. 25
3.5 實例驗證....................................................................................................... 26
第四章失效機率密度分佈之探討............................................................................ 62
4.1 機率密度函數之介紹................................................................................... 62
4.2 機率密度分佈之對稱性與集中性之討論................................................... 63
4.2.1 以面積比值討論對稱性.................................................................... 63
4.2.2 以時間間隔比值討論集中性............................................................ 65
4.2.3 特定分佈對稱性之描述.................................................................... 65
4.3 (A0 , A1
*
, n)模型之對稱性與集中性 ............................................................ 67
4.4 (A0 , b)模型之對稱性與集中性 .................................................................... 68
4.5 (A0 , A1 , b)模型之對稱性與集中性 ............................................................. 68
4.6 (A0 , A1 , b*)模型之對稱性與集中性 ............................................................ 69
第五章結論與建議.................................................................................................... 80
參考文獻...................................................................................................................... 83

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指導教授

王國雄(Kuo-Shong Wang)

審核日期

2008-7-23

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