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研究生:林士豪
研究生(外文):Shih-hao Lin
論文名稱:加速衰變實驗中隨機線性模型之實驗規畫
論文名稱(外文):Design Planing for Accelerated Degradation Tests with Linear Random Coefficient Model
指導教授:鄭順林鄭順林引用關係
指導教授(外文):Shuen-lin Jeng
學位類別:碩士
校院名稱:國立成功大學
系所名稱:統計學系碩博士班
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:2008
畢業學年度:96
語文別:英文
論文頁數:91
中文關鍵詞:結合模型漸近變異數部分觀察.完全觀察隨機係數最佳實驗規劃門檻值
外文關鍵詞:Asymptotic varianceRandom coefficientTotally observed CaseOptimal test plansThreshold levelPartially observed Case.Joint modelling
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  • 收藏至我的研究室書目清單書目收藏:0
估計高可靠度設備的長期表現是一個困難的問題. 因為即使在加速壽命測試中, 高應力的測試下常常獲得少量的失效觀察值. 為了克服這個問題, 加速衰變實驗採取測量退化的實驗方式, 並隨著時間而監控它. 這些退化量提供了對於設備失效有價值的訊息. 這也是加速衰變實驗在目前工業上越來越普遍被採用的原因.
本研究的主要貢獻, 考慮一結合模型, 將退化與壽命訊息結合而進行實驗規畫. 我們稱之為加速壽命與衰變實驗. 依據加速壽命與衰變實驗而進行的實驗規畫, 對於在估計設備的壽命時間上, 擁有較佳的效率. 我們著重在具有測量誤差的隨機係數線性模型. 舉例來說, 像是在實務上常見的電性反應或磨損過程. 很多非線性的退化關係也可以被轉換成線性的, 因此我們的實驗規劃方式也可以被使用.
我們研究的主要目的, 在於使用兩應力的加速衰變實驗時, 找到低應力的最佳位置, 使得我們在實驗後估計設備壽命上有較佳的精準度. 藉由使用結合模型, 加速壽命與衰變實驗比加速衰變實驗在分位數的估計上更有效率. 我們考慮兩種資料蒐集方式: 一種為完全觀察,代表當設備持續運作超過門檻值後仍持續蒐集退化資料;另一種為部分觀察,意味著當設備運作超過門檻值後,我們只能再觀察到一個退化量.
Estimating the long term performance of highly reliable devices has been a di cult problem because accelerated life tests (ALT’s), which involve testing at highly elevated stress, often result in too few falures. To overcome this problem, accelerated degradation tests (ADT’s) take measurements along experiment to exhibit degradation and monitor it over time. These measurements provide valuable information on the failure mechanisms of the devices. This is the reason why ADT’s are getting more popular in industry today.
The major contribution of this research is to consider a joint modelling of degradation measurements and lifetime data for the design planing. We name such approach an
accelerated life-degradation test (ALDT). The design planning based on the ALDT will provide more efficient estimator of device life time. We focus on linear random coe cient degradation model with measurement error, which arises in many practical situations, for example, a electronic reaction or a wearing processs. A lot of nonlinear degradation relationships may be transformed into linear forms, hence our approach can also be used.
The main purpose of our study is to decide the level of the optimal lower stress of a two-level ADT design such that the life of devices can be estimated with higher precision. By using the joint modelling, the ALDT will improve the e ciency in quantile estimation over the ADT. Two schemes of data collection are investigated: one is the totally observed case (TOC) which means the device continuously works after the threshold level and degradation measurements are collected through the test; the other one is the partially observed case (POC) which means we can only obtain one more degradation measurement of the device after the threshold level.
1.Introduction ...........................................1
1.1 Planning of Reliability Tests ....................... 2
1.2 Problem Considered ...................................3
1.3 Literature Review ....................................6
1.3.1 Accelerated Life Test Plans ........................6
1.3.2 Degradation Models and Analysis ....................7
1.3.3 Accelerated Degradation Test Plans .................8
1.3.4 Joint Modelling of Degradation Measurements and
Lifetime Data ..................................... 9
1.4 Overview ............................................10
2. The Totally Observed Case (TOC) ......................11
2.1 Likelihood and Failure Time Distribution ............11
2.2 Asymptotic Distribution .............................14
3. Joint Modelling for the TOC ..........................19
3.1 The Joint Likelihood Function .......................19
3.2 Asymptotic Variance of Quantile Function ............21
3.3 Optimal Plan ........................................24
4. The Partially Observed Case (POC) ....................32
4.1 The Likelihood Function .............................33
4.2 Asymptotic Variance of Quantile Function ............35
5. Joint Modelling for the POC ..........................38
5.1 The Joint Likelihood Function .......................38
5.2 Asymptotic Variance of Quantile Function ............40
5.3 Optimal Plan ........................................43
6. Second Situation of the POC ..........................51
6.1 The Likelihood Function .............................51
6.2 Asymptotic Covariance Matrix for Test Planning ......53
6.3 An Alternative Approach .............................56
7. Conclusion ...........................................60
7.1 Main Results ........................................60
7.2 Future Research .....................................61
Appendix 67
A. The Totally Observed Case (TOC) using Linear Model with
Random Intercept(M+) .................................68
A.1 Likelihood and Failure Time Distribution ............68
A.2 Asymptotic Distribution .............................71
A.3 Optimal Plan ........................................74
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