進階搜尋


 
系統識別號 U0026-0812200914181844
論文名稱(中文) 加速衰變實驗中隨機線性模型之實驗規畫
論文名稱(英文) Design Planing for Accelerated Degradation Tests with Linear Random Coefficient Model
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 96
學期 2
出版年 97
研究生(中文) 林士豪
研究生(英文) Shih-hao Lin
電子信箱 r2695102@ncku.edu.tw
學號 r2695102
學位類別 碩士
語文別 英文
論文頁數 91頁
口試委員 口試委員-路繼先
指導教授-鄭順林
口試委員-張升懋
中文關鍵字 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 
英文關鍵字 Asymptotic variance  Random coefficient  Totally observed Case  Optimal test plans  Threshold level  Partially observed Case.  Joint modelling 
學科別分類
中文摘要 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.
英文摘要 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.
論文目次 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
參考文獻 Boulanger, M., and Escobar, L. A. (1994), “Experimental
Design for a Class of Accelerated Degradation Tests,”
Technometrics, 36(3), 260–272.
Chiao, C. H., and Hamada, M. (2001), “Analyzing
Experiments With Degradation Data for Improving
Reliability and for Achieving Robust Reliability,”
Quality and Reliability Engineeringg International, 17,
333–344.
Condra, L. W. (2001), Reliability Improvement with Design
of Experiments, New Tork: Marcel Dekker.
Chao, M. T. (1999), “Degradation Analysis and Related
Topics: Some Thoughts and a Review,” Proceedings of the
National Science Council 23, 555-566
Dowling, N. E. (2006), Mechanical Behavior of Materials:
Engineering Methods for Deformation, Fracture, and
Fatigue, NJ: Prentice Hall.
Ding, J.M., Wang, J.L. (2008), “Modeling longitudinal data with nonparametric multiplicative random effects jointly with survival data,” Biometrics, 64, 546–556
Escobar, L. A., Meeker, W. Q. (1995), “Planning
accelerated life tests with two or more experimental
factors,” Technometrics, 37, 411–427.
Henderson, R., Diggle, P., and Dobson, A. (2000), “Joint
Modelling of Logitudinal Measurements and Event Time
Data,” Biostatistica, 1(4), 465–480.
Johnson, N. L., Kotz, S., and Balakrishnan, N. (1994),
Continuous Univariate Distributions, Vol. 1, New York:
Wiley.
Kuo, M. H. (2001), “The Optimum Plan and Accurate
Inference for Accelerated Life Test under Inverse Gaussian Distribution,” Master Thesis, Dept. of Statistics, Tunghai University.
Lu, C. J., and Meeker, W. Q. (1993), “Using Degradation
Measures to Estimate a Timeto-Failure Distribution,”
Technometrics, 35(2), 161–174.
Lu, C. J., Meeker, W. Q. and Escobar, L. A. (1996),
“Comparison of Degradation and Failure-Time Analysis
Methods for Estimating a Time-To-Failure Distribution,”
Statistica Sinica, 6, 531–546.
Lu, J. C., Park, J., and Yang, Q. (1997), “Statistical
Inference of a Time-to-Failure Distribution Derived from
Linear Degradation Data,” Technometrics, 39(4), 391–400.
Lawless, J. F. (2003), Statistical Models and Methods for
Lifetime Data, New York: Wiley.
Liao, H. T., and Elsayed, E. A. (2004), “Reliability
Prediction and Testing Plan Based on an Accelerated
Degradation Rate Model” Int. J. Materials and
Technology, 21, 402–422.
Meeker, W. Q. (1984), “A Comparison of Accelerated Life
Test Plans for Weibull and Lognormal Distributions and
Type I Censoring,” Technometrics, 26(2), 157–171.
-----(1993), “A Review of Recent Research and Current
Issues in Accelerated Testing”, International
Statistical Review, 61(1), 147–168.
Meeter, C. A., and Meeker, W. Q. (1994), “Optimum
Accelerated Life Tests with a Nonconstant Scale
Parameter,” Technometrics, 35(1), 71–83.
Meeker, W. Q., and Escobar, L. A. (1998), Statistical
Methods for Reliability Data Analysis, New York: Wiley.
Meeker, Q. W., Escobar, L. A., and Lu, C. J. (1998),
“Accelerated Degradation Tests: Modeling and Analysis,”
Technometrics, 40(2), 89–99.
Nair, V. N. (1988), Disscussion of “Estimation of
Reliability in Field-Performance Studied,”
Technometrics, 30, 379–383.
Nelson, W. (1990), Acceleratd Testing: Statistical Model,
Test Plans, and Data Analyses, New York: Wiley.
Nelson, W. (1995b), “Defect initiation and Growth - a
generalstatistical model & data analysis,” 2nd annual
Spring Research Conference
Park, J. I., and Yum, B. J. (1997), “Optimal Design of
Accelerated Degradation Tests for Estimating Mean
Lifetime at the Use Condition,” Engineering
Optimization, 28(3), 199–230.
Pascual, F. G., and Montepiedra, G. (2005), “Lognormal and Weibull Accelerated Life Test Plans Under Distribution
Misspecification,” IEEE Transaction on Reliability,
54(1), 43–52.
Su, C., Lu, J.C., Chen, D. and Hughes-Oliver, J.M. (1999),
“A Random Coe cient Degradation Model with Random Sample
Size,” Life Data Analysis, 5, 173–183.
Song, X. and Wang C.Y. (2008), “Semiparametric approaches
for joint modeling of longitudinal and survival data with
time-varying coe cients,” Biometrics 64, 557–566
Tomsky, P. A. (1982), “Regression models for detecting
reliability degradation,” Proceedings of the Annual
Reliability and Maintainablity Conference, New York:
Institute of Electrical and Electronics Engineers.
Tsou, T. S. (2003a), “Parametric Robust Inferences for
Regression Parameters under Generalized Linear Models,”
(Sumitted.)
Tang L. C., Yang G. Y., and Xie M. (2004), “Planning of
Step-stress Accelerated Degradation Test,” IEEE, 17,
287–292.
Tseng, Y. K., Hsieh, F., and Wang J. L. (2005), “Joint
Modelling of Accelerated Failure Time and Longitudinal
Data,” Biometrika, 92(3), 587–603.
----(2006), “Parametric Robust Test for Several Variances
with Unknown Underlying Distributions,” Metrika, 64,
333–349.
Venables, W. N., and Ripley, B. D. (2002), Modern Applied
Statistics with S, New York: Springer-Verlag.
Wulfsohn, M. S., and Tsiatis, A. A. (1997), “A Joint Model for Surval and Longitudinal Data Measured with Error,” Biometrics, 53(1), 330–339.
Yu, H. F., and Chiao, C. H. (2002a), “An Optimal Designed
Degradation Experiment for Reliability Improvement,”
IEEE Transactions on Reliability, 51(4), 427–433.
-----(2002b), “Designing an Accelerated Degradation
Experiment by Optimizing the Interval Estimation of the
Mean-Time-to-Failure,” Journal of the Chinese Institute
of Industrial Engineers, 19(5), 23–33.
Yu, H. F. (2003), “Designing an Accelerated Degradation
Experiment by Optimizing the Estimation of the
Percentile,” Quality and Reliability Engineering
International, 19, 197–214.
Yu, M., Law, N. J., Taylor, J . M. G., and Sandler, H. M.
(2004), “ Joint Longitudinalsurvival-cure Models and
Their Application to Prostate Cancer,” Statistica
Sinica, 14, 835–862.
------(2006), “Designing an Accelerated Degradation
Experiment with a Reciprocal Weibull Degradation Rate,”
Journal of Statistical Planning and Inference, 136, 282–
297.
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2011-07-21起公開。
  • 同意授權校外瀏覽/列印電子全文服務,於2011-07-21起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw