為了在有限的時間內推估高功率LED 晶粒的可靠度, 本論文使用雙應力變數對高功率LED 晶粒進行恆定應力加速退化測試實驗。假設加速退化實驗所收集的元件之累積損害退化資料服從Wiener 隨機過程, 我們建議以逆高斯分配建立了加速退化模型, 進而推導出產品壽命百分位數的點估計值及信賴下界。本文並以高功率LED 晶粒退化資料實例來說明本方法之應用。

It is difficult to evaluate the lifetimes of high reliable products in limited experimental time. In this thesis, statistical methods based on a two-variable constant-stress loading accelerated degradation test are developed to overcome this difficulty. Assuming the cumulative damage information of test units due to degradation has a Wiener process, the inverse Gaussian distribution is used to derive the lifetime percentiles and their low confidence bounds. A real example of LED chips data set is used to demonstrate the application of the proposed method.

目錄
第一章緒論.... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 1
1.1 研究背景.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 1
1.2 研究動機與目的.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 3
1.3 文獻探討與相關研究.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 4
第二章加速退化測試之統計推論.. .. .. .. .. .. .. .. .. .. .. .. .. .. 7
2.1 加速退化模型.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 7
2.2 選取加速變數之應力水準.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 10
2.3 壽命時間的百分位數之推論.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 13
第三章實例分析.... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 15
第四章結論.... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 26
附錄.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 27
參考文獻.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 28

圖目錄
2.1 Wiener 隨機過程. . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 高功率LED 晶粒在(35◦C,600mA) 組合下之累積損害圖. . . . . 17
3.3 高功率LED 晶粒在(55◦C,600mA) 組合下之累積損害圖. . . . . 18
3.4 高功率LED 晶粒在(70◦C,400mA) 組合下之累積損害圖. . . . . 19
3.5 高功率LED 晶粒在(70◦C,500mA) 組合下之累積損害圖. . . . . 20
3.6 高功率LED 晶粒在(70◦C,600mA) 組合下之累積損害圖. . . . . 21
3.7 高功率LED 晶粒百分位數之壽命(其中C=30(—–), C=40(- - -)
及C=50(-．-．-)) . . . . . . . . . . . . . . . . . . . . . . . . . 25

表目錄
3.1 實驗組合. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 轉換後之應力水準. . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 參數估計. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.4 當C = 30% 時不同百分位數之spL 和spL,LB . . . . . . . . . . 24
3.5 當C = 40% 時不同百分位數之spL 和spL,LB . . . . . . . . . . 24
3.6 當C = 50% 時不同百分位數之spL 和spL,LB . . . . . . . . . . 24

[1] Cox, D.R. and Miller, H.D. (1965). Theory of Stochastic Processes. John
Wiley & Sons: New York.
[2] Doksum, K.A. and H´oyland, A. (1992). Models for variable-stress accel-
erated life testing experiments based on Wiener processes and the inverse
gaussian distribution. Technometric, 34(1), pp. 74-82.
[3] Durham S.D. and Padgett, W.J. (1997). A cumulative damage model for
system failure with application to carbon fibers and composites. Technometrics
, 39, pp. 34-44.
[4] Karlin, S. and Taylor, H.M. (1975). A First Course in Stochastic Process.
2nd edition, New York, Academic Press.
[5] Lu, C.J., Meeker, W.Q. and Escobar, L.A. (1996). A comparison of degra-
dation and failure-time analysis methods for estimating a time-to-failure
distribution. Statistica Sinica, 6, pp. 531-546.
[6] Liao, C.M. and Tseng, S.T. (2006). Optimal design for step-stress accel-
erated degradation tests. IEEE Transaction on Reliability, 55, pp.59-66.
[7] Lim, H. and Yum, B.J. (2011). Optimal design of accelerated degradation
tests based on wiener process models. Journal of Applied Statistics, 38(2),
pp.309-325.
[8] Meeker, W.Q. and Escobar, L.A. (1998). Statistical Methods for Reliability
Data. John Wiley & Sons: New York.
[9] Nelson, W. (1990). Accelerated Testing: Statistical Models, Test Plans,
and Data Analysis. John Wiley & Sons, New York.
[10] Padgett, W.J. and Tomlinson, M.A. (2004). Inference from accelerated
degradation and failure data based on Gaussian process models. Lifetime
Data Analysis, 10, pp. 191-206.
[11] Park, C. and Padgett, W.J. (2006). Stochastic degradation models with
several accelerating variables. IEEE Transaction on Reliability, 55, pp.
370-390.
[12] Pan, Z. and Balakrishnan, N. (2010). Multiple-steps step-stress acceler-
ated degradation modeling based on wiener and gamma processes. Communications
in Statistics Simulation and Computation, 39, pp. 1384-
1402.
[13] Peng, C.Y. and Tseng, S.T. (2010). Progressive-stress accelerated degra-
dation test for highly-reliable products. IEEE Transaction on Reliability,
59(1), pp. 30-37.
[14] Tseng, S.T. and Wen Z.C. (2000). Step-stress accelerated degradation
analysis for highly reliable products. Journal of Quality Technology, 32,
pp. 209-216.
[15] Tang, L.C., Yang, G.Y. and Xie, M. (2004). Planning of step-stress ac-
celerated degradation test. Reliability and Maintainability Annual Symposium
, Los Angeles, CA.
[16] Tseng, S.T., Balakrishnan, N. and Tsai, C.C. (2009). Optimal step-stress
accelerated degradation test plan for gamma degradation process. IEEE
Transactions on Reliability, 58, pp. 611-618.
[17] Tsai, T.R., Lin, C.W., Sung, Y.L., Chou, P.T., Chen, C.L. and Lio, Y.L.
(2011), Inference from lumen degradation data under Wiener diffusion
process. Technical Report, Department of Statistics, Tamkang University.
[18] Waltraud, K. and Axel, L. (2010). The Wiener Process as a degradation
model: modeling and parameter estimation. Birkhauser Boston, a part of
Springer Science+Business Media.
[19] Zhang H., Chen Y., and Kang R. (2010). Optimal design of step stress
accelerated degradation test and reliability assessment for quartz flexi-
ble accelerometers Proceedings of Reliability and Maintainability Symposium
(RAMS), 25-28, pp. 1-6.