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姓名 童義軒(Yi-Hsuan Tung)  查詢紙本館藏   畢業系所 統計研究所
論文名稱 逆高斯過程之貝氏加速衰變試驗分析與序列預測
(Bayesian Accelerated Degradation Analysis and Sequential Prediction based on Inverse Gaussian Processes)
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摘要(中) 對高可靠度產品,常用加速衰變試驗 (accelerated degradation test) 評估產品的壽命資訊。試驗中將產品置於較正常使用環境應力更嚴苛的高應力下,隨時間紀錄和產品壽命相關的品質特徵值 (quality characteristic) 之變化,建構與應力有關的加速衰變模型。衰變試驗中,定義產品壽命為衰變路徑首次抵達給定門檻值 (threshold) 的時間,在加速衰變試驗中經由衰變模型與應力的關係,可經外插至正常應力推估產品的壽命分布,因此應力與模型的關係也會對壽命推論產生影響。本文針對單調加速衰變資料,分別考慮三種應力與參數的關係,配適逆高斯 (inverse Gaussian) 過程,同時考量產品間不同的個別差異性,建構三種具隨機效應 (random-effects) 的貝氏階層模型 (Bayesian hierarchical model),利用共軛先驗分布 (conjugate prior) 以吉布斯抽樣(Gibbs sampler) 得參數的近似後驗樣本。經貝氏準則及適合度檢定選取最佳的衰變模型提供完整的貝氏壽命預測推論。此外,對類似產品之可靠度推論,本文提出利用過去加速衰變試驗資料的後驗分布作為先驗資訊,配合逐次收集資料與先驗分布的更新,探討序列預測可靠度分析及試驗終止之準則,以縮短試驗時間。最後,並以三筆實例和模擬資料驗證所提方法之可行性。
摘要(英) Accelerated degradation tests (ADTs) are widely used to assess the lifetime information of highly reliable products. In an ADT, products are placed in harsher environmental stress levels than the normal use condition and values of a quality characteristic (QC) related to the lifetime are observed over time. The ADT model, including a link function between the model parameter(s) and the stress levels, is formulated based on the degradation paths of values of QC with respect to time. The product lifetime can be inferred under normal use condition through extrapolation based on the link function. Therefore, the relationship between the parameter and the stress level is essential to deduce the lifetime inference in an ADT. In this thesis, three types of parameter-stress relationship for monotonic accelerated degradation data based on the inverse Gaussian processes are considered. In addition, to describe the unit-to-unit variation, three different random-effects models are used under ING {color{black}(inverse normal-gamma)} mixture distributions. Individual heterogeneity among products is taken into account by using Bayesian hierarchical models with latent variables. Taking advantage of the ING conjugate structure, the Markov chain Monte-Carlo procedure can be speeded up. A comprehensive Bayesian inference for lifetime prediction is provided through model selection and model checking. Furthermore, we propose a predictive inference which is constructed by the prior distribution sequentially to determine the optimal experimental time under a pre-specified accuracy for predicting the lifetime information. The feasibility of the proposed methods is demonstrated through three examples and the simulation study.
關鍵字(中) ★ 逆高斯過程
★ DIC準則
★ 邊際密度函數
★ 後驗預測p-值
★ 貝氏預測
關鍵字(英) ★ inverse Gaussian process
★ DIC criterion
★ marginal likelihood function
★ posterior p-value
★ Bayesian prediction
論文目次 摘要 v
Abstract vi
誌謝 vii
目錄 viii
圖目錄 x
表目錄 xi
第一章 緒論 1
1.1 研究背景與動機 1
1.2 文獻探討 2
1.3 研究方法 4
1.4 本文架構 5
第二章 逆高斯過程之貝氏加速衰變模型 6
2.1 逆高斯加速衰變模型 6
2.2 概似函數 8
2.2.1 固定效應模型 9
2.2.2 隨機效應模型 9
2.3 貝氏架構 12
2.3.1 固定效應貝氏模型 12
2.3.2 隨機效應貝氏模型 13
2.4 貝氏選模與適合度檢定 17
2.4.1 偏差訊息法則 (DIC) 17
2.4.2 對數邊際概似函數法則 (LML) 18
2.4.3 適合度檢定 19
第三章 貝氏可靠度推論與序列預測分析 21
3.1 壽命分布 21
3.2 平均失效時間及 q-分位數 23
3.3 偽失效時間 24
3.4 序列預測分析 25
3.4.1 先驗分布之更新 26
3.4.2 序列預測 27
第四章 實例分析與模擬結果 29
4.1 分析步驟 9
4.2 Device-B 資料 29
4.3 接觸電阻資料 34
4.4 金屬磨損資料 40
4.5 模擬分析 45
4.5.1 參數估計 45
4.5.2 模型選擇 46
4.5.3 序列分析 47
第五章 結論與未來研究 52
參考文獻 53
附錄 Gelman-Rubin 統計量收斂圖 57
參考文獻 [1] Akaike, H. (1974). A new look at the statistical model identification, IEEE Trans-
actions on Automatic Control, 19, 716-723.
[2] Andrieu, C., De Freitas, N., and Doucet, A. (1999). Sequential MCMC for Bayesian
model selection, Proceedings of the IEEE Signal Processing Workshop on Higher-
Order Statistics. SPW-HOS ’99, 130-134.
[3] Bae, S. J. and Kvam, P. H. (2004). A nonlinear random-coefficients model for
degradation testing, Technometrics, 46, 460-469.
[4] Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis (Second
Edition), Springer-Verlag, New York.
[5] Carlin, B. P. and Louis, T. A. (2008). Bayesian Methods for Data Analysis, Chap-
man and Hall, London.
[6] Celeux, G., Forbes, F., Robert, C. P., and Titterington, D. M. (2006). Deviance
information criteria for missing data models, Bayesian Analysis, 1, 651-673.
[5] Duan, F. and Wang, G. (2018). Optimal step-stress accelerated degradation test
plans for inverse Gaussian process based on proportional degradation rate model.
Journal of Statistical Computation and Simulation, 88, 305-328.
[7] Fan, T. H. and Chen, C. H. (2017). A Bayesian predictive analysis of step-stress
accelerated tests in gamma degradation-based processes, Quality and Reliability
Engineering International, 33, 1417-1424.
[8] Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D.
B. (2013). Bayesian Data Analysis (Third Edition), Chapman and Hall, Londo
[9] Gelman, A., Meng, X. L., and Stern, H. (1996). Posterior predictive assessment of
model fitness via realized discrepancies, Statistica Sinica, 6, 733-807.
[10] Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and
the Bayesian restoration of images, IEEE Transactions on Pattern Analysis and
Machine Intelligence, PAMI-6, 721-741.
[11] Gronau, Q. F., Sarafoglou, A., Matzke, D., Ly, A., Boehm, U., Marsman, M., Leslie,
D. S., Forster, J. J., Wagenmakers, E. J., and Steingroever, H. (2017). A tutorial
on bridge sampling. Journal of Mathematical Psychology, 81, 80-97.
[12] Jefferys, W. H. and Berger, J. O. (1991). Sharpening Occam’s Razor on a Bayesian
strop, In Bulletin of the American Astronomical Society, 23, 1259.
[13] Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and
their applications, Biometrika, 57, 97-109.
[14] Lawless, J. and Crowder, M. (2004). Covariates and random effects in a gamma
process model with application to degradation and failure, Lifetime Data Analysis,
10, 213-227.
[15] Meeker, W. Q. and Escobar, L. A. (1998). Statistical Methods for Reliability Data,
John Wiley and Sons, New York.
[16] Meeker, W. Q., Escobar, L. A., and Pascual, F. G. (2022). Statistical Methods for
Reliability Data (Second Edition), John Wiley and Sons, New York.
[17] Meeker, W. Q., Escobar, L. A., and Lu, C. J. (1998). Accelerated degradation tests:
modeling and analysis, Technometrics, 40, 89-99.
[18] Meng, X. L. (1994). Posterior predictive p-values, The Annals of Statistics, 22,
1142-1160.
[19] Meng, X. L. and Schilling, S. (2002). Warp bridge sampling, Journal of Computa-
tional and Graphical Statistics, 11, 552-586.
[20] Meng, X. L. and Wong, W, H. (1996). Simulating ratios of normalizing constants
via a simple identity: a theoretical exploration. Statistica Sinica, 6, 831-860
[21] Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E.
(1953). Equation of state calculations by fast computing machines, The Journal of
Chemical Physics, 21, 1087-1092.
[22] Miazhynskaia, T. and Dorffner, G. (2006). A comparison of Bayesian model selec-
tion based on MCMC with an application to GARCH-type models, Statistical Papers,
47, 525-549.
[23] Nelson, W. (1980). Accelerated life testing step-stress models and data analyses,
IEEE transactions on reliability, 29, 103-108.
[24] Nelson, W. B. (1990). Accelerated Testing: Statistical Models, Test Plans, and Data
Analysis, John Wiley and Sons, New York.
[25] Ntzoufras, I. (1985). Bayesian Modeling Using WinBUGS, John Wiley and Sons,
New York.
[26] Peng, C. Y. (2015). Inverse Gaussian processes with random effects and explanatory
variables for degradation data, Technometrics, 57, 100-111.
[27] Peng, C. Y. and Tseng, S. T. (2009). Mis-Specification analysis of linear degradation
models, IEEE Transactions on Reliability, 58, 444-455.
[28] Peng, W., Li, Y. F., Yang, Y. J., Huang, H. Z., and Zuo, M. J. (2014). Inverse
Gaussian process models for degradation analysis: A Bayesian perspective, Relia-
bility Engineering & System Safety, 130, 175-189.
[29] Pieruschka, E. (1961). Relation between lifetime distribution and the stress level
causing the failures, LMSD-800440, Lockhead Missiles and Space Division, Sunny-
vale.
[30] Qin, H., Zhang, S. and Zhou, W. (2013). Inverse Gaussian process-based corrosion
growth modeling and its application in the reliability analysis for energy pipelines,
Frontiers of Structural and Civil Engineering, 7, 276-287.
[31] Rodr ́ıguez-Narciso, S. and Christen, J. A. (2016). Optimal sequential Bayesian
analysis for degradation tests. Lifetime Data Analysis, 22, 405-428.
[32] Ross, S. M. (2022). Simulation (Sixth Edition), Elsevier, New Yor
[33] Spiegelhalter, D. J., Best, N. G., Carlin, B. P., and Van Der Linde, A. (2002).
Bayesian measures of model complexity and fit, Journal of the Royal Statistical
Society: Series B (Statistical Methodology), 64, 583-639.
[34] Vacar, C., Giovannelli, J. F., and Roman, A. M. (2012). Bayesian texture model
selection by harmonic mean, 2012 19th IEEE International Conference on Image
Processing, 2533-2536.
[35] Wang, L., Jones, D. E., and Meng, X. L. (2016). Warp bridge sampling: The next
generation, arXiv preprint arXiv: 1609.07690
[36] Wang, H., Teng, K., and Zhou, Y. (2018). Design an optimal accelerated-stress
reliability acceptance test plan based on acceleration factor, IEEE Transactions on
Reliability, 67, 1008-1018.
[37] Wang, H and Xi, W. (2016). Acceleration factor constant principle and the applica-
tion under ADT. Quality and Reliability Engineering International, 32, 2591-2600.
[38] Wang, X. and Xu, D. (2010). An inverse Gaussian process model for degradation
data, Technometrics, 52, 188-197.
[39] Whitmore, G. A. (1995). Estimating degradation by a Wiener diffusion process
subject to measurement error, Lifetime Data Analysis, 1, 307-319.
[40] Ye, Z. S. and Chen, N. (2014). The inverse Gaussian process as a degradation
model, Technometrics, 56, 302-311.
[41] Yuan, R., Tang, M., Wang, H., and Li, H. (2019). A reliability analysis method of
accelerated performance degradation based on Bayesian strategy, IEEE Access, 7,
169047-169054.
[42] 古立丞 (2021) 逆高斯過程之完整貝氏衰變分析,國立中央大學碩士論文。
[43] 張孟筑 (2017) 應用累積暴露模式至單調過程之加速衰變模型,國立中央大學碩士
論文。
[44] 董奕賢 (2019) 累積暴露模式之單調加速衰變試驗,國立中央大學碩士論文。
指導教授 樊采虹(Tsai-Hung Fan) 審核日期 2023-7-18
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