累積暴露模式之單調加速衰變試驗

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：14

、訪客IP：3.146.221.204

姓名

董奕賢(Yi-Shian Dong) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

累積暴露模式之單調加速衰變試驗
(Monotonic Accelerated Degradation Tests With Cumulative Exposure Law)

相關論文

★ 串聯系統加速壽命試驗之最佳妥協設計	★ 加速破壞性衰變模型之貝氏適合度檢定
★ 學生-t 過程之破壞性衰變分析

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

至系統瀏覽論文 ( 永不開放)

摘要(中)

加速衰變試驗已廣泛應用於評估高可靠度產品在正常使用條件下的壽命資訊。然而在加速衰變模型與環境變數間的關聯性中，相關的物理化學機制及其統計意義卻較少被探討。因此本文以 Tweedie 過程作為加速衰變模型之基礎，結合物理/化學機制之累積暴露模式，從理論上得到模型中參數與環境變數的關聯性，並賦予其統計/工程意義；此外在加速因子不變原則下，藉由泛函等式推導出隨機過程中時間項函數之充分必要條件，提供非線性時間函數的物理意義。最後以三組實例分析呈現在不同參數與應力關係下，Tweedie 加速衰變模型的優點、壽命推估的精準性、相對應的逐點信賴區間及模型的適合性等。

摘要(英)

Accelerated degradation tests (ADTs) are widely used to assess lifetime information under normal use condition for high-reliability products. However, the physical/chemical
mechanism as well as the statistical/engineering interpretation between the ADT model with the environmental variables is rarely discussed. In this thesis, we consider the ADT models based on Tweedie process by adopting the assumption of cumulative exposure law, due to the physical/chemical mechanism, to derive the relationship between model parameters and environment variables.Moreover, from the functional equation with the
assumption of acceleration factor constant principle, we also obtain the explicit functional form for the time structure of the stochastic process, which gives the physical interpretation of the non-linear function of time. Finally, three datasets are analyzed to show the advantages of the proposed degradation models and the accuracy of product’s lifetime inference, including pointwise confidence intervals and goodness-of-fit tests, under various relationships between model parameters and environment variables.

關鍵字(中)

★ Hougaard 過程
★ 伽瑪過程
★ 逆高斯過程
★ 拔靴法
★ 模型選擇

關鍵字(英)

★ Hougaard process
★ gamma process
★ inverse Gaussian process
★ bootstrap
★ model selection

論文目次

摘要....................................................i
Abstract...............................................ii
目錄..................................................iii
圖目錄..................................................v
表目錄.................................................vi
1 第一章緒論...........................................1
1.1 背景介紹與研究動機..................................1
1.2 文獻回顧............................................2
1.3 研究方法............................................4
1.4 本文架構............................................5
2 第二章累積暴露模式下單調連續過程參數與應力之關聯 ....6
2.1 累積暴露模式與加速因子不變原則......................6
2.2 Tweedie 過程........................................8
2.3 單調連續過程參數與環境變數之關聯...................11
2.3.1 具隨機效應之伽瑪過程.............................14
2.3.2 具隨機效應之逆高斯過程...........................17
2.4 Tweedie 過程之非線性結構...........................20
3 第三章實例分析......................................22
3.1 加速衰變模型之分析方法.............................22
3.1.1 參數估計之最大概似法.............................22
3.1.2 平均失效時間及分位數壽命.........................23
3.1.3 加速衰變模型之適合度檢定.........................23
3.1.4 拔靴法信賴區間...................................24
3.1.5 加速應力結構.....................................24
3.2 接觸電阻資料.......................................25
3.3 LED 資料...........................................29
3.4 壓力鬆弛資料.......................................34
4 第四章結論與未來研究................................39
參考文獻...............................................40

參考文獻

[1] 張孟筑 (2017). 應用累積暴露模式至單調過程之加速衰變模型，國立中央大學統計研究所，碩士論文。

[2] Bar-Lev, S. K. and Enis, P. (1986). Reproducibility and natural exponential families with power variance functions, The Annals of Statistics, 14, 1507–1522.

[3] Castillo, E., Iglesias, A. and Ruíz-Cobo, R. (2005). Functional equations in applied sciences, Amsterdam: Elsevier.

[4] Carey, M. B. and Koenig, R. H. (1991). Reliability assessment based on accelerated degradation: a case study, IEEE Transactions on Reliability, 40, 499–506.

[5] Dunn, P. K. and Smyth, G. K. (2005). Series evaluation of Tweedie exponential dispersion model densities, Statistics and Computing, 15, 267–280.

[6] Dunn, P. K. and Smyth, G. K. (2008). Evaluation of Tweedie exponential dispersion model densities by Fourier inversion, Statistics and Computing, 18, 73–86.

[7] Feinberg, A. A. and Widom, A. (1996). Connecting parametric aging to catastrophic failure through thermodynamics, IEEE Transactions on Reliability, 45, 28–33.

[8] Hougaard, P. (1986). Survival models for heterogeneous populations derived from stable distributions, Biometrika, 73, 387–396.

[9] Jiang, P., Wang, B. and Wu, F. (2019). Inference for constant-stress accelerated degradation test based on gamma process, Applied Mathematical Modelling, 67, 123–134.

[10] Jørgensen, B. (1997). The theory of dispersion models, London: Chapman & Hall.

[11] Küchler, U. and Sørensen, M. (1997). Exponential Families of Stochastic Processes, New York: Springer.

[12] 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.

[13] Liao, C. M. and Tseng, S. T. (2006). Optimal design for step-stress accelerated degradation tests, IEEE Transactions on Reliability, 55, 59–66.

[14] Liao, H. and Elsayed, E. A. (2006). Reliability inference for field conditions from accelerated degradation testing, Naval Research Logistics, 53, 576–587.

[15] Lim, H. and Yum, B. J. (2011). Optimal design of accelerated degradation tests based on Wiener process models, Journal of Applied Statistics, 38, 309–325.

[16] Ling, M. H., Tsui, K. L., and Balakrishnan, N. (2015). Accelerated degradation analysis for the quality of a system based on the gamma process, IEEE Transactions
on Reliability, 64, 463–472.

[17] Lu, C. J. and Meeker, W. Q. (1993). Using degradation measures to estimate a time-to-failure distribution, Technometrics, 35, 161–174.

[18] Meeker, W. Q. and Escobar, L. A. (1998). Statistical Methods for Reliability Data, New York: John Wiley & Sons.

[19] Nelson, W. (1980). Accelerated life testing step-stress models and data analyses, IEEE Transactions on Reliability, 29, 103–108.

[20] Nelson, W. (1981). Analysis of performance-degradation data from accelerated tests, IEEE Transactions on Reliability, 30, 149–55.

[21] Pan, Z. and Balakrishnan, N. (2010). Multiple-steps step-stress accelerated degradation modeling based on Wiener and gamma processes, Communications in Statistics
- Simulation and Computation, 39, 1384–1402.

[22] Park, C. and Padgett, W. J. (2005). Accelerated degradation models for failure based on geometric Brownian motion and gamma processes, Lifetime Data Analysis, 11, 511–527.

[23] Park, C. and Padgett, W. J. (2006). Stochastic degradation models with several accelerating variables, IEEE Transactions on Reliability, 55, 379–390.

[24] Peng, C. Y. (2015). Inverse Gaussian processes with random effects and explanatory variables for degradation data, Technometrics, 57, 100–111.

[25] Pieruschka, E. (1961). Relation between lifetime distribution and the stress level causing failures, LMSD-800440, Lockhead Missiles and Space Division, Sunnyvale.

[26] Prasad, M., Gopika, V., Sridharan, A., Parida, S. and Gaikwad, A. J. (2018). Hougaard process stochastic model to predict wall thickness in flow accelerated corrosion, Annals of Nuclear Energy, 117, 247–258.

[27] Ting Lee, M. L. and Whitmore, G. A. (1993). Stochastic processes directed by randomized time, Journal of Applied Probability, 30, 302–314.

[28] Tsai, C. C., Tseng, S. T. and Balakrishnan, N. (2012). Optimal design for degradation tests based on gamma processes with random effects, IEEE Transactions on Reliability, 61, 604–613.

[29] Tseng, S. T., Balakrishnan, N. and Tsai, C. C. (2009). Optimal step-stress accelerated degradation test plan for gamma degradation processes, IEEE Transactions on Reliability, 58, 611–618.

[30] Tseng, S. T. and Lee, I. C. (2016). Optimum allocation rule for accelerated degradation tests with a class of exponential-dispersion degradation models, Technometrics, 58, 244–254.

[31] Tweedie, M. C. K. (1984). An index which distinguishes between some important exponential families, Statistics: applications and new directions. Proceedings of the indian statistical institute golden jubilee international conference (Eds. J. K. Ghosh and J. Roy), 594–604.

[32] Vinogradov, V. (2007). On infinitely divisible exponential dispersion model related to Poisson-exponential distribution, Communications in Statistics–Theory and
Methods, 36, 253–263.

[33] 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.

[34] Wang, H., Wang, G. and Duan, F. (2016). Planning of step-stress accelerated degradation test based on the inverse Gaussian process, Reliability Engineering and System Safety, 154, 97–105.

[35] Wang, H., Zhao, Y., Ma, X. and Wang, H. (2016). Optimal design of constant-stress accelerated degradation tests using the M-optimality criterion, Reliability Engineering and System Safety, 164, 45–54.

[36] Wang, H. and Xi, W. (2016). Acceleration factor constant principle and the application under ADT, Quality and Reliability Engineering International, 32, 2591–2600.

[37] Wang, X. (2009). Nonparametric estimation of the shape function in a gamma process for degradation data, The Canadian Journal of Statistics, 37, 102–118.

[38] Whitmore, G. A. and Schenkelberg, F. (1997). Modeling accelerated degradation data using Wiener diffusion with a time scale transformation, Lifetime Data Analysis, 3, 27–45.

[39] Yang, G. B. (2007). Life cycle engineering, New York: John Wiley & Sons.

[40] Ye, Z., Chen, L., Tang, L. and Xie, M. (2014). Accelerated degradation test planning using the inverse Gaussian process, IEEE Transactions on Reliability, 63, 750–763.

[41] Yurkowski, W., Schafer, R. E. and Finkelstein, J. M. (1967). Accelerated testing technology, RADC-TR-67-420, Griﬀiss Air Force Base, New York.

[42] Zhou, S. and Xu, A. (2019+). Exponential dispersion process for degradation analysis, IEEE Transactions on Reliability, doi:10.1109/TR.2019.2895352.

指導教授

樊采虹彭健育(Tsai-Hung Fan Chien-Yu Peng)

審核日期

2019-6-25

推文