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研究生:洪嘉妤
研究生(外文):Jia-Yu Hong
論文名稱:具ED過程之兩因子加速衰退試驗建模研究
論文名稱(外文):Modeling Two Factors Accelerated Degradation Testing Based on ED Process
指導教授:樊采虹樊采虹引用關係鄭順林鄭順林引用關係
指導教授(外文):Tsai-Hung FanShuen-Lin Jeng
學位類別:碩士
校院名稱:國立中央大學
系所名稱:統計研究所
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:2019
畢業學年度:107
語文別:中文
論文頁數:72
中文關鍵詞:加速衰退試驗兩因子交互作用隨機過程ED過程
外文關鍵詞:accelerated degradation testtwo-factor interaction termstochastic processED process
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產品的可靠度常用一因子的加速衰退試驗進行測試,並推論產品壽命。但可能影響產品壽命的不只一個因子,
因此本文考量了具ED過程之兩因子恆定應力加速衰退試驗(CSADT)的隨機過程模型,並使用數值方法推估產品失效壽命分佈。常見的三種隨機過程Wiener, Gamma, Inverse-Gaussian 過程都是Tweedie ED 過程的特例。
我們考慮兩因子試驗可能有交互作用影響,故交互作用項列入模型的考量。
我們使用兩組兩因子加速衰退試驗的真實資料,進行比較。考慮兩因子是否有交互作用、不同的加速模型,以及Wiener, Gamma, Inverse-Gaussian和ED 過程組合不同的隨機過程模型。主要結論為Tweedie ED process模型在資料上配適上優於其他模型。
Product's reliability is often obtained by an one-factor accelerated
degradation testing and then calculated by the inferred lifetime distribution of products.
However, there may be more than one factor that can affect the life of the product. This thesis considers stochastic process model of two-factor constant-stress accelerated degradation testing based on ED process. The numerical method is used to estimate the product's failure lifetime distribution. The three common stochastic processes: Wiener, Gamma and Inverse-Gaussian, are special cases of Tweedie ED process. We consider that the two-factor test may have an interaction effect and put the interaction term into the models. We used two sets of real two-factor accelerated degradation data to compare with the models by considering the interaction term, different accelerated forms and four stochastic processes. The main conclusion is that the Tweedie ED process model is better than others in model fitting.
摘要 i Abstract ii 目錄 iii 圖目錄 vii 表目錄 viii
第一章 緒論
1.1 研究動機.................................... 1
1.2 文獻探討 .................................... 2
1.3 研究方法 .................................... 4
1.4 本文架構 .................................... 5
2 第二章 加速衰退模型 6
2.1 隨機過程模型.................................. 6
2.1.1 物理加速模型.............................. 6
2.1.2 具維納過程之加速衰退模型...................... 9
2.1.3 具單調性質之加速衰退模型...................... 11
2.1.4 具ED過程之加速衰退模型...................... 13
2.2 概似函數與最大概似估計量.......................... 17
2.2.1 具維納過程之加速衰退模型參數估計................. 17
2.2.2 具伽碼過程之加速衰退模型參數估計................. 18
2.2.3 具逆高斯過程之加速衰退模型參數估計............... 19
2.2.4 具TweedieED過程之加速衰退模型參數估計. . . . . . . . . . . . 20
2.3產品壽命分佈與可靠度資訊......................... 20
2.3.1 具維納過程之加速衰退模型的產品失效壽命分佈 . . . . . . . . . . 21
2.3.2 產品壽命q分數推論 ........................ 24
3 第三章 實例分析 27
3.1 LED(Xiao) ................................... 27
3.2 LED(Liao).................................... 38
3.3 討論....................................... 47
3.3.1 LED(Xiao)............................... 47
3.3.2 LED(Liao) ............................... 51
4 第四章 結論與未來研究方向 54
A 附錄
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[3]Duan, F. and Wang, G. (2018).
Exponential-Dispersion Degradation Process Models With Random Effects and Covariates, IEEE Transactions on Reliability 67, 1128–1142.

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


[5]Huang, S. H. (2015). A empirical bayesian reliability analysis of linear degradation model, Master Thesis, Nation Central University.
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Liao, H. and Elsayed, A. (2006). Reliability inference for field conditions from accelerated degradation testing, Naval Research Logistics (NRL) 53, 576–587.
[10]Liu, Z. R. (2018). Bayesian goodness-of-fit tests for accelerated destructive degradation models, Master Thesis, Nation Central University.
[11]Meeker, W. Q. and Escobar, L. A. (1998). Statistical Methods for Reliability Data, John Wiley and Sons, New York.
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[13]
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[14]
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[15]Peng, C. Y. and Tseng, S. T. (2009). Mis-specification analysis of linear degradation models, IEEE Transactions on Reliability, 58, 444-455.

[16]
Peng, C. Y. (2015). Inverse Gaussian processes with random effects and explanatory variables for degradation data, Technometrics, 57, 100–111.

[17]
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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.
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Tseng, S. T. and Peng, C. Y. (2007). Stochastic diffusion modeling of degradation data, Journal of Data Science, 5, 315–333.
[20]
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Xiao, C. D., Liu, C.J., Liu, W. D. and others (2014). Reliability assessment of led lamps based on acceleration degradation test, Chinese journal of luminescence, 1143–1151.
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Ye, Z. S. and Chen, N. (2014). The inverse gaussian process as a degradation model. Technometrics, 56, 302–311.
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