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題名 簡單加速壽命試驗及型二混合設限之Weibull資料分析
Analysis for Weibull Data under Simple Step-Stress and Type II Hybrid Censoring作者 陳朝逸
Chen, Chao Yi貢獻者 陳麗霞
Chen, Li Shya
陳朝逸
Chen, Chao Yi關鍵詞 加速壽命試驗
型二混合設限
簡單加速試驗
累積暴露模型
Weibull分配
最大概似估計量的漸進信賴區間
基於概似比的漸進信賴區間
拔靴信賴區間
Accelerated life testing
type II hybrid censoring
simple step-stress testing
cumulative exposure model
Weibull distribution
asymptotic confidence interval
likelihood ratio-based confidence interval
bootstrap confidence interval日期 2013 上傳時間 12-八月-2014 14:02:03 (UTC+8) 摘要 本論文探討的是在簡單加速壽命試驗及型二混合設限下Weibull資料的估計問題。由於實驗單位在兩階段的應力水準不同，在累積暴露模型之假定下，解出最大概似估計值並求得觀察到的訊息矩陣。進而介紹各參數之最大概似估計量的漸進信賴區間、基於概似比的漸進信賴區間，以及三種拔靴信賴區間。在不同的樣本數、應力改變的時間及實驗預定的終止時間之下，利用蒙地卡羅法模擬計算各參數估計量的偏差和均方誤差等指標，以評估其與應力改變的時間及實驗預定終止的時間之關係；再對各參數的各種信賴區間分別計算覆蓋率以評估區間估計之表現。其中，最大概似估計量的漸進信賴區間不但計算時間短且覆蓋率之表現較佳。
In this thesis, the estimation problems for Weibull data under simple step-stress and type II hybrid censoring are considered. Due to different stress level undertaken by those experiment units surviving through the first stage, the maximum likelihood estimators (MLEs) of the parameters and the corresponding observed information matrix are derived under the cumulative exposure model. Then, asymptotic confidence intervals derived from the asymptotic distributions of the MLEs, likelihood ratio-based confidence intervals and three bootstrap confidence intervals are introduced. With different sample sizes, change-points for changing the stress-level, and preplanned stopping times, Monte-Carlo simulations are carried out and the average biases, mean squared errors, and other criterions are computed to discover the relations between these criterions and change-points and preplanned stopping times. Coverage rates for confidence intervals are also computed to evaluate their performances. Finally, the asymptotic confidence interval is recommended due to taking less computation time and achieving better coverage rate than other methods.參考文獻 1.Balakrishnan, N. and Kundu, D. (2013). Hybrid censoring: models, inferential results and applications. Computational Statistics & Data Analysis, 57(1), 166-209.2.Balakrishnan, N., Kundu, D. , Ng, H.K.T. and Kannan, N. (2007). Point and interval estimation for a simple step-stress model with Type-II censoring. Journal of Quality Technology, 39(1), 35-47.3.Balakrishnan, N. and Xie, Q. (2007a). Exact inference for a simple step-stress model with Type-I hybrid censored data from the exponential distribution. Journal of Statistical Planning and Inference, 137(11), 3268-3290.4.Balakrishnan, N. and Xie, Q. (2007b). Exact inference for a simple step-stress model with Type-II hybrid censored data from the exponential distribution. Journal of Statistical Planning and Inference, 137(8), 2543-2563.5.Banerjee, A. and Kundu, D. (2008). Inference based on type-II hybrid censored data from a Weibull distribution. IEEE Transactions on Reliability, 57(2), 369-378.6.Childs, A., Chandrasekar, B., Balakrishnan, N. and Kundu, D. (2003). Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution. Annals of the Institute of Statistical Mathematics, 55(2), 319-330.7.Epstein, B. (1954). Truncated life tests in the exponential case. The Annals of Mathematical Statistics, 25(3), 555-564.8.Nelson, W. (1980). Accelerated life testing-step-stress models and data analyses. IEEE Transactions on Reliability, 29(2), 103-108.9.Nelson,W.B. (1990). Accelerated Testing, Statistical Models, Test Plans and Data Analysis, Wiley, New York, NY., .10.Kateri, M. and Balakrishnan, N. (2008). Inference for a simple step-stress model with Type-II censoring, and Weibull distributed lifetimes. IEEE Transactions on Reliability, 57(4), 616-626.11.Sinha, S. K. (1986). Reliability and life testing. John Wiley & Sons, Inc.12.Venzon, D. J. and Moolgavkar, S. H. (1988). A method for computing profile-likelihood-based confidence intervals. Applied Statistics, 87-94.13.Xiong, C. (1998). Inferences on a simple step-stress model with type-II censored exponential data. IEEE Transactions on Reliability, 47(2), 142-146.14.洪紹媛(2013)，韋伯型I混合設限資料之加速壽命試驗的推論，淡江大學數學學系碩士班碩士論文 描述 碩士
國立政治大學
統計研究所
101354025
102資料來源 http://thesis.lib.nccu.edu.tw/record/#G1013540251 資料類型 thesis dc.contributor.advisor 陳麗霞 zh_TW dc.contributor.advisor Chen, Li Shya en_US dc.contributor.author (作者) 陳朝逸 zh_TW dc.contributor.author (作者) Chen, Chao Yi en_US dc.creator (作者) 陳朝逸 zh_TW dc.creator (作者) Chen, Chao Yi en_US dc.date (日期) 2013 en_US dc.date.accessioned 12-八月-2014 14:02:03 (UTC+8) - dc.date.available 12-八月-2014 14:02:03 (UTC+8) - dc.date.issued (上傳時間) 12-八月-2014 14:02:03 (UTC+8) - dc.identifier (其他 識別碼) G1013540251 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/68529 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計研究所 zh_TW dc.description (描述) 101354025 zh_TW dc.description (描述) 102 zh_TW dc.description.abstract (摘要) 本論文探討的是在簡單加速壽命試驗及型二混合設限下Weibull資料的估計問題。由於實驗單位在兩階段的應力水準不同，在累積暴露模型之假定下，解出最大概似估計值並求得觀察到的訊息矩陣。進而介紹各參數之最大概似估計量的漸進信賴區間、基於概似比的漸進信賴區間，以及三種拔靴信賴區間。在不同的樣本數、應力改變的時間及實驗預定的終止時間之下，利用蒙地卡羅法模擬計算各參數估計量的偏差和均方誤差等指標，以評估其與應力改變的時間及實驗預定終止的時間之關係；再對各參數的各種信賴區間分別計算覆蓋率以評估區間估計之表現。其中，最大概似估計量的漸進信賴區間不但計算時間短且覆蓋率之表現較佳。 zh_TW dc.description.abstract (摘要) In this thesis, the estimation problems for Weibull data under simple step-stress and type II hybrid censoring are considered. Due to different stress level undertaken by those experiment units surviving through the first stage, the maximum likelihood estimators (MLEs) of the parameters and the corresponding observed information matrix are derived under the cumulative exposure model. Then, asymptotic confidence intervals derived from the asymptotic distributions of the MLEs, likelihood ratio-based confidence intervals and three bootstrap confidence intervals are introduced. With different sample sizes, change-points for changing the stress-level, and preplanned stopping times, Monte-Carlo simulations are carried out and the average biases, mean squared errors, and other criterions are computed to discover the relations between these criterions and change-points and preplanned stopping times. Coverage rates for confidence intervals are also computed to evaluate their performances. Finally, the asymptotic confidence interval is recommended due to taking less computation time and achieving better coverage rate than other methods. en_US dc.description.tableofcontents 第一章 緒論 11.1 研究背景、動機與目的 11.2 論文結構 2第二章 文獻探討 3第三章 模型簡介及估計 63.1 模型假設 63.2 最大概似估計法 93.3 參數的區間估計 113.3.1 最大概似估計量的漸進信賴區間 113.3.2 基於概似比的漸進信賴區間 113.3.3 拔靴信賴區間 123.3.3.1 百分位數拔靴信賴區間 143.3.3.2 調整百分位數拔靴信賴區間 153.3.3.3 拔靴t信賴區間 16第四章 模擬結果 184.1 點估計之評估 184.2 區間估計之評估 19第五章 結論與建議 26參考文獻 28附錄 30 zh_TW dc.format.extent 725315 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G1013540251 en_US dc.subject (關鍵詞) 加速壽命試驗 zh_TW dc.subject (關鍵詞) 型二混合設限 zh_TW dc.subject (關鍵詞) 簡單加速試驗 zh_TW dc.subject (關鍵詞) 累積暴露模型 zh_TW dc.subject (關鍵詞) Weibull分配 zh_TW dc.subject (關鍵詞) 最大概似估計量的漸進信賴區間 zh_TW dc.subject (關鍵詞) 基於概似比的漸進信賴區間 zh_TW dc.subject (關鍵詞) 拔靴信賴區間 zh_TW dc.subject (關鍵詞) Accelerated life testing en_US dc.subject (關鍵詞) type II hybrid censoring en_US dc.subject (關鍵詞) simple step-stress testing en_US dc.subject (關鍵詞) cumulative exposure model en_US dc.subject (關鍵詞) Weibull distribution en_US dc.subject (關鍵詞) asymptotic confidence interval en_US dc.subject (關鍵詞) likelihood ratio-based confidence interval en_US dc.subject (關鍵詞) bootstrap confidence interval en_US dc.title (題名) 簡單加速壽命試驗及型二混合設限之Weibull資料分析 zh_TW dc.title (題名) Analysis for Weibull Data under Simple Step-Stress and Type II Hybrid Censoring en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 1.Balakrishnan, N. and Kundu, D. (2013). Hybrid censoring: models, inferential results and applications. Computational Statistics & Data Analysis, 57(1), 166-209.2.Balakrishnan, N., Kundu, D. , Ng, H.K.T. and Kannan, N. (2007). Point and interval estimation for a simple step-stress model with Type-II censoring. Journal of Quality Technology, 39(1), 35-47.3.Balakrishnan, N. and Xie, Q. (2007a). Exact inference for a simple step-stress model with Type-I hybrid censored data from the exponential distribution. Journal of Statistical Planning and Inference, 137(11), 3268-3290.4.Balakrishnan, N. and Xie, Q. (2007b). Exact inference for a simple step-stress model with Type-II hybrid censored data from the exponential distribution. Journal of Statistical Planning and Inference, 137(8), 2543-2563.5.Banerjee, A. and Kundu, D. (2008). Inference based on type-II hybrid censored data from a Weibull distribution. IEEE Transactions on Reliability, 57(2), 369-378.6.Childs, A., Chandrasekar, B., Balakrishnan, N. and Kundu, D. (2003). Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution. Annals of the Institute of Statistical Mathematics, 55(2), 319-330.7.Epstein, B. (1954). Truncated life tests in the exponential case. The Annals of Mathematical Statistics, 25(3), 555-564.8.Nelson, W. (1980). Accelerated life testing-step-stress models and data analyses. IEEE Transactions on Reliability, 29(2), 103-108.9.Nelson,W.B. (1990). Accelerated Testing, Statistical Models, Test Plans and Data Analysis, Wiley, New York, NY., .10.Kateri, M. and Balakrishnan, N. (2008). Inference for a simple step-stress model with Type-II censoring, and Weibull distributed lifetimes. IEEE Transactions on Reliability, 57(4), 616-626.11.Sinha, S. K. (1986). Reliability and life testing. John Wiley & Sons, Inc.12.Venzon, D. J. and Moolgavkar, S. H. (1988). A method for computing profile-likelihood-based confidence intervals. Applied Statistics, 87-94.13.Xiong, C. (1998). Inferences on a simple step-stress model with type-II censored exponential data. IEEE Transactions on Reliability, 47(2), 142-146.14.洪紹媛(2013)，韋伯型I混合設限資料之加速壽命試驗的推論，淡江大學數學學系碩士班碩士論文 zh_TW
