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| Title: | 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 |
| Authors: | 陳朝逸
Chen, Chao Yi |
| Contributors: | 陳麗霞
Chen, Li Shya
陳朝逸
Chen, Chao Yi |
| Keywords: | 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 |
| Date: | 2013 |
| Issue Date: | 2014-08-12 14:02:03 (UTC+8) |
| Abstract: | 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. |
| Reference: | 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.
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IEEE Transactions on Reliability, 29(2), 103-108.
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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.
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12.Venzon, D. J. and Moolgavkar, S. H. (1988). A method for computing profile-likelihood-based confidence intervals. Applied Statistics, 87-94.
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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 |
| Description: | 碩士
國立政治大學
統計研究所
101354025
102 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G1013540251 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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