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中文論文名稱 型 I 混合設限於定應力加速壽命試驗之研究
英文論文名稱 On Constant Stress Accelerated Life Tests Terminated by Type-I Hybrid Censoring at One of the Stress Levels
校院名稱 淡江大學
系所名稱(中) 數學學系碩士班
系所名稱(英) Department of Mathematics
學年度 102
學期 2
出版年 103
研究生中文姓名 許耀宇
研究生英文姓名 Yao-Yu Hsu
學號 601190241
學位類別 碩士
語文別 英文
第二語文別 中文
口試日期 2014-06-24
論文頁數 17頁
口試委員 指導教授-林千代
委員-蔡志群
委員-彭健育
中文關鍵字 期望費雪信息矩陣  對數線性尺度應力  最大概似估計法  粒子群最佳化 
英文關鍵字 Expected Fisher information matrix  log-linear scale stress relationship  maximum likelihood method  particle swarm optimization 
學科別分類 學科別自然科學數學
中文摘要 本論文討論型 I混合設限於某一定應力的加速壽命試驗。所使用的模型是具有一般性的對數位置尺度壽命分佈,其平均壽命和應力的關係是呈現一個線性關係, 而尺度變數是一個常數。我們利用最大概似法求得參數估計, 並且推導出期望費雪信息矩陣, 進而求得參數最大概似估計的近似變異數。此外, 我們利用模擬計算觀測費雪信息矩陣, 並且發現其值與所推導的期望費雪信息矩陣是一致。
最後,在成本限制條件下,我們討論最佳化設計。亦即,在無加應力情況下,我們想找出最適當的樣本個數、失敗個數、以及檢測時間的配置使得所估計的第p個百分位數的一般訊息為最大。
英文摘要 In this paper, we consider a constant stress accelerated life tests terminated by a hybrid Type-I censoring regime at one of the stress levels. A model based on a general log-location-scale lifetime distribution with mean life which is a linear function of stress, along with constant scale, is discussed. The exact expectations associated with the likelihood function for the asymptotically valid variances of maximum likelihood estimates of model parameters are derived. The agreement with observed counterparts for finite samples in simulation study is also assessed. Finally, under the constraint that the total experimental cost does not exceed a pre-specified budget, the design yields better estimate of 100p-th percentile at normal operating condition is obtained.
論文目次 1 Introduction 1
2 Assumptions and Model Description 2
3 Maximum Likelihood Estimation 3
4 Particle Swarm Optimization 5
5 Simulation Study 7
6 Optimal Test Plan 7
7 CONCLUDING REMARKS 10
Appendix 14
References 16
參考文獻 Bagdonavicius, V. and Nikulin, M. (2002). Accelerated Life Models: Modeling and Statistical Analysis. Chapman & Hall/CRC, Boca Raton, Florida.

Bai, Q. (2010). Analysis of Particle Swarm Optimization Algorithm. Computer and Information Science, Vol. 3, No. 1, 180–184.

Bansal, J. C., Singh, P. K., Saraswat, M., Verma, A., Jadon, S. S. and Abraham. A. (2011). Inertia weight strategies in particle swarm optimization. Third World Congress on Nature and Biologically Inspired Computing, 640-647.

Balakrishnan, N. (2009). A synthesis of exact inferential results for exponential step-stress models and associated optimal accelerated life-tests. Metrika 69, 351–396.

Balakrishnan, N. and Kundu, D. (2013). Hybrid censoring: models, inferential results and applications. Computational Statistics & Data Analysis 57, 166–209.

Bergh, F. V. D. and Engelbrecht, A. P. (2006). A study of particle swarm optimization particle trajectories. Information Sciences 176, 937–971.

Dube, S., Pradhan, B. and Kundu, D. (2011). Parameter estimation of the hybrid censored log-normal distribution. Journal of Statistical Computation and Simulation 81, 275–
287.

Gouno, E. and Balakrishnan, N. (2001). Step-stress accelerated life test. In Handbook of Statistics 20: Advances in Reliability (Eds., N. Balakrishnan and C. R. Rao), 623–639, North-Holland, Amsterdam.

Kennedy, J. and Eberhart, R. (1995). Particle swarm ptimization. Proceedings of IEEE International Conference on Neural Networks IV, 1942–1948.

Lin, C. T., Chou, C. C. and Balakrishnan, N. (2012a). Planning step-stress test plans under Type-I censoring for the log-location-scale case. Journal of Statistical Computation and Simulation 83, 1852–1867.

Lin, C. T., Chou, C. C. and Balakrishnan, N. (2012b). Planning step-stress test under Type-I censoring for the exponential case. Journal of Statistical Computation and
Simulation. online first.

Ma, H. and Meeker, W. Q. (2008). Optimum step-stress accelerated life test plans for loglocation-scale distributions. Naval Research Logistics 55, 551–562.

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

Nelson, W. B. (1990). Accelerated Testing: Statistical Models, Test Plans, and Data Analysis. John Wiley & Sons, New York.

Nelson, W. B. (2005a). A bibliography of accelerated test plans. IEEE Transactions on Reliability 54, 194–197.

Nelson, W. B. (2005b). A bibliography of accelerated test plans, Part II–references. IEEE Transactions on Reliability 54, 370–373.

Nelson, W. B. and Meeker, W. Q. (1978). Theory for optimum accelerated censored life tests for Weibull and extreme value distributions. Technometrics 20, 171–177.

Shi, Y. H. and Eberhart, R. C. (1998). A modified particle swam optimizer. IEEE Word Congress on Computational Intelligence, 69–73.

Shi, Y. H. and Eberhart, R. C. (1999). Empirical study of particle swarm optimization. Proceedings of the IEEE International Conference on Evolutionary Computation, 1945–1950, Washington, DC, USA.

Tang, L. C. (2003). Multiple-steps step-stress accelerated life test. In Handbook of Reliability Engineering (Ed., H. Pham), 441–455, Springer, London.

Watkins, A. J. and John, A. M. (2008). On constant stress accelerated life tests terminated by Type II censoring at one of the stress levels. Journal of Statistical Planning and Inference 138, 768–786.

Xin, J., Chen, G. and Hai, Y. (2009). A particle swarm optimizer with multistage linearlydecreasing inertia weight. Proceedings of the International Joint Conference on Computational Sciences and Optimization (CSO ’09), Sanya, China, April.
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