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標題: 使用未分類資料估計遮蔽系統的元件平均壽命
Estimation of component mean lifetimes of a masked system using unclassified system life data
作者: 許莉敏
Hsu, Li-Min
關鍵字: masked system;遮蔽系統;Weibull distribution;maximum likelihood estimation;stochastic approximation;韋伯分佈;最大概似估計;隨機近似方法
出版社: 應用數學系所
引用: [1] S.C. Chang, Classification on Quality Control Using Unsupervised Learning, doctoral dissertation, National ChungHsing University, 2004. [2] S.C. Chang, T. F. Li, Estimation of Component Mean Lifetimes of A Masked System Using Unclassified System Life Data, Applied Mathematics and Computation, 169 (2) 797-805, 2005. [3] B. J. Flehinger, B. Reiser, E. Yashchin, Parametric Modeling for Survival with Competing Risks and Masked Failure Causes, 8 (2) 177-203, 2002. [4] K. Fukunaga, Introduction to Statistical Pattern Recognition, Academic Press, Boston, 1990. [5] R.L. Kashyap, C.C. Blayton, K.S. Fu, Stochastic Approximation, in: J.M. Mendel, K.S. Fu (Eds.), Adaption, Learning and Pattern Recognition Systems: Theory and Applications, Academic, New York, 1970. [6] S. Kullback, Information Theory and Statistics, Peter Smith, Gloucester, Mass, 1978. [7] L. Kuo, T. Y. Yang, Bayesian Reliability Modeling for Masked System Lifetime Data, Statistics and Probability Lettersm, 47 (3) 229-241, 2000. [8] T. L. Lai, Stochastic Approximation, Technical Report number 2002-31, 2002. [9] H. M. Moustafa, The efficiency of a nonlinear discriminant function based on unclassified initial samples from a mixture of two Weibull populations, Journal of Statistical Computation and Simulation, 75 (1) 65-73, 2005. [10] C. Mukhopadhyay, Maximum likelihood analysis of masked series system lifetime data, Journal of statistical planning and inference, 136, 803-838, 2006. [11] H. Robbins. S. Monro, A Stochastic Approximation Method, The Annals of Mathematical Statistics, 22 (3) 400-407, 1951.
隨機近似方法(stochastic approximation)是一個遞迴式的演算方法,在隨機的環境下作參數估計。這個方法在最佳化、控制及信號處理的相關研究上,已經成為很重要的議題。在一般的情況下,隨機近似方法的收斂效果是受到肯定的。
本論文使用隨機近似方法去逼近遮蔽系統(masked system)中重要元件平均壽命的真實值。所謂的遮蔽系統,是指該系統基於某些因素(譬如經費或醫療診斷的限制)不能將其拆解,使得我們無法確定是哪一個元件導致系統失效,只能獲得系統的壽命資料。本論文假設遮蔽系統的元件壽命長度分佈情形符合韋伯分佈(Weibull distribution),在考慮一個重要元件失效會導致整個系統失效的情況下,使用未分類的系統壽命資料來估計元件的平均壽命。實驗結果說明本論文的方法確實可以逼近遮蔽系統元件平均壽命的真實值。

Stochastic approximation which is used for parameter estimation is an iterative algorithm for random environments. It has become an important and vibrant subject in optimization, control and signal processing. In general, stochastic approximation is guaranteed to converge.
In this paper, we use a stochastic approximation to calculate and approximate to the true values of mean lifetimes which are the important components of a masked system. Because of cost and diagnostic, a masked system can not be decomposed. And the exact component which causes the system fail is unknown. We suppose that if one of the components fails, the whole system fails. And we also suppose that the distributions of the lifetimes for each component are Weibull distribution. The objective is to estimate the components mean lifetimes by using the unclassified life data. The experimental results show that the proposed method can approach the true values of the lifetimes for each component.
其他識別: U0005-2706200620303500
Appears in Collections:應用數學系所

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