混合型韋伯分配是可應用於存活分析與可靠度分析的重要統計分配。本論文主要在探討混合型韋伯分配在多重設限資料下，利用最大概似估計法做參數估計，且透過 PSO 演算法、擬牛頓法與 EM 演算法對概似函數進行優化求解。本研究藉由模擬的分析，比較三種演算法參數估計之結果，而我們可以得知利用PSO演算法求得之結果是優於其他兩種演算法。此外，再藉由實際案例來驗證結果是否與模擬結果為一致。

The mixture Weibull distributions can be applied to survival analysis and reliability analysis which is the field of statistical research. In this study we used the maximum likelihood estimation (MLE) to estimate the mixture of two Weibull parameters with multiple censored data via particle swarm optimization (PSO) algorithm, quasi-Newton method and expectation-maximization (EM) algorithm. We used the simulation study to compare the three algorithms. The simulation results showed that the PSO algorithm outperforms the quasi-Newton method and the EM algorithm. Two numerical examples are used to demonstrate the performance of our proposed method.

中文文獻
[1]江峰政，2005。有關EM法於具韋伯之設限資料其參數之估計，國立成功大學碩士論文。
[2]林竹青，2004。年齡縮減之不完全預防維護模型參數估計，私立朝陽科技大學碩士論文。
[3]詹鎬陽，2010。短尾對稱分配之詹森-內曼非顯著區域，私立逢甲大學碩士論文。

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