隨著行動電子產品 (如筆電、手機等) 的迅速發展，鋰電池 (lithium-ion battery) 在此類電子產品皆扮演極為重要的電源供應角色。因此如何精確地推估鋰電池的壽命及探討其最適試驗配置是製造商極為重要之研究課題。本研究首先將電池從充電到放電之回充系統視為重現事件 (recurrent event)，同時由於電池的性能會隨著使用次數的增加而逐漸下降，故本文採用Lindqvist, et al. (2003) 提出的trend renewal process (TRP) 模型來探討電池壽命之相關推論問題。具體而言，本研究先建構出TRP模型之概似函數 (Likelihood function)，並推導出TRP模型中未知參數的最大概似估計量 (MLE)。最後，配合 BAN Property 及Delta Method可獲得電池平均壽命之點估計及其區間估計。除此之外，本研究亦探討如何決定受試電池之最適樣本數，及其最適實驗測試週期數，方可在給定的試驗成本限制下，獲得電池平均壽命較精確的估計值。

Rechargeable batteries are critical components for the performance of portable electronics and electric vehicles. The long term health performance of rechargeable batteries is characterized by state of health which can be quantified by end of performance (EoP). Focusing on EoP prediction, this thesis first proposed a trend renewal process (TRP) model to address this decision problem. Specifically, we derive an approximate formula for EoP and derive its 95% confidence interval. The proposed model is also applied to analyze a rechargeable battery dataset. Finally, we also use a simulation study to address the issue of the optimal design of TRP model, which includes the determinations of the test samples (units) and its corresponding measurement times. The results demonstrate that the prediction performance of the proposed procedure is very robust even when the process parameters in TRP model are not precisely estimated.

第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 2
1.3 研究架構 3
第二章 鋰電池資料簡介與文獻探討 4
2.1 資料簡介與目的 4
2.2 相關文獻探討 6
2.3 鋰電池資料轉換成重現資料 (recurrent-event data) 8
第三章 TRP建模與資料分析 10
3.1 Trend Renewal Process (TRP) 簡介 10
3.2問題描述 12
3.3 TRP建模及參數估計 14
3.4 End of performance (EoP) 之估計 18
3.5 End of performance (EoP) 信賴區間之建構 22
第四章 最適實驗配置問題 24
4.1生成電池衰變資料 26
4.2最適試驗設計問題 27
4.3敏感度分析 31
第五章 結論 35
附錄 37
附錄一 37
附錄二: 39
參考文獻 40

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