隨著可攜式電子產品的普及，作為電源供應角色的鋰電池成為不可或缺的一環。隨科技的發達，故鋰電池擁有高壽命的特性，則如何在有限的測試時間內，準確地估計出鋰電池的壽命，是電池製造商所面臨的重要課題。吳璟賢 (2016) 使用固定效應的TRP模型來推估鋰電池壽命，唯電池與電池之間確實存在有 unit-to-unit 變異，因此應將電池之間的差異性考慮進模型中，故採用隨機效應 TRP模型來分析電池壽命較為適合。本研究在考量TRP模型的可辨識性問題下，首先提出兩種隨機效應的TRP模型。其次，分別在此兩種模型下探討模型中未知參數的估計問題及推導EOP的預測公式，並以吳璟賢 (2016) 的實例來說明固定效應與隨機效應TRP模型的EOP預測值之差異。最後，本文亦探討如何決定電池之樣本數及實驗週期數，方可獲得較為精確的電池壽命估計值。從模擬分析可發現，當 σ_0=1.0896 ，且實驗週期數超過217週期時，方可控制電池EOP之預測值的relative bias (RB) 小於1% 且其root of relative variability (RRV) 小於2。

Rechargeable batteries are the critical components for information and communication technology (ICT) products. Therefore, how to assess (or predict) the lifetime information of rechargeable batteries is an important and challenging issue to their manufacturers. Recently, a fixed effect trend renewal process (TRP) model has been proposed in literature to characterize the capacity ratio (CR) of rechargeable battery, and used this model to predict end of performance (EOP). On practical applications, this approach may not be appropriate due to unit-to-unit variation. In this thesis, we proposed a random effect TRP model to overcome this difficulty. Specifically, 2 different versions of random effect TRP model are proposed. The MLEs for the unknown parameters and the approximate formulas for EOP are derived. In addition, the EOP prediction performance of fixed effect and random effect are compared. Finally, we also use a simulation study to address the optimal design of random effect TRP model. The results demonstrate that under σ_0=1.0896, the test cycle times (n) are larger than 217 cycles, respectively to ensure that the relative bias (RB) ≤ 1%, and root of relative variability (RRV) ≤ 2.

目錄
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 1
1.3 研究架構 2
第二章 鋰電池資料簡介與文獻探討 3
2.1 資料簡介與目的 3
2.1.1 鋰電池資料轉換成重現資料 (recurrence-event data) 4
2.2 相關文獻探討 5
2.2.1 電池資料的TRP模型之參數估計 6
2.2.2 TRP模型之預測分析 9
2.3 本研究之問題描述 10
第三章 隨機效應TRP模型之建構與分析 13
3.1 隨機效應TRP簡介 13
3.2在case 1下的隨機效應 TRP模型之建構 13
3.2.1模型參數估計 14
3.2.2 EOP公式 15
3.2.3電池壽命資料分析 16
3.3 在case 2下的隨機效應 TRP模型之建構 17
3.3.1模型參數估計 17
3.3.2 EOP公式 18
3.3.3電池壽命分析 19
3.4 固定效應TRP模型與隨機效應TRP模型之比較 19
第四章 電池實驗配置之模擬分析 22
4.1 生成電池衰變資料 22
4.2 EOP及其MSE的理論值之近似值 23
4.3 電池實驗設計問題 24
4.4模擬結果分析 26
第五章 結論 35
附錄：公式 (3.11) 之證明 36
參考文獻 38

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