可回充式鋰離子電池 (rechargeable lithium-ion batteries) 在各類型的無線電子產品中扮演極為重要的電源供應角色，因此如何準確地預測鋰離子電池壽命，對於現今的製造商而言是十分重要的研究課題。文獻上曾有學者提出transformed step-stress accelerated trend renewal process (TSS_ATRP) 模型來分析鋰離子電池的循環式逐步應力衰變試驗資料，唯此方法的分析結果與學理知識似乎不太吻合。為了改善此缺點，本研究以multi-run SS_ATRP模型的概念作為基礎，提出cyclic SS_ATRP模型來針對鋰離子電池的循環式逐步應力衰變試驗資料進行分析。文中分別使用最小平方法 (OLS) 與最大概似估計法 (MLE) 來估計模型中的未知參數，進而推估鋰離子電池在正常使用條件下的壽命 (EOP)。同時亦利用模擬方法比較TSS_ATRP模型和cyclic SS_ATRP模型在估計電池EOP時的準確度，與決定此試驗之適當終止時間。總體而言，cyclic SS_ATRP模型可以改善TSS_ATRP模型的缺點，故在估計電池EOP的準確度也較高。此外由模擬試驗可以發現，若控制EOP的相對估計誤差 (\varepsilon) 為20%時，則此試驗之適當終止時間至少須超過150個充放電循環。

Rechargeable lithium-ion batteries play an extremely important role as power suppliers in various types of wireless electronic products. Therefore, accurately predicting the lifespan of lithium-ion batteries is a highly significant research topic for manufacturers today. In the literature, scholars have previously proposed the transformed step-stress accelerated trend renewal process (TSS_ATRP) model to analyze data from cyclic step-stress degradation tests of lithium-ion batteries. However, the results of this method seem to deviate from established scientific knowledge. To address this limitation, this study is based on the concept of the SS_ATRP model and presents the cyclic SS_ATRP model for analyzing data from cyclic step-stress degradation tests of lithium-ion batteries. The study uses both the Ordinary Least Squares (OLS) and Maximum Likelihood Estimation (MLE) methods to estimate the unknown parameters in the model and consequently assess the End of Performance (EOP) of the lithium-ion batteries under normal operating conditions. Additionally, simulation methods are utilized to compare the accuracy of the TSS_ATRP model and cyclic SS_ATRP model in estimating the EOP of the batteries and determining an appropriate termination time for the experiments. Overall, the cyclic SS_ATRP model improves upon the shortcomings of the TSS_ATRP model, leading to higher accuracy in estimating the battery's EOP. Additionally, the simulation experiments indicate that when the relative estimation error of controlling EOP (\varepsilon) is 20%, the appropriate termination time for this experiment should be at least 150 charging and discharging cycles.

第一章 緒論 1
1.1 前言 1
1.2 研究動機 1
1.3 研究架構 2
第二章 文獻探討與問題描述 4
2.1 文獻探討 4
2.1.1 TRP模型簡介 5
2.1.2 TRP模型在逐步應力資料上的應用 6
2.2 問題描述 8
第三章 循環式逐步應力衰變試驗之建模與分析 10
3.1 動機例子 10
3.2 循環式逐步應力衰變試驗的建模 12
3.2.1 以 \mathbit{N}(\mathbit{t}|\mathbit{Sl}) 描述 \mathbit{N}(\mathbit{t}|\mathbit{SS}) 15
3.2.2 \mathbit{N}(\mathbit{t}|\mathbit{Sl}) 之TRP建模分析 16
3.2.3 Cyclic SS_ATRP(F, \mathbit{\lambda}) 模型的統計推論工作 17
3.2.4 決定F分配及 \mathbit{\lambda}(\bullet) 之初步分析 19
3.2.5 模型未知參數的最大概似估計 22
3.2.6 Eq (3.7) 中 \mathbit{a}(\mathbit{Sl}),\mathbit{b}(\mathbit{Sl}),\mathbit{\sigma}(\mathbit{Sl}) 關係式之決定 23
3.2.7 模型的配適度分析 26
3.3 EOP 預測分析 27
第四章 方法比較及試驗終止時間之決定 32
4.1 方法比較 32
4.2 試驗終止時間之決定 33
第五章 結論與後續研究 36
附錄一 38
附錄二 39
附錄三 41
參考文獻 42

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