科技進步日新月異，現代的科技產品展現了較高的可靠度，這使得在給定的試驗時間內觀察到試驗
樣品的失效資料變得相對困難。為了克服此問題，可將試驗樣品置於較高的環境壓力下，使其加速
衰變過程，從而縮短產品的驗收時間，此種方法稱為加速應力驗收試驗 (accelerated-stress 
acceptance test)。本篇文章以一組晶片電阻器的衰變數據為例，運用半參數方法建構出 B 樣條衰變
模型，用以描述電阻器在不同應力下，其電阻值相對變化率的衰變路徑，以預估不同應力下的最佳
加速應力驗收時間。同時，在給定的信心水準下，使用拔靴法 (bootstrap method) 求得最佳加速壓
力驗收時間的信賴區間。此外，本文亦探討當錯誤使用有母數衰變模型時，對於最佳加速應力驗收
時間推估的精準度影響，並與本文所提的方法進行比較。

Technological advancements are rapid and continuous, resulting in modern tech products 
that exhibit higher reliability. This made it relatively difficult to observe failure data of test 
samples within the reasonable experimental time. To address this issue, test samples can be
subjected to higher environmental stresses to accelerate the degradation process, thereby 
shortening the acceptance time of the products. This method is known as accelerated-stress 
acceptance test. Motivated by degradation data of the resistors, a semi-parametric with Bspline method is utilized to establish its degradation model that describes the degradation 
path for the relative changes of resistance values under different stress conditions, in order to
estimate the optimal accelerated stress acceptance time for various stress levels. Additionally, 
at a specified confidence level, the bootstrap method is used to obtain the confidence interval 
for the optimal accelerated stress acceptance time. Furthermore, the thesis investigates the 
impact on the accuracy and precision of the estimated optimal accelerated stress acceptance 
time when erroneously using a parametric degradation model, and compares it with the 
proposed method.

1 緒論 ...................................................................................................................................... 1
1.1 前言................................................................................................................................................1
1.2 文獻探討........................................................................................................................................3
1.2.1 衰變模型................................................................................................................................3
1.2.2 B 樣條 ....................................................................................................................................5
1.2.3 拔靴法....................................................................................................................................9
1.3 研究動機與目的..........................................................................................................................12
1.4 研究架構......................................................................................................................................16
2 加速應力驗收試驗......................................................................................................... 17
2.1 B 樣條半參數衰變模型 ..............................................................................................................17
2.2 驗收時間......................................................................................................................................21
3 資料與模擬分析............................................................................................................. 23
3.1 節點選擇......................................................................................................................................23
3.2 半參數選擇與資料分析..............................................................................................................25
3.3 模擬分析......................................................................................................................................28
4 結論與未來發展............................................................................................................. 31
參考文獻 ....................................................................................................................................... 32

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