基於通用趨勢過程之加速衰變分析

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题名:	基於通用趨勢過程之加速衰變分析
作者:	謝宇宸;HSIEH, YU-CHEN
贡献者:	統計研究所
关键词:	加速衰變試驗;通用趨勢過程;趨勢函數;隨機過程;隨機效應;壽命推論
日期:	2025-07-30
上传时间:	2025-10-17 12:16:37 (UTC+8)
出版者:	國立中央大學
摘要:	高可靠度產品廣泛應用於航太、醫療與光電等關鍵領域，因其低故障率與長壽命特性，使得傳統壽命試驗在資料蒐集與試驗成本上面臨諸多挑戰。加速衰變試驗透過施加控制性應力，促使品質特徵值的衰變行為加速進行，藉由衰變模型與應力參數關係建立模型架構，已成為高壽命產品可靠度評估的重要方法。然而，傳統模型多假設應力僅影響參數，忽略其對衰變路徑形狀可能造成的改變所導致壽命推論結果的偏誤。本文結合趨勢函數 (trend function) 與常用於分析衰變資料的隨機過程建構加速通用趨勢過程模型 (accelerated generic trend process; AGTP) ，在趨勢函數因應力改變而調整下，得以同時描述衰變速率變異與路徑型態轉變；而 AGTP 模型亦涵蓋傳統加速衰變隨機過程模型，是以更具備了理論整合性與延展性。在對數線性連結函數之加速模式下，進一步建立隨機效應模型可描述產品間的差異性，使模型配適更具彈性。在壽命推論中，本文推導出通用趨勢過程首次抵達衰變門檻值之時間，在 AGTP 模型中經外插建立正常應力下產品的壽命分布，並引入偽失效時間與適合度檢定，驗證模型與資料的擬合性。最後應用於實例分析，基於模型選擇與適合度檢定，AGTP 模型展現出優於目前文獻中之最佳結果；也為 AGTP 模型在加速衰變資料之建模與可靠度分析提供突破性的新思維做出具體的佐證。;High-reliability products are widely used in critical fields such as aerospace, medical, and optoelectronics. Due to their low failure rates and long lifespans, traditional life testing faces challenges in data collection and high experimental costs. Accelerated degradation testing (ADT) addresses these issues by applying controlled stress to accelerate the degradation of quality characteristics, allowing lifetime estimation through degradation-stress models. However, conventional models often assume that stress only affects model parameters, overlooking its potential influence on the shape of degradation paths, which may lead to biased inference. This study proposes the accelerated generic trend process (AGTP) model, which integrates trend functions with commonly used stochastic processes. By assuming the trend function to vary with stress, AGTP captures both changes in degradation rates and path shapes. It also generalizes ADT models based on traditional stochastic processes, enhancing theoretical integration and extensibility. Furthermore, random-effects models are introduced to account for unit-to-unit variability under log-linear acceleration link functions, improving model flexibility. For lifetime inference, we derive the first-passage time to a degradation threshold and extrapolate the lifetime distribution under normal stress. Pseudo failure times and goodness-of-fit tests are used to assess model adequacy. Real data analyses demonstrate the AGTP model′s structural advantages and its superiority over existing models, offering a novel perspective in modeling and reliability analysis of accelerated degradation data.
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