根據Wiener過程的特性，產品首次通過恆定失效閥值的壽命時間將服從逆高斯分配。同樣地，當衰退路徑通過一非失效閥值時，其通過時間亦服從逆高斯分配。此通過時間即為所謂的中間數據，代表產品在尚未失效前已達到一定衰退程度之觀測數據。本研究即利用此特性作為分類分析的理論基礎。
首先，透過最大概似法估計良品與不良品之漂移率與擴散係數，建立衰退模型並導出對應之逆高斯分配。接著，以最小化期望判別錯誤成本為目標，利用不同非失效閥值下的通過時間分布，求解最佳分類時間切點，並將其作為預燒時間。將判別錯誤成本與運行成本納入總成本函數，評估不同非失效閥值對總成本之影響。最後以最小總成本之非失效閥值及其最佳分類時間切點進行預燒分類，維持分類準確度的同時，有效控制測試資源的投入。
本研究所提出的分析流程與決策依據，有助於提升高可靠度產品預燒試驗中，產品品質分類的效率與準確性，提供一套兼具理論基礎與實務應用的產品預燒分類策略。為驗證本研究方法於實務應用之可行性，以GaAs雷射設備的衰退數據作為實證案例，說明如何透過中間數據進行預燒分類判斷。結果顯示，即便不依賴最終失效資料，仍能有效區分潛在不良品與良品，展現本研究預燒分類策略於高可靠度產品預燒試驗中的實用價值。

According to the properties of the Wiener process, a product’s lifetime, defined as the time when its degradation path first crosses the failure threshold, follows an Inverse Gaussian distribution. Similarly, when the degradation path crosses the nonfailure threshold, the product’s passage time also follows an Inverse Gaussian distribution. This passage time constitutes the so-called intermediate data, which represents observed data indicating that the product has reached a certain degree of degradation prior to failure. This study adopts this characteristic as the theoretical basis for classification analysis.
With the objective of minimizing the expected cost of misclassification, the distribution of passage times under various nonfailure thresholds is utilized to determine the optimal cut-off time point, which is then adopted as the burn-in time. By incorporating both the expected cost of misclassification and the operational cost into the total cost function, the study evaluates the impact of different nonfailure thresholds on the total cost. The nonfailure threshold and its corresponding optimal cut-off time point that yield the minimum total cost are ultimately used for burn-in classification. This approach aims to maintain classification accuracy while effectively controlling the testing resource expenditure.
The proposed method enhances the efficiency and accuracy of product quality classification during the burn-in test of highly reliable products. To validate the feasibility of this method, GaAs laser data is used as a case study to demonstrate how intermediate data can be applied for burn-in classification decisions. The results show that even without relying on final failure data, the proposed strategy can effectively distinguish weak items from normal items, highlighting its practical value in the burn-in testing of highly reliable products.

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