破壞性衰變試驗在量測過程中，產品需經破壞方能取得與壽命相關之品質特徵值，卻無法再測試，導致每個樣本只有一筆衰變資料，提供非常有限的可靠度資訊。而高斯過程被廣泛地應用於衰變分析，但對厚尾資料之配適未臻理想。本文以包含高斯過程之學生-t 過程為基礎， 建立具有隨機效應之 (加速) 破壞性衰變模型，期能擬合具厚尾特徵的 (加速) 破壞性衰變資料，進而推論 (在正常應力下) 產品之壽命分配與相關性質。同時以多組實際資料說明產品壽命之可靠度估計、信賴區間以及模型之適合度診斷等。

In a destructive degradation test, one must destroy the products to obtain values of the quality characteristic. As a result, only one meaningful measurement of the quality characteristic can be taken from each test unit. To analyze the degradation data, Gaussian process is a general model although it is not so appropriate to deal with heavy-tailed data. This thesis proposes a Student-t process, which includes Gaussian process as a special case, to assess the possibly heavy-tailed behavior of the degradation data and to draw the corresponding reliability inferences on the lifetime distribution. Random effects are introduced into the model to address the possible unit-to-unit variation. Five data sets are analyzed by the Student-t process and the resulting reliability analyses of products’ lifetime distributions as well as the goodness-of-fit tests are made based on the models selected via Akaike information criterion.

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