加速衰變試驗目前已廣泛地被使用，以評估高可靠度產品在正常應力下的壽命資訊。然而加速衰變模型與環境應力之間的關連性中，相關的物理/化學機制和統計意義卻鮮少探討。因此本文考慮加速衰變模型為具隨機效應 (random effects) 之單調過程，以累積暴露 (cumulative exposure) 模式為物理/化學機制，推得模型中參數與加速應力之間的關係式，進而賦予其統計意義。再以常用的逆高斯 (inverse Gaussian) 和伽瑪(gamma) 過程為例，和文獻上常用的加速衰變模型做詳細比較，並提出 EM 演算法估計新加速衰變模型的未知參數。最後，藉由三組實例分析，呈現在不同關係式的假設下，模型配適的差異性、產品壽命推論的精準性、相對應的信賴區間以及加速衰變模型的適合性等。;Accelerated degradation tests are widely used to assess lifetime information under normal stress for high-reliability products. However, the physical/chemical mechanism as well as the statistical interpretation of the relationship between the accelerated degradation model and the environmental stress is rarely addressed. In this thesis, we consider accelerated degradation models based on monotonic processes with random effects. By adopting the assumption of cumulative exposure model due to the physical/chemical mechanism, relationships between the model parameters and the acceleration factor are derived which also provide sensible statistical interpretation. Inverse Gaussian and gamma processes are used as examples in which the proposed method is applied and compared with common accelerated degradation models in literature. Expectation-Maximization (EM) algorithm is employed to estimate the unknown parameters of the proposed accelerated degradation model. Finally, three data sets are analyzed to illustrate the performance of the degradation models under different relationships based on the model adequacy, the accuracy of product′s lifetime inference and the corresponding confidence intervals and the goodness of fit.
