本論文探討的是在簡單加速壽命試驗及型二混合設限下Weibull資料的估計問題。由於實驗單位在兩階段的應力水準不同，在累積暴露模型之假定下，解出最大概似估計值並求得觀察到的訊息矩陣。進而介紹各參數之最大概似估計量的漸進信賴區間、基於概似比的漸進信賴區間，以及三種拔靴信賴區間。在不同的樣本數、應力改變的時間及實驗預定的終止時間之下，利用蒙地卡羅法模擬計算各參數估計量的偏差和均方誤差等指標，以評估其與應力改變的時間及實驗預定終止的時間之關係；再對各參數的各種信賴區間分別計算覆蓋率以評估區間估計之表現。其中，最大概似估計量的漸進信賴區間不但計算時間短且覆蓋率之表現較佳。

In this thesis, the estimation problems for Weibull data under simple step-stress and type II hybrid censoring are considered. Due to different stress level undertaken by those experiment units surviving through the first stage, the maximum likelihood estimators (MLEs) of the parameters and the corresponding observed information matrix are derived under the cumulative exposure model. Then, asymptotic confidence intervals derived from the asymptotic distributions of the MLEs, likelihood ratio-based confidence intervals and three bootstrap confidence intervals are introduced. With different sample sizes, change-points for changing the stress-level, and preplanned stopping times, Monte-Carlo simulations are carried out and the average biases, mean squared errors, and other criterions are computed to discover the relations between these criterions and change-points and preplanned stopping times. Coverage rates for confidence intervals are also computed to evaluate their performances. Finally, the asymptotic confidence interval is recommended due to taking less computation time and achieving better coverage rate than other methods.

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