在工業製程中，壽命檢測是用來評估產品品質的方法。然而，在實際應用方面，由於時間、成本的限制或資料蒐集時人為的疏失，而要提前結束實驗，致無法取得完整樣本，取得的部份則稱為設限樣本。為了解決這些問題，所以發展出數種設限與逐步移除的方法。本論文即利用型二逐步設限資料對極值和柏拉圖分配之參數做統計推論。 本文中，首先對隨機移除與二項移除與方法做討論，再分別推導極值分配和柏拉圖分配在隨機與二項移除方法下，其參數的信賴區間和聯合信賴區域，並對參數做假設檢定。最後，比較各個樞鈕量在信賴區間、聯合信賴區域及假設檢定下的優劣。 In many industrial processes, life test is conducted in order to assess the quality of a product. However, in practice, life tests are usually terminated before the complete lifetimes of the n products are observed due to the time, cost or mistakes of operating. This results in a censored data. The Type II progressive censoring with random removals is thus arisen. This research is mainly concentrating on the statistical inferences for the parameters of the Extreme-value and Pareto distributions based on the Type II progressive censored data. To begin with, the methods of binomial and random removal are discussed. We propose the confidence interval, joint confidence region, and hypothesis testing among the parameters of Extreme-value and Pareto distributions under binomial and random removals respectively. Finally, the performances of the proposed pivotal quantities based on the length of confidence interval, the area of confidence region, and the power of hypothesis testing are presented.
