在許多自然科學及工業生產的研究中，生物與產品的壽命往往是研究的重點。由於在現實生活中，我們常會遇到無法取得完整樣本的情況。例如，由於人為疏失，或是成本時間的考量等等因素，我們必須提前結束試驗；或者在某些醫學的臨床實驗中，某些病人因為某種因素，在實驗未結束前即提前退出試驗；又可能某些實驗對實驗對象有ㄧ定的危險性，而提前結束實驗，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。本文主要利用二項移除與隨機移除之型二逐步設限資料對Gompertz與Rayleigh分配做統計推論。 本文中，首先在二項與隨機移除之型二逐步設限下，分別推導Gompertz分配的信賴區間、聯合信賴區域及假設檢定，及Rayleigh分配的最短信賴區間及假設檢定，最後比較各個樞紐量在信賴區間、聯合信賴區域及假設檢定的優劣。 Studies in the lifetimes of the organisms and products are often the main researches topics in the nature and industries. The situation that we can not obtain the complete samples may occur from time to time in our real life due to several reasons. For example, we have to end the testing in advance because of the neglect and failure of mankind or the consideration of cost and time; in some medical clinical experiment, some patients might not proceed the experiments for some specific reasons, or the testing itself may come to an end ahead of time in order not to cause any possibility of danger to people undertaking it. The Type II progressive censoring with random removals is thus arisen. This research is mainly concentrating on the statistical analysis of two-parameters Gompertz distribution and Rayleigh distribution under type II progressive censoring with random removals.
In this thesis, we establish the confidence interval , confidence region, and hypothesis testing for the parameters of Gompertz distribution under the type II progressive cencered samples with binomial and random removals separately. In addition, we also establish the shortest confidence interval and hypothesis testing for the parameter of Rayleigh distribution under the type II progressive censored samples with binomial and random removals. Finally, we compare 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.
