型II柏拉圖分配未來觀測值之貝式預測區間
學年 97
學期 1
出版（發表）日期 2009-01-01
作品名稱 型II柏拉圖分配未來觀測值之貝式預測區間
作品名稱（其他語言） The Bayesian Predictive Interval for the Future Observation for the Type II Pareto Distribution
著者 吳淑妃
單位 淡江大學統計學系
描述 計畫編號：NSC98-2118-M032-004 研究期間：200908~201007 研究經費：582,000
委託單位 行政院國家科學委員會
摘要 指數分配在壽命檢測與可靠度問題上佔據一個很重要的地位，但此分配假設產品的失敗率為固定常數，但對整個生產線之產品而言，由於生產環境的不同，或製造過程中所容許的變動，其所產生的產品失敗率會不同。若產品失敗率呈一Gamma分配，此混合母體之壽命分配則為一型II柏拉圖(Pareto)分配。在研究有關產品可靠度方面的問題時，通常需進行壽命試驗，而在試驗進行時，通常希望能預測產品未來壽命時間，作為決定是否要變更生產計畫或改採行其他決策的參考。但實驗當中因時間、成本或其他限制的考量而往往無法取得完整的樣本資料，而需面對不完整設限資料。 本研究第一年考慮樣本壽命觀測值服從雙參數柏拉圖分配，在逐步型II設限下, 利用貝氏方法對未被觀察到的產品壽命進行區間預測，做為評估及改善產品可靠度的依據。本研究亦會舉一些數值例子來示範如何建立未來觀測值之貝氏預測區間，並做模擬分析以了解貝氏預測區間是否能達到名目的信心水準, 以及不同設限計畫對貝氏預測區間長度和覆蓋率的影響. 第二年則針對雙樣本問題，提出獨立的第二組樣本未來觀測值之貝氏預測區間，亦會舉一些數值例子來示範如何建立, 並做模擬分析, 以了解貝氏預測區間是否能達到名目的信心水準. 以及不同設限計畫對貝氏預測區間長度和覆蓋率的影響. 第三年則針對若第一組樣本為排序集合樣本, 利用其第i個有序樣本, 預測另一獨立的生產線上第s個尚未發生故障的壽命, 本研究會提出其貝氏預測區間, 此亦為一雙樣本預測的問題, 最後, 我们會做模擬分析, 以了解貝氏預測區間是否能達到名目的信心水準. In most literatures of reliability, the exponential distribution is widely used as a model of lifetime data. The assumption of constant failure rate may not be true for some cases. If the failure rate follows a Gamma distribution, then the lifetime distribution is so-called the type II Pareto distribution. In life testing experiments, the experimenter may not always be in a position to observe the life times of all the items put on test. Censoring is thus arisen. Some experimenters desire to remove units (accidental breakage of units) at points other than the final termination point. The Progressively Type II censoring will allow such intermediate removals of units. In the first year, we want to propose a Bayesian predictive interval of future observation for the Pareto distribution based on a progressively Type II censored sample. Some numerical examples under various censoring schemes are given to demonstrate the proposed Bayesian predictive interval. A simulation study is done to see if the simulated coverage percentage can reach the nominal coverage percentage and to analyze the effect of different censoring schemes on the average interval length and coverage percentage. In the second year, a two-sample problem is considered. We will propose a Bayesian predictive interval of unobserved lifetime for the other independent sample based on a progressively Type II censored sample from the first sample. Some numerical examples under various censoring schemes are given to demonstrate the proposed Bayesian predictive interval. A simulation study is done to see if the simulated coverage percentage can reach the nominal coverage percentage and to analyze the effect of different censoring schemes on the average interval length and coverage percentage. In the third year, we will use the ith ordered sample from the ranked set sample to construct the Bayesian predictive interval for the sth unobserved lifetime for the other independent sample. Some numerical examples are given to demonstrate the proposed predictive interval. A simulation study is done to see if the simulated coverage percentage can reach the nominal coverage percentage.
關鍵字 逐步型II設限樣本; 排序集合樣本; 柏拉圖(Pareto)分配; 貝氏預測區間; 雙樣本預測; Progressively Type-II censored sample; Ranked Set sample; Pareto Distribution; Bayesian Prediction Interval
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