利用逐步型II設限樣本對雙參數柏拉圖分配之未來觀測值做貝氏預測區間

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题名:	利用逐步型II設限樣本對雙參數柏拉圖分配之未來觀測值做貝氏預測區間
其它题名:	The Bayesian prediction interval of the future observation for the pareto distribution based on the progressively type II censored sample
作者:	李銘凱;Li, Ming-kai
贡献者:	淡江大學統計學系碩士班吳淑妃;Wu, Shu-fei
关键词:	型II逐步設限;型II柏拉圖分配;貝氏預測;預測區間;Type II progressive censoring;Type II Pareto Distribution;Bayesian prediction;Prediction Interval
日期:	2008
上传时间:	2010-01-11 04:37:17 (UTC+8)
摘要:	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。本文假設產品壽命時間服從雙參數柏拉圖分配，利用貝氏方法在逐步型II設限下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。本文亦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，模擬研究結果顯示貝氏預測區間皆有達到名目的信心水準。對於雙樣本的問題，本文也有提出其觀測值的貝氏預測區間，模擬結果也顯示有達到名目信心水準。 For reliability analysis, the lifetime test is usually needed. Experimenters usually want to predict the lifetime of unobserved sample so that they can determine whether the production schedule is needed to be redesigned. In many life testing experiments, we may not be able to obtain a complete sample due to time limitation, budget of or other restrictions. This paper is proposing a Bayesian predictive interval of future observation for the Pareto distribution based on a progressively Type II censored sample. Some numerical examples are given to demonstrate all predictive intervals. A simulation study is done and the results show that the coverage percentage of proposed predictive interval can reach the nominal confidence coefficient. The two-sample problem is also discussed in this paper. At last, some examples are given to illustrate the predictive intervals.
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