淡江大學覺生紀念圖書館 (TKU Library)
進階搜尋


下載電子全文限經由淡江IP使用) 
系統識別號 U0002-1906200819020700
中文論文名稱 利用單樣本及雙樣本資料對Burr type X分配之參數做貝氏預測區間估計
英文論文名稱 Bayesian predictive interval estimation for the parameters of Burr Type X distribution based on one-sample and two-sample data.
校院名稱 淡江大學
系所名稱(中) 統計學系碩士班
系所名稱(英) Department of Statistics
學年度 96
學期 2
出版年 97
研究生中文姓名 許慧瑛
研究生英文姓名 Huei-Ying Hsu
學號 695650167
學位類別 碩士
語文別 中文
口試日期 2008-06-02
論文頁數 42頁
口試委員 指導教授-吳錦全
委員-吳淑妃
委員-賴耀宗
中文關鍵字 Burr type X分配  右型II設限  排序集合抽樣  貝氏預測  單樣本及雙樣本資料 
英文關鍵字 Burr type X distribution  Type II censoring  Rank set sampling  Bayesian prediction  One-sample and two-sample data 
學科別分類 學科別自然科學統計
中文摘要 當進行產品可靠度的分析及改善時,通常需要做產品的抽樣壽命實驗,希望能利用已觀測到的產品壽命來預測尚未發生故障的樣本壽命。本文假設所取得的樣本型態分兩種,第一種資料型態為右型II設限樣本觀測值,第二種資料型態為排序集合樣本,在所取得的樣本壽命觀測值下,利用貝氏方法預測未來產品發生故障的壽命區間。
本文主要分為兩部份,第一部份探討當產品樣本壽命服從Burr type X分配的右型II設限樣本,給定在最後一筆失效的樣本觀測值
,預測同一條生產線上尚未發生故障元件的壽命區間,此情形稱為單樣本預測;第二部份探討產品樣本壽命服從Burr type X分配的排序集合樣本,得到的資料為整組樣本的主對角線觀測值,利用給定在第i個發生故障的排序集合樣本之下,預測另一條生產線第s個尚未發生故障元件的壽命區間,此情形稱為雙樣本預測。同時分別利用電腦模擬資料加以數值計算與分析。
英文摘要 In the researching on the reliability of products and improvement, usually need to carry out life test. During life testing, the future observations in an ordered sample are often expected to be predicted. In this thesis, we have
two different data types: one is under the type II censored
samples,the other is ranked set samples. We adopted Bayesian method to obtain the prediction intervals of future ordered observation for the products.
This paper presents two parts, one is under the type II censored sample from Burr type X distribution, adopted Bayesian method only based on the only ordered observation to obtain the prediction intervals of the future observations, this called one-sample case. The second part is under ranked set samplesfrom Burr type X distribution, we adopted Bayesian method only based on the onlyto obtain the prediction intervals of the future type II censored lifetime observations. Finally, we give some examples and Monte Carlo simulation to assess the behavior of the method based on the failure samples.
論文目次 第一章 緒論.............................................1
1.1研究目的......................................1
1.2文獻探討......................................4
1.3本文架構......................................6
第二章 母體分配為Burr type X分配之未來有序觀測值的單樣本貝
氏預測區間.......................................7
2.1單樣本預測....................................7
2.2數值範例.....................................14
2.3統計模擬.....................................17
第三章 母體分配為Burr type X分配之未來有序觀測值的雙樣本
貝氏預測區......................................26
3.1雙樣本預測...................................26
3.2排序集合樣本.................................27
3.3統計模擬.....................................34
第四章 結論............................................39
參考文獻................................................41
圖目錄
圖2.1 sigma固定下,theta變動時Burr type X分配機率密度函數變
動型態............................................17
圖2.2 sigma固定下,theta變動時Burr type X分配失效函數變動型
態................................................17
表目錄
表2.1 當n=20,n-r=15時,Burr type X分配中Y(r+s)的95%預測區間
及區間長度(cl)....................................16
表2.2 Burr type X分配在雙參數皆未知,且設限個數n-r=5,
alpha=0.05,0 間長度............................................20
表2.3 Burr type X分配在雙參數皆未知,且設限個數n-r=5,
alpha=0.01,0 間長度............................................20
表2.4 Burr type X分配在雙參數皆未知,且設限個數n-r=5,
alpha=0.05,0.5 間長度............................................21
表2.5 Burr type X分配在雙參數皆未知,且設限個數n-r=5,
alpha=0.01,0.5 間長度............................................21
表2.6 Burr type X分配在雙參數皆未知,且設限個數n-r=5,
alpha=0.05,1 長度..............................................22
表2.7 Burr type X分配在雙參數皆未知,且設限個數n-r=5,
alpha=0.01,1 長度..............................................22
表2.8 Burr type X分配在雙參數皆未知,且設限個數n-r=5,
alpha=0.05,3 長度..............................................23
表2.9 Burr type X分配在雙參數皆未知,且設限個數n-r=5,
alpha=0.01,3 長度..............................................23
表2.10 Burr type X分配在雙參數皆未知,且設限個數n-r=5,
alpha=0.05,theta<5時的覆蓋機率值、均方誤及平均區間
長度.............................................24
表2.11 Burr type X分配在雙參數皆未知,且設限個數n-r=5,
alpha=0.01,theta<5時的覆蓋機率值、均方誤及平均區間
長度.............................................24
表3.1 n組樣本大小為n的集合..............................27
表3.2 排序後n組樣本大小為n的集合........................28
表3.3 對於n=5,10,15,20,25,30,m=5,10,15,20,25,30,z(1)和z(m)
的95%貝氏預測水準下之平均覆蓋機率值及均方誤.......36
表3.4 對於n=5,10,15,20,25,30,m=5,10,15,20,25,30,z(1)和z(m)
的95%貝氏預測水準下之平均區間長度.................36
表3.5 對於n=5,10,15,20,25,30,m=5,10,15,20,25,30,z(1)和z(m)
的99%貝氏預測水準下之平均覆蓋機率值及均方誤.......37
表3.6 對於n=5,10,15,20,25,30,m=5,10,15,20,25,30,z(1)和z(m)
的99%貝氏預測水準下之平均區間長度.................37
參考文獻 一、中文部分:
[1]王盟發,曾玉玲(民91),採集合排序樣本時常態平均值之較佳檢
定,中國統計學報第40卷第3期,391-418頁。
[2]王顗熒(民94),利用排序集合樣本對柏拉圖分配作貝氏預測區
間,淡江大學統計學系應用統計學碩士班論文。
[3]余靜媺(民94),利用右型II設限樣本對柏拉圖分配的未來順序
觀測值作貝氏預測,淡江大學統計學系應用統計學碩士班論文。
二、英文部分:
[1] Aitchison, J. and Dunsmore, I. R. (1975), Statistical Prediction Analysis, Cambridge University Press, Cambridge.
[2] Al-Saleh, M. Fraiwan, Al-Shrafat, Khalaf and Muttlak, H. (2000), Bayesian estimation using ranked set sampling, Biometrical Journal 42 (4), 489-500
[3] Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1992), A first course in order statistics, John Wiley and Sons, New York.
[4] Burr, I.W. (1942), Cumulative frequency distribution, Annals of Mathematical Statistics, 13, 215-232.
[5] David, H. A. (1981), Order Statistics, 2nd ed., John Wiley and Sons,Inc., New York.
[6] Dunsmore, I. R. (1974), The Bayesian predictive distribution in life testing models, Technometrics, Vol. 16, No. 3. pp. 455-460.
[7] Jaheen, Z. F. and Al-Matrafi B. N. (2002), Bayesian prediction bounds from the scaled Burr type X model, Journal of Computers and Mathematics Applications 44, 587-594.
[8] Jsheen, Z. F. (1995), Bayesian approach to prediction with outlers from the Burr type X model, Microelectron. Reliab. 35, 45-47.
[9] McIntyre, G. A. (1952), A method for unbiased selective sampling, using ranked sets, Australian J. Agricultural Research 3, 385-390.
[10] Nigm, A. M., Al-Hussaini, E. K. and Jaheen, Z. F. (2003), Bayesian one-sample prediction of future observation under Pareto distribution, Statistics, 37(6), 527-536.
[11] Nigm, A.M. and Hamdy, H.I. (1987), Bayesian prediction bounds for the Pareto lifetime model, Communications in Statistics–Theory and Methods, 16(6). 1761-1772.
[12] Raqab, M.Z. and Kundu, D. (2006), Burr Type X distribution: revisited, Journal of Probability and Statistical Sciences, vol. 4, no.2, 179-193.
[13] Sartawi, H.A. and Abu-Salih, M.S. (1991), Bayesian prediction bounds for Burr type X model, Communications in Statistics–Theory and Methods, 20(7). 2307-2330.
[14] Surles, J. G., Padgett, W. J. (2005), Some properties of a scaled Burr type X distribution, Journal of Statistical Planning and Inference 128, 271-280.
[15] Wu, Jong-Wuu, Wu, Shu-Fei and Yu, Chin-Mei. (2007), One-Sample Bayesian predictive interval of future ordered observations for the Pareto distribution, Quality and Quantity, 41,251-263.
論文使用權限
  • 同意紙本無償授權給館內讀者為學術之目的重製使用,於2009-06-27公開。
  • 同意授權瀏覽/列印電子全文服務,於2009-06-27起公開。


  • 若您有任何疑問,請與我們聯絡!
    圖書館: 請來電 (02)2621-5656 轉 2281 或 來信