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。

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.

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<theta<0.5時的覆蓋機率值、均方誤及平均區
      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<theta<0.5時的覆蓋機率值、均方誤及平均區
      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<theta<1時的覆蓋機率值、均方誤及平均區
      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<theta<1時的覆蓋機率值、均方誤及平均區
      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<theta<3時的覆蓋機率值、均方誤及平均區間
      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<theta<3時的覆蓋機率值、均方誤及平均區間
      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<theta<5時的覆蓋機率值、均方誤及平均區間
      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<theta<5時的覆蓋機率值、均方誤及平均區間
      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

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。
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