在研究有關產品可靠度方面的問題時，通常需要進行壽命試驗，而在試驗進行當中，常常希望能預測部份尚未發生故障的樣本壽命，以決定是否變更生產計畫或採行其他決策的參考。本文即希望能利用所取得之產品發生故障之排序集合樣本壽命觀測值來預測未來型II 設限樣本產品發生故障之壽命觀測值的貝氏預測區間和平均覆蓋機率，做為評估及改善產品可靠度的依據。
研究有關產品可靠度方面的文獻，大部分選擇產品壽命分配為指數分配。指數壽命分配適用於失敗率穩定的產品；但是，如果假設每條生產線之產品壽命皆為指數分配具有失敗率 ，而經其生產線產出的產品之失敗率 為隨機變數服從Gamma分配，那麼由此混合母體隨機抽取的生產線之產品，其產品壽命便服從第二類型的柏拉圖分配。
本文主要探討的分配為柏拉圖分配，以求取未來型II 設限樣本之貝氏預測區間和平均覆蓋機率。其中，第二章是討論其樣本壽命觀測值服從指數分配的排序集合樣本，則樣本壽命觀測值為 的情況之下，分別針對尺度參數已知、尺度和形狀參數皆未知及一般化無資訊的事前分配，求取未來型 設限樣本壽命觀測值的貝氏預測區間和平均覆蓋機率。第三章舉出數值範例，以及利用蒙地卡羅(Monte Carlo)模擬方法以建立給定在 下，求取未來型 設限樣本壽命觀測值的貝氏預測區間和平均覆蓋機率。最後第四章則是結論。

In the researching of Products’ reliability, the result of life testing is used as the basis for the evaluation and improvement of reliability. During life testing, however, the future observation in an ordered sample is often expected to be predicted so as to determine whether the life testing experiment be redesigned or used as the reference for other decisions.
     In most literatures, the exponential distribution is widely used as a model of lifetime data. The distribution is characterized by a constant failure rate. But in a population of component there could be a ubiquitous variation in failure rate because of small fluctuations in manufacturing tolerances so that a component selected at random can be regarded as belonging to a random subpopulation. Let the lifetime of a particular component have an exponential distribution with failure rate and let the failure rate follow a Gamma distribution, then the failure time of a component selected at random from such a mixed population has a Pareto distribution of the second kind.
    This paper presents that under a ranked set sample  from a Pareto distribution, we adopted Bayesian method only based on the only   to obtain the prediction intervals of the future Type II censored lifetime observations.

目錄
表目錄 …………..………………………….……………………… III
第一章 緒論 …..………………….………………………………….. 1
1.1 研究動機與目的 ……………………………………………. 1
1.2 文獻探討 ……………………………………………………. 3
1.3 本文架構 ……………………………………………………. 5
第二章 未來樣本壽命觀測值之貝氏預測區間 ……..………………7
2.1 排序集合樣本 ………………………………………………. 9
2.2 未來型 設限樣本壽命觀測值之貝氏預測區間 ………… 10
2.2.1 當分配的尺度參數(Scale Parameter)已知時之貝氏預測區間 …...……………………………………………... 11
2.2.2 當分配的尺度參數(Scale Parameter)和形狀參數(Shape Parameter)皆未知時之貝氏預測區間 ….………….. 19
2.2.3一般化無資訊事前分配之貝氏預測區間 …………. 25
第三章 數值模擬 ……………………………………………..……. 32
3.1 數值範例 ………………………..……………..………..… 32
3.1.1 尺度參數已知的未來型II 設限樣本壽命觀測值之貝氏預測區間 …………………………………………… 32


3.1.2 尺度和形狀參數皆未知的未來型II 設限樣本壽命觀測值之貝氏預測區間 ………………………………… 34
3.2統計模擬 ………………..………………………………..…. 36
第四章 結論 ……………..…………………………………….….... 42
參考文獻 …………………………...……………………………….. 45
 
表目錄

表 2.1.1 n組樣本大小為n之集合 ….……………………………… 9
表 2.1.2 n組樣本大小為n之排序集合 ………………..…………. 10
表3.1-1 尺度參數 已知下的n組樣本大小為n之樣本集合 ……………………………………………………….… 33
表 3.1-2對於 , 和 的未來型II 設限樣本壽命觀測值   之95%貝氏預測區間 …..……………… 33
表 3.1-3 尺度和形狀參數皆未知下的n組樣本大小為n之樣本集合 ………….………………………………………… 34
表 3.1-4 對於 、 和 的未來型II 設限樣本壽命觀測值   之95%貝氏預測區間 …..…………… 35
表3.2.1 對於 , , 和 之
  和 的95%貝氏預測水準下之平均覆蓋機率及其均方
誤 …….…………………………………………………… 39
表3.2.2 對於 , , 和 之
 和 的95%貝氏預測水準下之平均區間長度 …..… 40
表3.2.3 對於 , , 和 之
        和 的99%貝氏預測水準下之平均覆蓋機率及其均方
誤 ………………………………………………………… 40

表3.2.4 對於 , , 和 之
        和 的99%貝氏預測水準下之平均區間長度 ……... 41

[中文部份]
王盟發，曾玉玲，採集合排序樣本時常態平均值之較佳檢定，中國統計學報，九十一年，391-418頁

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