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，而在試驗進行當中，常希望能預測部份尚未發生故障的樣本壽命，已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產品發生故障之右型II設限樣本壽命觀測值來預測未來產品發生故障之區間，做為評估及改善產品可靠度的依據。
本文主要探討的是樣本壽命觀測值服從柏拉圖分配的右型II設限樣本 ，以貝氏的論點在給定最後一筆故障觀測值下來求取未來觀測值之預測區間並與Nigm et al. (2003)所提出的方法進行比較。如果 由於人工疏忽導致遺失，那Nigm et al.的方法就不適用；此外，順序觀測值 的條件機率密度函數給定在 並與給定在 的條件密度函數ㄧ致。最後提出數值範例來說明。

While researching on the reliability of products, usually need to carry on life test. The result of life testing is used as the basis for the evaluation and improvement of reliability. During life testing, the future observations in an ordered sample are often expected to be predictor as to determine whether the production schedule should be altered or adopting other decision of conduct.
This paper presents that under the right type II censored samples
from Pareto distribution, adopted Bayesain method only based on the only to obtain the prediction intervals of the future observations and compares with the method proposed by Nigm et al. (2003). If some of are missing since artificial negligence occur, then Nigm et al.’s method may not be an appropriate choice. Moreover, the conditional probability density function of the ordered observation given is equivalent to the conditional p.d.f. of given . Numerical examples are provided to illustrate these results.

第一章 緒論 1
1.1 研究動機 1
1.2 文獻探討 3
1.3 本文架構 4
第二章 母體分配為柏拉圖分配的未來順序觀測值之貝氏預測區間 6
2.1 已知尺度參數下未來順序觀測值之貝氏預測區間 8
2.2 尺度及形狀參數未知下未來順序觀測值之貝氏預測區間 15
2.3 在一般化無資訊事前分配下的未來觀測值之貝氏預測區間 20
第三章 數值模擬 23
3.1 數值實例 23
3.1.1 尺度參數已知下的未來觀測值預測區間 23
3.1.2 尺度及形狀參數皆未知下的未來觀測值預測區間 26
3.2 統計模擬 31
第四章 結論 37
參考文獻 39

表3-1 單參數已知下，當n = 20, r = 15時，柏拉圖分配中 的95%預測區間及區間長度 25
表3-2 單參數已知下，其餘n-r個壽命時間 的95%貝氏預測區間，當s=n-r=5, 和c=0.5 26
表3-3 雙參數皆未知下，當n = 20, r = 15時，柏拉圖分配中 的95%預測區間及區間長度 29
表3-4 雙參數皆未知下，當n = 20, r = 15時，柏拉圖分配中 的95%預測區間及區間長度 29
表3-5雙參數皆未知下，其餘n-r個壽命時間 的95%貝氏預測區間，當s=n-r=5, 和 30
圖3-1 雙參數柏拉圖分配的機率密度函數圖 32
表3-6 兩種方法下，柏拉圖分配單參數已知(c=0.5)下的平均覆蓋機率值及均方誤，其中 , 35
表3-7 兩種方法下，柏拉圖分配單參數已知(c=0.5)下的平均覆蓋機率值及均方誤，其中 , 36

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