本文評估單因子隨機效應模型中多種容許界限在非常態隨機變數資料的表現。我們使用Mee和Owen(1983)、Vangel(1992)、Krishnamoorthy和Mathew(2004) 、Harris和Chen (2006a) 及Chen和Harris (2006b)這五篇論文所建構的七種容許界限，並利用蒙地卡羅模擬方法求得不同情況下各種容許界限的模擬涵蓋率、平均值與標準差，就模擬方法所產生的結果進行比較與總結。模擬的結果顯示，根據常態分布的性質所建構出的容許界限，應用於伽瑪分布的數據時導致大部份的情況下涵蓋率表現不如預期。如需改善則需要根據在單因子隨機效應模型下推導出適用於伽瑪分布或其它非對稱性機率分布的容許界限。

This paper gives the results from a computer simulation study concerning the estimated coverage rate and the average of the tolerance limits with their standard deviation for seven one-sided tolerance limits under the one-way random effects model when data are generated from non-normal distributions. These procedures are from Mee and Owen (1983), Vangel (1992), Krishnamoorthy and Mathew (2004), Harris and Chen (2006a) and Chen and Harris (2006b). The simulation results indicate that the coverage rates of all tolerance limits are mostly below the nominal confidence level of 0.95.  It suggests that the tolerance limits derived under the one-way random effects model based on the assumption of normality may not suit the non-normal distributed data.

目錄
誌謝	i
中文摘要	ii
英文提要	iii
目錄	iv
1	緒論	1
1.1	容許區間與容許界限的定義	1
1.2	單因子隨機效應模型	2
1.3	隨機變數的設定	2
1.4	本文架構	3
2	文獻回顧	4
2.1	常用符號使用對照說明	4
2.2	七種容許界限	5
2.2.1	Mee和Owen (1983) 的方法	5
2.2.2	Vangel (1992) 的方法	6
2.2.3	Krishnamoorthy和Mathew (2004) 的方法	7
2.2.4	Chen和Harris (2006a) 的方法	9
2.2.5	Chen和Harris (2006b) 的方法	10
3	蒙地卡羅模擬研究分析	11
3.1	生成隨機變數	11
3.2	結果觀察	12
4	結論與未來研究方向	16
4.1	結論	16
4.2	未來研究	17
4.2.1	母體平均數 與 	17
4.2.2	參數的估計	18
參考文獻	21
附表	23
附錄	51

參考文獻
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