在工業應用上，對於單因子隨機效應模型中，建構一個容許界限是極重要的問題，已有不少學者研究及提出方法。本篇則針對Mee和Owen(1983)、Vangel(1992)、Harris和Chen(2001)、Chen和Harris(2006)及Krishnamoorthy和Mathew(2004)五篇論文所推導出來的容許界限，利用蒙地卡羅法模擬方法去計算這些容許界限的涵蓋率、平均值、標準差，及引用三個實際的例子，比較其結果。從模擬和實例的結果，顯示出Harris和Chen(2001)、Chen和Harris (2006)所導出的容許界限比其他容許界限較不保守，且提供較精確的覆蓋率和較小的標準差。

In engineering applications, the problem of constructing tolerance limits in the one-way random effects model has been investigated by several authors. In this paper, an extensive simulation study is carried out to compare the performance of tolerance limits of Harris and Chen (2001), Chen and Harris (2006), Mee and Owen (1983), Vangel(1992), and Krishnamoorthy and Mathew (2004). In addition, we include three examples  from Lemon (1977) and Vangel (1992) to compare the methods . The simulation results and numerical examples show that the tolerance limits based on Harris and Chen (2001)and Chen and Harris (2006) are less conservative than other methods and also provides more accurate coverage rates as well as smaller standard deviations.

本論文常用符號對照說明                                    1
1. 前言                                                   2
2.文獻回顧                                                3
  2.1 單因子隨機效應模型下的容許界限                      3
2.2 七種容許界限                                          4
2.2.1 Mee和Owen(1983)                                     4
    2.2.2 Vangel(1992)                                    5
    2.2.3 Krishnamoorthy和Mathew(2004)                    6
    2.2.4 Harris和Chen (2001)                             8
    2.2.5 Chen和Harris (2006)                             8
3.蒙地卡羅模擬研究分析                                   10
4.實例比較                                               15
4.1 實例一                                               15
4.2 實例二                                               16
4.3 實例三                                               17
5.結論                                                   19
參考文獻                                                 20
附表                                           
表2-1:單因子隨機效應模型的變異數分析表                  3
表2-2: Mee和Owen(1983)的eta值                           5
表4-1觀測值                                             16
表4-2觀測值                                             17
Table A1. η values for p =.90 γ=.90                     22
Table A2. η values for p =.90 γ=.95                     23
Table A3. η values for p =.90 γ=.99                     24
Table A4. η values for p =.95 γ=.90                     25
Table A5. η values for p =.95 γ=.95                     26
Table A6. η values for p =.95 γ=.99                     27
Table A7. η values for p =.975 γ=.90                    28
Table A8. η values for p =.975 γ=.95                    29
Table A9. η values for p =.975 γ=.99                    30
Table A10. η values for p =.99 γ=.90                    31  
Table A11. η values for p =.99 γ=.95                    32
Table A12. η values for p =.99 γ=.99                    33
Table B1.p=0.90和γ=0.95,蒙地卡羅模擬估計
七種容許上界的涵蓋率,平均值和標準差                       34                                       
Table B2.p=0.90和γ=0.95,蒙地卡羅模擬估計
七種容許上界的涵蓋率,平均值和標準差                       35
Table B3.p=0.90和γ=0.95,蒙地卡羅模擬估計
七種容許上界的涵蓋率,平均值和標準差                       36
Table B4.p=0.90和γ=0.95,蒙地卡羅模擬估計
七種容許上界的涵蓋率,平均值和標準差                       37
Table B5.p=0.90和γ=0.95,蒙地卡羅模擬估計
七種容許上界的涵蓋率,平均值和標準差                       38
附錄                                                      
Fortran程式                                            39
R程式                                                  42

1.蔡雅屏(2004)台北大學統計學系碩士論文,”多個容許界限在單因子隨機效應模型下的表現”

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