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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/110909

    Title: 評估單因子隨機效應模型中多種單邊容許界限在非常態隨機分布下的表現
    Other Titles: An evaluation of various one-sided tolerance limits for one-way random effects model under non-normal distributions
    Authors: 張凱雲;Chang, Kai-Yun
    Contributors: 淡江大學數學學系碩士班
    陳順益;Chen, Shun-Yi
    Keywords: 單因子隨機效應模型;非常態隨機變數;伽瑪分布;單邊容許界限;蒙地卡羅模擬方法;One-Way Random Effects Model;Non-Normal Distributions;Gamma Distribution;One-Sided Tolerance Limits;Monte Carlo Simulation
    Date: 2016
    Issue Date: 2017-08-24 23:39:06 (UTC+8)
    Abstract: 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.
    Appears in Collections:[數學學系暨研究所] 學位論文

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