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

An Evaluation of Various One-Sided Tolerance Limits for One-Way Random Effects Model under Non-Normal Distributions

張凱雲(Kai-Yun Chang)

指導教授 ： 陳順益

淡江大學/理學院/數學學系碩士班/碩士(2016年)

https://doi.org/10.6846/TKU.2016.00442

摘要

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。

關鍵字

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

並列摘要

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.

並列關鍵字

One-Way Random Effects Model ； Non-Normal Distributions ； Gamma Distribution ； One-Sided Tolerance Limits ； Monte Carlo Simulation

參考文獻

[20] 王志遠 (2007), “單因子隨機效應模型下的替代容許界限,” 淡江大學數學學系碩士論文.

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[2] Bain, L. J., Engelhardt, M. and Shiue W. K. (1984) , “Approximate Tolerance Limits and Confidence Limits on Reliability for the Gamma Distribution,” IEEE Transactions On Reliability, 33, 184–187.

[3] Chen, S. Y. and Harris, B. (2006a), “On Lower Tolerance Limits with Accurate Coverage Probabilities for the Normal Random Effects Model,” Journal of the American Statistical Association, 101, 1039–1049.

[4] Chen, S. Y. and Harris, B. (2006b), “Alternative Lower Tolerance Limits for the Normal Random Effects Model,” Unpublished Manuscript.