單因子隨機效應模型下雙邊容許界限之比較探討

Comparison of Two-Sided Tolerance Limits for the Normal Random Effects Model

黃彗瑜(Hui-Yu Huang)

指導教授 ： 陳順益

淡江大學/理學院/數學學系碩士班/碩士(2009年)

https://doi.org/10.6846/TKU.2009.00016

摘要

本文我們考慮在平衡單因子常態隨機效應模型下去建構一個雙邊的β-content容許界限，其方法是根據Chen and Harris (2006)限制於未知期望均方比率的估計量所推導出。本文並探討比較Mee(1984)、Beckman 和Tietjen (1989)及Liao 和 Iyer(2004)所提及的雙邊容許界限，透過蒙地卡羅模擬方法去計算這四種方法的雙邊容許界限的覆蓋率、平均值和標準差；及引用三個實際例子，比較這四種方法的雙邊容許界限的表現。模擬方法研究表示本文的方法比目前存在的方法較不保守且有較準確的覆蓋率。本文亦提供所需要的統計表格。

關鍵字

容許界限 ； 覆蓋率

並列摘要

We consider in this article a method of constructing a two-sided β-content tolerance limits for the balanced one-way normal random effects model. The technique is derived by conditioning on an estimator of the unknown expected mean square ratio as that in Chen and Harris (2006). We also compare the present procedure with the tolerance limits of Mee (1984), Beckman and Tietjen (1989), and Liao and Iyer (2004). In addition, we include three examples from Lemon (1977) and Vangel (1992). Simulation studies indicate that the present procedure is less conservative than several current existing methods and gives more accurate coverage rates. Statistical tables needed to implement the procedure are also included.

並列關鍵字

tolerance limits ； coverage rate

參考文獻

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3. Beckman, R. J. and Tietjen, G. L. (1998).Correction: Two-Sided Tolerance Limits for Balanced Random-Effects ANOVA Models. Technometrics 40, 269.

4. Chen, S. Y. and Harris, B. (2006).On Lower Tolerance Limits With Accurate Coverage Probabilities for the Normal Random Effects Model. Journal of the American Statistical Association 101, 1039-1045.

5. Jordan, P. (1995).Estimation of Tolerance Limits from Reference Data.Computational Statistics & Data Analysis 19, 655-668.

6. Lemon, G. H. (1977).Factors for One-Sided Tolerance Limits for Balanced One-Way-ANOVA Random-Effects Model. Journal of the American Statistical Association 72, 676-680.