單因子隨機效應模型下的替代容許界限

An Alternative tolerance Limit for A One-way Random Effects model

王志遠(Chih-Yuan Wang)

指導教授 ： 陳順益

淡江大學/理學院/數學學系碩士班/碩士(2007年)

https://doi.org/10.6846/TKU.2007.00461

摘要

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。

關鍵字

容許界限 ； 涵蓋率

並列摘要

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.

並列關鍵字

tolerance limits ； converage rate

參考文獻

2. Chen, S. Y. and Harris, B. (2006), ”An Alternative Lower Tolerance Limits for the Normal Random Effects Model”.Umpublished manuscript

3. Harris, B. and Chen, S. Y. (2001), ”Accurate Lower Tolerance Limits for the Normal Random Effects Model”.University of Wisconsin-Madison Technical Report, NO.1036.

4.Krishnamoorthy, K. and Mathew, T. (2004), ”One-Sided Tolerance Limits in Balanced and Unbalanced One-Way Random Models Based on Generalized Confidence Intervals”. Technometrics ,46, 44--52.

5.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.

6.Mee, R. W. and Owen, D. B. (1983), ”Improved Factors for One-Sided Tolerance Limits for Balanced One-Way ANOVA Random Model's”. Journal of the American Statistical Association ,78, 901--905.