本論文針對平衡的雙因子套層隨機效應模型 (two-way nested random effects model) 推導出單邊容許界限。我們藉由 Chen 和 Harris(2006) 所提出的方法，即在估計量為未知期望均方比值 (unknown expected mean square ratio)的條件下，求條件機率密 度函數，而所找到的統計量與均方比值獨立且具有最大自由度的卡 方分配，並以此統計量建立一個精準 (exact)的單邊容許界限。利 用統計模擬來驗證此方法的可行性，其結果顯示在此模型下亦有準 確的模擬涵蓋率及較小的平均值與標準差，因此經數值探討後發現 本方法比其他方法不僅不保守且更準確。最後舉出三個實際的例子 來做方法比較，並提出利用此方法所需的表格。 We consider in this article a method of constructing accurate $beta$-content tolerance limits for a two-way nested model with normal random effects. The procedure is derived by conditioning on an estimator of the unknown expected mean square ratio as proposed in Chen and Harris (2006). Simulation studies indicate that the present procedure is less conservative than current existing methods and gives more accurate coverage rates. Statistical tables needed to implement the procedure are included.
