建立容許區間衡量製程特性在製造業與醫藥等領域廣泛地被使用於制定品質控制系統。我們在本論文中分別提出有母數與無母數的兩種方法，用以建立混合二項分配的容忍界限，而這兩種方法亦可以被使用於許多應用問題之中。本文將其進行模擬並比較兩種方法，而無母數的方法在此表現較佳因為它的覆蓋率可以達到我們給定的標準且容許界限也有令人滿意的結果。

1 Introduction 1
2 Mixture Model 2
2.1 Binomial Mixture Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Gibbs sampler 5
3.1 The algorithm for GIBBS sampling . . . . . . . . . . . . . . . . . . . . . . 6
4 Condence Interval for a Binomial Distribution 7
5 Tolerance limit for a Binomial Distribution 8
6 Tolerance limit for a Binomial Mixture Model 9
6.1 Tolerance limit based on a mixture model . . . . . . . . . . . . . . . . . . 9
6.2 Distribution-Free Tolerance Interval . . . . . . . . . . . . . . . . . . . . . . 10
7 Simulation 11
8 Conclusions 17
Reference 18

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