藉由合併的血液樣本來估計人體內毒素的含量是合併檢測中非常重要的一個應用.傳統二項式合併檢測模型必須假設沒有檢驗誤差.我們考慮檢驗的有限精確性所引起的量測誤差會導致嚴重的偏誤及不真確的結論。
　　本論文將提出一個由二項及指數分配所混合而成的稀釋效用模型.我們將得到參數的最大概似估計量，並討論其性質.在不考慮檢驗誤差的情形下，建立一個含零觀測值的模型並得到參數的最大概似估計量與動差估計量.因為最大概似估計量並無解析解，因此使用模擬的方式來比較跟動差估計量之間的差異。

　　One of the most important application of group testing is in the assembling drop of blood to estimate the amount of toxin in human body. The classical binomial group testing model must assume that groups are tested and classified without error. Our consideration is that the presence of measurement errors resulting from the limited precision of test may lead to severe bias and unrealistic conclusion.
　　This thesis will propose a dilution effect model which is a mixture of binomial and exponential distribution. We derive maximum likelihood estimator of parameters and discuss the corresponding property of .Without considering testing error ,we set up a group testing model in the presence of zero observations and derive maximum likelihood estimator and method of moment estimator of parameters. Since the has no analytic solution, so we compare it with by using simulation technique.

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