二项分布的Bayes截尾序贯检验方法及其应用

BAYES CUTTING SEQUENTIAL TEST METHOD OF BINOMIAL DISTRIBUTION AND ITS APPLICATION

论述了二项分布的Bayes截尾序贯概率比检验(SPRT)方法,提出了平均风险相当的原则,即要求α_(π_0)=β_(π_1),从而使Bayes SPRT方法更趋合理,并且推导出了Bayes风险定理,指出了Bayes方法的应用价值。另外还讨论了Bayes截尾SPRT方案的平均风险实际值、平均试验数及验前概率P_(H_0)的计算。通过计算及分析可知,Bayes截尾SPRT方法能充分利用验前信息和过程信息,它适用于小子样场合,这对于昂贵的武器系统试验来说很有价值。本方法可应用于武器系统命中概率和飞行可靠性等的评定。

The Bayes cutting sequential probility ratio test (SPRT) method of Binomial distribution is dis- cussed. The principle of mean risk match ,that is α_π_0=β_π_0, is presented. So the method will be more reason- able. The Bayes Risk Theorem is also deduced, the genuine application value is pointed out. In addition, the calculation of the real mean risk value, the mean test number and prior probability P_H_0 are discussed. The process information and prior imformation can be fully utilized in the method, and the method is applied to small sample test.