基于参数优化的截尾序贯检验法

Truncated Sequential Test Based on Parameter Optimization

截尾序贯概率比检验法和序贯网图检验法（SMT）是在序贯概率比检验法（SPRT）的基础上发展起来的2种方法,可进一步控制试验次数。但是这些截尾序贯方法的停止边界仍有待优化,本文以最常见的截尾SPRT为例,说明决定停止边界的参数的取值直接影响了最大试验样本量,且存在最佳取值。并以此为基础,对SMT和传统的SPRT进行了综合比较,发现截尾SMT并不优于传统的截尾SPRT,它不过是一种广义形式的截尾序贯检验法,SPRT的研究重点应该是截尾形式的构造。最后本文提供了一种曲线形式的截尾序贯检验法.

Numerous methods are derived from sequential probability ratio test（SPRT） to reduce sample times and truncated SPRT and sequential mesh test（SMT） are two of them.However,the stopping boundaries of truncated sequential methods are yet to be optimized.Taking truncated SPRT as an example,the paper demonstrates that the parameters deciding the stopping boundary directly impact the maximum sample number of truncated SPRT.The paper also demonstrates the existence of the optimal value of those parameters.Based on this,truncated SMT and truncated SPRT are compared in a comprehensive manner.The results show that truncated SMT is no better than truncated SPRT.Generally speaking,SMT also belongs to the cluster of truncated SPRT and thus more attention should be paid to construction of the truncated scheme of SPRT.At the end of the paper,a method to construct a truncated sequential test is given together with curve forms.