中文摘要：

方差估计是抽样调查的重要组成部分，在实际的抽样设计中，往往通过复杂的细分层提高样本的代表，平衡半样本方法成为方差估计的主要方法之一。本文主要阐述Fay平衡半样本方法的基本原因和应用，并对针对该方法存在的问题进行改进，最后通过一个实例模拟阐述其在实际调查中的应用。

英文摘要：

The variance estimation is very important part in sample survey. In practice, we often use many stratums to improve representativeness of sample in sample design. Balanced repeated replication method is one of important methods in variance estimation. This paper expatiates the theory of Fay balanced repeated replication, then we improve this method. In the end, we use a practical example to show the application of this method.