文中首先提出兩種對於線性系統抽樣作修正的抽樣方法, 均衡餘數系統抽樣是結合均衡系統抽樣與餘數線性系統抽樣方式的抽樣方法, 而環狀均衡餘數系統抽樣是結合均衡系統抽樣與環狀餘數系統抽樣方式的抽樣方法。這兩種抽樣方法皆可用於母體數被樣本數整除或不整除的情況。我們推導出這兩種新抽樣方法的包含機率並導出母體均值的不偏估計式與其變異數估計。將這兩種抽樣方法與餘數線性系統抽樣、環狀餘數系統抽樣與簡單隨機抽樣在數種母體比較其有效性。由於, 環狀餘數系統抽樣的有效性不盡理想, 因此再對環狀餘數系統抽樣作了一些修正。

　　In this paper, we propose two sampling procedures to modify linear systematic sampling. One is balanced remainder systematic sampling which is a combination of remainder linear systematic sampling and balanced systematic sampling, and another is circular balanced remainder systematic sampling which is a modification of remainder circular systematic sampling and balanced systematic sampling. All procedures can be used when the population size is not a multiple of the sample size or N=nk. The inclusion probability of the two sampling procedures and the corresponding estimator of population mean and its variance estimator are derived. We discuss the efficiency of the proposed sampling design with respect to simple random sampling, remainder linear systematic sampling, and remainder circular systematic sampling under various types of populations. However, efficiency of circular balanced remainder systematic sampling is not good enough. A slight modification of circular balanced remainder systematic sampling at end.

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