Random sampling with fuzzy replacement

•The proposed method provides a bridge between sampling with and without replacement.•This study provides more reliable modelling by adding a variability in the variance.•Contrary to the literature, variability is added to the variance in sampling with replacement.•With this study, the sampling command of many statistical software can be easily updated. In this study, the probability of selecting unit again of the selecting sample is determined by the fuzzification parameter. Accordingly, a random sampling method has been proposed providing a transition between with replacement or without replacement of selecting sample. Especially, this paper provides a bridge between sampling with and without replacement with the fuzzification parameter which takes values in the range [0,1]. When it is zero, the proposed method performs as 'without replacement', and when it is one, it performs 'with replacement'. A simulation study is carried out to examine the performance of the proposed method and it is carefully studied how is the behavior of the difference between the effective sample size, the expectation of sample size, and the actual sample size. In real life problems modelling, only two different random sampling is performed in the literature. However, this study provides more reliable modelling by adding a variability in the variance. Lastly, a scenario is presented for which the introduced sampling design is sensible to be implemented and it produces some desire properties.