Virtually expanded sample estimation method for extremely small-scale sample test

Bootstrap method was used to estimate small-scale sample test, whose samples exceed 10 in number. But for a large-scale complicated structure, the sample test consists of only 1 or 2 samples. We aim to provide an estimation method that can utilize Bootstrap method to estimate an extremely small-scale sample test. We provide a virtually expanded sample estimation method that can do so. If the shape of experimentally determined life distribution of similar samples and their standard deviation are known, the original 1 or 2 samples can be expanded to 13; the mean of 13 virtually expanded samples is kept the same as that of the original 1 or 2 samples; the standard deviation of 13 virtually expanded samples and that of similar samples are also kept the same. Based on these virtually expanded samples, the modified empirical cumulative distribution function can be built. At last, the inference about unknown parameter can be obtained by use of the Bootstrap method. An example is provided to show the application of the virtually expanded sample estimation method presented in this paper.