Data processing of small samples is an important and valuable research problem in the electronic equipment test. Because it is difficult and complex to determine the probability distribution of small samples, it is difficult to use the traditional probability theory to process the samples and assess the degree of uncertainty. Using the grey relational theory and the norm theory, the grey distance information approach, which is based on the grey distance information quantity of a sample and the average grey distance information quantity of the samples, is proposed in this article. The definitions of the grey distance information quantity of a sample and the average grey distance information quantity of the samples, with their characteristics and algorithms, are introduced. The correlative problems, including the algorithm of estimated value, the standard deviation, and the acceptance and rejection criteria of the samples and estimated results, are also proposed. Moreover, the information whitening ratio is introduced to select the weight algorithm and to compare the different samples. Several examples are given to demonstrate the application of the proposed approach. The examples show that the proposed approach, which has no demand for the probability distribution of small samples, is feasible and effective. Data processing of small samples is an important and valuable research problem in the electronic equipment test. Because it is difficult and complex to determine the probability distribution of small samples, it is difficult to use the traditional probability theory to process the samples and assess the degree of the uncertainty. Using the gray relational theory and the norm theory, the gray distance information approach, which is based on the gray distance information quantity of a sample and the average gray distance information quantity of the samples, is proposed in this article. The definitions of the gray distance information quantity of a sample and the average gray distance information quantity of the samples, with their characteristics and algorithms, are introduced. The correlative problems, including the algorithm of estimated value, the standard deviation, and the acceptance and rejection criteria of the samples and estimated results, are also proposed n whitening ratio is introduced to select the weight algorithm and to compare the different samples. Several examples are demonstrated to demonstrate the application of the proposed approach. which examples show that the proposed approach, which has no demand for the probability distribution of small samples. is feasible and effective.