A Short Note on SANS

In the SANS [O'Brien, G. G., H. S. Sherwood, R. E. Trueman. 1960. SANS, a simplified account numbering system. New York University J. Retailing (April); Trueman, R. E. 1961. Development of an efficient account-numbering method. Management Sci.7 265.] system, which attempts to reduce alphabetical and numerical files to a single file, problems of overflow occur when new members fall between two existing members with consecutive numbers. A method is given for determining the probability distributions of overflows in a cell of size 2^k, and the mean value and variance of these distributions as functions of the growth of the system. In this paper we use some of the results of another paper on a related problem [Jewell, W. S. 1962. A filing problem. Management Sci.8 210.] to formulate the problem and obtain a solution. The mathematical treatment outlined can be extended to the calculation of other important parameters, including the expected number of entries which will be out-of-order within a group of areas, and the probability that the last overflow area will itself have an overflow.