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Selecting multiple samples from the same sampling frame presents many problems. Efficient estimation of periodic change often requires the use of fixed panel designs or one-level rotation samples with large overlaps between samples (see Chapter 8 for details). However, most business populations are subject to rapid changes due to births, deaths, splits, mergers, and changes in size or activity. List frames and samples must be periodically updated to reflect such changes. The desire to draw up-to-date samples may seem incompatible with planned overlaps between successive samples. This chapter discusses the permanent random number (PRN) technique, which provides a simple solution to this problem. Even when frames are updated or surveys redesigned, the PRN technique generally produces sizable overlap between successive samples. For Australia's Commonwealth Bureau of Census and Statistics, Brewer et al. (1972) suggested the use of PRNs in connection with Poisson sampling. Independent of the Australian work, Atmer et al. (1975) introduced a PRN technique for simple random sampling without replacement (srswor) at Statistics Sweden. In most