One-cluster sampling designs for an autocorrelated population

The variance of the sampling distribution of the sample mean is derived for two sampling designs in which a single cluster is randomly drawn from an autocorrelated population. The derivations are motivated by potential applications to statistical quality control, where a "one-cluster" sampling design may often be used because of ease of implementation, and where it is likely that process output is autocorrelated Scenarios in statistical process control for which either non-overlapping or overlapping clusters are appropriate are described The sampling design variance under non-overlapping clusters is related to the sampling design variance under overlapping clusters through the use of a circular population.