Statistical Process Control and Data Analytics, 8th Edition

Appendix IAutocorrelation

A basic assumption in constructing control charts, such as those for $\overline{X}$ R, moving $\overline{X}$ and moving R, is that the individual data points used are independent of one another. When data are taken in order, there is often a tendency for the observations made close together in time or space to be more alike than those taken further apart. There is often a technological reason for this serial dependence or ‘autocorrelation’ in the data. For example, physical mixing, residence time or capacitance can produce autocorrelation in continuous processes.

Autocorrelation may be due to shift or day of week effects or may be due to identifiable causes that are not related to the ‘time’ order of the data. When groups of batches of material ...