Chaturvedi, Anoop; Dubey, Ashutosh Kumar; and Gulati, Chandra, Statistical process control for autocorrelated data on grid, National Institute for Applied Statistics Research Australia, University of Wollongong, Working Paper 13-15, 2015, 9.
Assumptions of normality and independence are key assumptions made in the development and use of control charts. However for much industrial data, the assumption of independence is hard to justify. Control charts for the sample mean and sample standard deviation are obtained, when the observations are taken over a grid on a two-dimensional surface. It is assumed that the observations follow an autoregressive process of order one in both the directions. The results have been applied to road pavement data on road corse thickness observed on a two dimensional grid.