Control chart for mean and standard deviation for observation following SAR (1,1) process

Control charts are designed to detect assignable causes of variation that may occur in production processes. When traditional control charts are used there is the implicit assumption that observations are independently and identically distributed over time. It is also assumed that the probability distribution representing the observations has a known functional form and is constant over time. However, in practice, observations generated by continuous as well as discrete production processes are often serially correlated. Autocorrelation not only violates the independence assumption of traditional control charts but also can affect the performance of control charts adversely. For monitoring in-control state of such processes, the traditional control charts fail and often lead to false out-of-control alarms.This point has received considerable attention in the past few decades. In this paper we developed control charts for the sample mean and sample standard deviation, when the observations are taken over a grid on a two dimensional surface. It has been assumed that the observations follow Spatial Autoregressive (SAR) process.