A self-starting control chart for simultaneous monitoring of mean and variance of autocorrelated simple linear profile

Sometimes, quality of a process can be described by a functional relationship between response variables and explanatory variables which called profile. In some situations, there is an autocorrelation structure within a profile. Most of the times in real practice there is no enough data to estimate the process parameters. In this case, we can use a self-starting control chart which does not need preliminary data to start monitoring in start-up stages. In this paper, we consider a simple linear profile in the presence of a first order autoregressive (AR(1)) autocorrelation structure within profile and propose a self-starting control chart to monitor mean and variance of a simple linear profile simultaneously.