I am trying to determine the effect of autocorrelation on the performance of standard control chart, but first have to model the auto-correlative structure of the standard control chart for the data set before I use the residuals for the control chart.
Auto-correlative data are, in most cases, time series which depend on time. For such data successional time series are applied in most times. So, you can build a regression model based on the succession order and the value. Most of times the model is non-linear and most importantly, when you get a new data you should know where it belongs in the succession series.
You should first of all use a linear model.
I suggest you perform a linear regression by means of an ARMA model (Auto-Regressive Moving Average model).
If I take X to denote the input and Y to denote the output, the ARMA(1,1) reads
Y(n+1)=a*Y(n)+b*X(n+1),
while the ARMA(1,2) reads
Y(n+1)=a*Y(n)+b*X(n+1)+c*X(n).
Theses two ARMA models correspond actually to an impulse response function between the input and the output defined with an exponential decay, which is the most simple description.
I have applied this technique to water pore pressure measurements in earth-dams (see attached).
Article Impulse response function analysis of pore pressures
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