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Assessing the impact of autocorrelation in misleading signals in simultaneous residual schemes for the process mean and variance: a stochastic ordering approach

Misleading signals (MS) correspond to the misinterpretation of a shift in the process mean (variance) as a shift in the process variance (mean). MS occur when:
- the individual chart for the mean triggers a signal before the one for the variance, even though the process mean is on-target and the variance is off-target;
- the individual chart for the variance triggers a signal before the one for the mean, although the variance is in-control and the process mean is out-of-control.

MS can lead to a misdiagnosis of assignable causes and to incorrect actions to bring the process back to target. Unsurprisingly, the performance assessment of simultaneous schemes for the process mean and variance requires not only the use of run length (RL) related performance measures, but also the probability of misleading signals (PMS). We assess the impact of autocorrelation on the PMS of simultaneous Shewhart and EWMA residual schemes for the mean and variance of stationary AR(1), AR(2) and ARMA(1,1) processes. This assessment is done by means of some stochastic ordering results and some illustrations.