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On the impact of falsely assuming i.i.d. output in the probability of misleading signals

Morais, M. C. ; Ramos, Patrícia F.; Pacheco, António; Schmid, W.

REVSTAT – Statistical Journal, 12(3) (2014), 221-245

Misleading signals (MS) are valid alarms which correspond to the misinterpretation of a shift in the process mean (resp. variance) as a shift in the process variance (resp.
mean), when we deal with simultaneous schemes for these two parameters. MS can be fairly frequent, as reported by some authors, and occur for instance 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; or
– 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.

This paper illustrates how (un)reliable are the traditional simultaneous Shewhart- and EWMA-type schemes in identifying which parameter has changed, under the false assumption of independence, namely when the output process within each sample follows AR(1), AR(2) or ARMA (1,1) models. This is done by means of Monte Carlo simulation and the estimation of the probability of a misleading signal (PMS). Finally, we go on to compare these estimates of PMS with the values of the PMS of simultaneous Shewhart- and EWMA-type residual schemes whose control statistics take into account the autocorrelation structure of the output process.