Misleading signals in simultaneous residual schemes for the mean and variance of a stationary process

Communications in Statistics-Theory and Methods, 38(16-17) (2009), 2923-2943
http://dx.doi.org/10.1080/03610920902947238

The performance assessment of simultaneous surveillance schemes for the process mean (mu) and variance (sigma^2) requires a special performance measure, in addition to the average run length. It refers to two events which can be likely to happen when such schemes are at use:
1) the individual chart for mu triggers a signal before the one for sigma^2, even though the process mean is on-target and the variance is off-target;
2) the constituent chart for sigma^2 triggers a signal before the one for mu, although the variance is in-control and the process mean is out-of-control.

These are called misleading signals since they correspond to a misinterpretation of a mean (variance) change as a shift in the process variance (mean) and can lead the quality control operator or engineer to a misdiagnosis of assignable causes and to deploy incorrect actions to bring the process back to target.

This article discusses the impact of autocorrelation on the probability of misleading signals of simultaneous Shewhart and EWMA residual schemes for the mean and variance of a stationary process.