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On the stochastic behaviour of the run length of EWMA control schemes for the mean of correlated output in the presence of shifts in sigma

Morais, M. C. ; Okhrin, Y.; Pacheco, António; Schmid, W.

Statistics & Decisions, 24(4) (2006), 397-413

This paper discusses in detail the impact of shifts on the process variance (sigma^2) on the run length (RL) of modified upper one-sided EWMA charts for the process mean (mu) when the output is correlated.
Quite apart from the relevance of a process variance change in its own right, a dilation in sigma^2 can cause an undesirable stochastic decrease in the detection speed of some specific shifts in mu. This and other stochastic results are proved and illustrated with a few examples.