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

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