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Counted data control charts sensitive to sudden increases of the summary statistic

Morais, M. C. ; Pacheco, António

Statistical Review, 1 (1999), 25-45
http://www.cs.math.ist.utl.pt/s84.www/cs/lcg/problog/99-MMAP-ine.pdf

The usual practice in maintaining an upper one-sided control chart is to give an
out-of-control signal whenever the summary statistic exceeds the upper control
limit. However, intuition would suggest that a sudden increase in the summary
statistic should also be taken as an indication of a deterioration in the production
process, even if that summary statistic is not above the upper control limit.
Using previously established results it is shown that: a) the decision rule proposed
here speeds up the detection of increases in the expected count of defects per
sample of fixed size s by an upper one-sided Poisson CUSUM chart; and b) the
associated run length has interesting stochastic monotonicity properties