To use control charts in practice, the in-control state usually has to be
estimated. This estimation has a detrimental effect on the performance of
control charts, which is often measured for example by the false alarm
probability or the average run length. We suggest an adjustment of the
monitoring schemes to overcome these problems. It guarantees, with a certain
probability, a conditional performance given the estimated in-control state.
The suggested method is based on bootstrapping the data used to estimate the
in-control state. The method applies to different types of control charts, and
also works with charts based on regression models, survival models, etc. If a
nonparametric bootstrap is used, the method is robust to model errors. We show
large sample properties of the adjustment. The usefulness of our approach is
demonstrated through simulation studies.Comment: 21 pages, 5 figure
