Guaranteed Conditional Performance of Control Charts via Bootstrap Methods

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

Some invariant test procedures for detection of structural changes; behavior under alternatives

summary:Regression- and scale-invariant $M$-test procedures for detection of structural changes in linear regression model was developed and their limit behavior under the null hypothesis was studied in Hušková [9]. In the present paper the limit behavior under local alternatives is studied. More precisely, it is shown that under local alternatives the considered test statistics have asymptotically normal distribution

Some invariant test procedures for detection of structural changes

summary:Regression and scale invariant $M$-test procedures are developed for detection of structural changes in linear regression model. Their limit properties are studied under the null hypothesis