Guaranteed Conditional Performance of Control Charts via Bootstrap Methods

TL;DR

This paper introduces a bootstrap-based adjustment method for control charts that guarantees conditional performance despite estimation errors, applicable across various chart types and robust to model misspecification.

Contribution

It proposes a novel bootstrap adjustment technique that ensures control chart performance guarantees conditioned on estimated in-control states, enhancing reliability in practical applications.

Findings

The method provides probabilistic guarantees on control chart performance.

Simulation studies demonstrate improved reliability and robustness.

Applicable to diverse control chart types and models.

Abstract

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.