Distribution-free cumulative sum control charts using bootstrap-based control limits

TL;DR

This paper introduces a distribution-free bootstrap-based method for CUSUM control charts that adaptively determines control limits, improving robustness and accuracy in process monitoring without assuming specific distributional forms.

Contribution

It proposes a novel bootstrap-based approach for setting control limits in CUSUM charts, making them distribution-free and more reliable in non-normal conditions.

Findings

The method maintains desired in-control average run length across various distributions.

It outperforms traditional CUSUM charts under non-normal data conditions.

The approach is robust and adaptable to different process distributions.

Abstract

This paper deals with phase II, univariate, statistical process control when a set of in-control data is available, and when both the in-control and out-of-control distributions of the process are unknown. Existing process control techniques typically require substantial knowledge about the in-control and out-of-control distributions of the process, which is often difficult to obtain in practice. We propose (a) using a sequence of control limits for the cumulative sum (CUSUM) control charts, where the control limits are determined by the conditional distribution of the CUSUM statistic given the last time it was zero, and (b) estimating the control limits by bootstrap. Traditionally, the CUSUM control chart uses a single control limit, which is obtained under the assumption that the in-control and out-of-control distributions of the process are Normal. When the normality assumption is not valid, which is often true in applications, the actual in-control average run length, defined to be the expected time duration before the control chart signals a process change, is quite different from the nominal in-control average run length. This limitation is mostly eliminated in the proposed procedure, which is distribution-free and robust against different choices of the in-control and out-of-control distributions.