Properties and enhancements of robust likelihood CUSUM control chart

In practice, the robust-likelihood cumulative sum (RLCUSUM) control charts, using truncation of the log-likelihood underpinnings of the CUSUM to ensure robust performance, which perform well to detect small shifts in the mean of heavy-tailed processes and have the ability to discount outliers. In this article, we evaluate the properties of RLCUSUM control schemes used to monitor the mean of contaminated normally distributed processes. An optimal design procedure for RLCUSUM control schemes is given, in addition, several enhancements to RLCUSUM are considered. These include a fast initial response feature that makes the RLCUSUM control schemes more sensitive to start-up cases, three types of truncation of RLCUSUM, which are cut off by horizontal ray, horizontal segment and oblique line respectively against both large and small shifts in a non-normality process. An extensive comparison with the conventional CUSUM and generalized likelihood ratio CUSUM (GCUSUM) in terms of average run length (ARL), shows that the RLCUSUM is more robust than the conventional CUSUM and GCUSUM control charts for its ARLs are monotonous against the process mean. Especially, the oblique line truncated RLCUSUM control chart has the best overall performance in the various cases of shifts. A final application based on monitoring packing 250 g containers is used to illustrate the implementation of RLCUSUM control schemes.