A Robust-Likelihood Cumulative Sum Chart

Abstract

In practice, the cumulative sum (CUSUM) control chart is often used to detect small shifts in the mean of a normally distributed process, but it performs poorly for thick-tailed processes and for large shifts. This article provides a robust-likelihood cumulative sum (RLCUSUM) chart that discounts outliers and yet has the ability to detect large shifts quickly. The new chart is motivated by the likelihood underpinnings of the CUSUM. It is based on the likelihood of a variate constructed to ensure robust performance of the resulting chart. The new chart is compared with the conventional CUSUM in terms of average run length, with the finding that the RLCUSUM is much better than the conventional CUSUM, especially for large shifts. For small shifts, the two charts are essentially equivalent. We study the properties of the conditional limiting distribution. A final application of the RLCUSUM in assessing livestock disease shows that the method is applicable in process control.