Two new nonparametric CUSUM control charts for joint monitoring of location and scale

This paper proposes two new Phase II cumulative sum (CUSUM) control charts for detecting shifts in the location and/or scale parameters of continuous processes. Both charts are constructed using Lepage-type statistics. The first chart utilizes the combination of van der Waerden (VW) and Ansari–Bradley (AB) tests, while the second utilizes the combination of VW and Mood tests. The performance of the proposed charts is evaluated numerically in terms of average run length and compared with two existing competitive charts under four different distributional models. In addition, the statistical design of the proposed charts is examined in detail, with particular attention to the effect of the reference value, and practical empirical guidelines for their implementation are provided. The results indicate that, across all considered distributions, the CUSUM chart based on the VW and Mood tests consistently outperforms its main competitors. Finally, the practical usefulness of the proposed charts is demonstrated through two real-data applications involving a hard-bake manufacturing process and a customer service time process.