Two New Nonparametric EWMA Control Charts for Joint Monitoring of Location and Scale

ABSTRACT Process data in modern industrial and service environments are frequently non‐normal and may exhibit concurrent shifts in both location and scale. In the control‐charting literature, two limitations are well recognized. First, most parametric joint‐monitoring charts rely on distributional assumptions; when these assumptions are violated, they can exhibit misleading performance. This motivates the development of nonparametric charts, which retain validity regardless of the underlying process distribution. Second, although many nonparametric charts exist for monitoring location or scale separately, relatively few methods provide joint monitoring, even though simultaneous shifts in location and scale occur frequently in practice. To fill this gap, we develop two new Phase II nonparametric exponentially weighted moving average (EWMA) Lepage‐type control charts that jointly monitor location and scale by combining (i) the van der Waerden (VW) and Ansari–Bradley (AB) tests, and (ii) the VW and Mood tests. Regression‐based analytical formulas are provided for computing charting constants corresponding to a desired in‐control ARL, eliminating the need for additional simulation at the implementation stage. Extensive Monte Carlo studies under normal, lognormal, Laplace, and logistic distributions are conducted to compare the statistical performance of the proposed charts with two existing competitors: the classical EWMA Lepage chart and the EWMA Cucconi chart. We find that the proposed VW–Mood chart delivers the strongest overall performance, particularly for detecting scale shifts and simultaneous location–scale shifts. The VW–AB chart also improves upon the classical EWMA Lepage chart and performs competitively with the EWMA Cucconi chart in several scenarios. Overall performance is further evaluated using the expected relative ARL (ERARL), under which the VW–Mood chart consistently achieves the lowest values across distributions and design settings, indicating robust detection capability over a wide range of joint location–scale shifts. In addition, post‐signal diagnostic analysis shows that the VW–Mood chart provides the most balanced classification accuracy for scale and simultaneous shifts, while the VW–AB chart is particularly effective for pure location shifts. A real‐data application further demonstrates the practicality of both proposed charts.