Traditional fixed sampling interval (FSI) nonparametric adaptive exponentially weighted moving average (AEWMA) control charts have limitations in detecting moderate to small shifts, especially when the shift type is unknown or time-varying. Most existing studies also focus on univariate parameter shifts, reducing their effectiveness in complex scenarios. To address these challenges, this paper proposes a variable sampling interval (VSI) nonparametric AEWMA control chart based on a weighted Cucconi statistic, termed the VSI-adaptively weighted EWMA-Cucconi (VSI-AWEC) chart, aimed at enhancing detection of joint location-scale shifts. The proposed chart integrates the Cucconi statistic with a variable sampling mechanism to construct a flexible monitoring framework. Its performance is assessed via Monte Carlo simulations, showing that VSI-AWEC outperforms FSI-based charts inaverage time to signal (ATS) when monitoring joint shifts, and offers improved sensitivity across various shift conditions. The chart's robustness is further validated under diverse distributional settings, and the influence of parameter choices on detection performance is examined. Results demonstrate that the VSI-AWEC chart provides fast and effective signaling without relying on distributional assumptions, and performs particularly well in detecting small shifts.