Fast initial response-based r-EWMA single control chart for joint monitoring of location and scale parameters with nonlinear multiple quality characteristics

Monitoring shifts in location and scale (L&S) parameters during production processes is crucial, and control charts serve as indispensable tools for this purpose. They can be categorized into single chart and two-chart, with the former being more advantageous due to their simplicity and effectiveness in identifying changes. The problem at issue is that existing methods for monitoring unknown process distributions inadequately address simultaneous shifts in both L&S parameters. This paper presents the rank-based Exponentially Weighted Moving Average (r-EWMA) control chart, designed to monitor multiple processes without relying on the conventional premise of a multivariate normal distribution. This method combines rank-based statistics with local statistics derived from the k-nearest neighbors method and employs an EWMA control scheme. To assess the effectiveness of the proposed scheme, a Monte Carlo simulation has been executed and real-world case studies have been examined. The results of the simulation demonstrate that r-EWMA outperforms comparative control charts regarding the Median Run Length (MRL), when detecting out-of-control (OC) signals across various changes in non-normally distributed and nonlinear mixed distributions. Two case studies further validate the superiority of r-EWMA in handling shifts in L&S parameters under unknown process distributions, particularly when considering nonlinear correlations in multiple quality characteristics.