Enhanced Multivariate Exponentially Weighted Moving Average Control Charts for Monitoring Gumbel Bivariate Exponential‐Distributed Data

Although one‐sided exponential weighted moving average (EWMA) control charts can effectively monitor high‐quality processes modeled by the exponential distribution, there is a lack of effective schemes for monitoring multivariate high‐quality processes under Gumbel's bivariate exponential (GBE) distribution. In this study, two multivariate EWMA (MEWMA) control charts are designed to effectively monitor GBE‐distributed data when interest is focused on specific parameter shift directions. By truncating the monitoring statistics and the raw GBE‐distributed data, respectively, the proposed MEWMA‐GBE charts reduce sensitivity to parameter shifts in directions that are not of interest, thereby improving monitoring efficiency. The average run length (ARL) properties of the proposed MEWMA‐GBE charts are evaluated through Monte Carlo simulation and compared with the existing MEWMA‐GBE charts. The simulation results demonstrate that the proposed MEWMA chart with the truncation method is generally more sensitive than the existing MEWMA chart when monitoring mean parameter shifts in GBE data across different scenarios, particularly in downward shift cases. Furthermore, several practical guidelines are provided to support the implementation of the proposed MEWMA‐GBE chart. Finally, a real‐world example is presented to illustrate the implementation of the proposed MEWMA‐GBE charts in practical monitoring.