Paired Individual CUSUM Charts for Monitoring Gumbel’s Bivariate Exponential Data

This article introduces CUSUM charts for monitoring Gumbel’s bivariate exponential (GBE) data, focusing on the shortcomings of existing multivariate CUSUM (MCUSUM) chart in diagnosing out-of-control signals. To address this, we propose new paired individual CUSUM charts tailored for detecting decreases or increases in the process means of GBE data. We assess the performance of these control charts in terms of average run-length and relative mean index. The results demonstrate that the newly developed charts generally outperform MCUSUM charts in detecting decreases, while maintaining comparable performance for increases, in the process means. An example using real data illustrates the implementation of the proposed charts and compares them with existing MCUSUM chart.