Monitoring bivariate exponential lifetime processes with CUSUM chart

This paper addresses the challenge of monitoring non-normal, correlated lifetime data in multivariate processes. We propose a new cumulative sum (CUSUM) chart framework for bivariate exponential processes linked by an FGM copula. Since the derived likelihood ratio statistic follows a chi-squared distribution, we apply three normalizing transformations—Fisher, cube-root, and logarithmic—to adapt it for standard CUSUM monitoring, comparing these against a direct, untransformed approach. Through simulation-based optimization and sensitivity analysis, we find that all charts require careful parameter tuning specific to the process, but the CUSUM-Fisher chart consistently demonstrates superior performance, detecting shifts faster and more reliably than its counterparts. We provide optimized design parameters for practical use and validate the method with an application in automotive manufacturing, establishing it as an effective tool for early fault detection in complex, real-world settings.