Toward Robust Monitoring of Exponential Processes: A Memory‐Driven Scheme for Zero‐ and Steady‐State Scenarios

ABSTRACT The most difficult aspect in statistical process monitoring is an extensive evaluation of memory‐type charts in zero‐state and steady‐state scenarios. In actual practice, a chart does well at the zero state but poorly at the steady state. Nevertheless, some researchers argued for the superiority of their charts merely based on performance under zero‐state conditions, which may not hold true with respect to long‐term monitoring stability. However, recent literature underlines that a chart can be regarded as superior only if it performs well both in zero‐state and in steady‐state scenarios. The novel Cumulative Sum (CUSUM) chart is accordingly constructed based on variable transformations under an exponential distribution, hence termed . The chart has been developed particularly for maximizing effectiveness in both zero‐state and steady‐state conditions. The Monte Carlo simulations have been carried out to assess the performance and demonstrate the utility of the approach. To thoroughly assess its performance, various traditionally accepted metrics, average run length (ARL), standard deviation of run length (SDRL), median run length (MDRL), extra quadratic loss (EQL), performance comparison index (PCI), and relative ARL (RARL), are applied. The proposed chart is compared with existing alternatives based on the metrics included. The analysis establishes that the is superior to its rivals in terms of shift detection under both zero‐state and steady‐state scenarios. The efficacy of the proposed chart has been illustrated through its application to two real healthcare datasets, which have verified its practicality for process monitoring.