Optimizing process monitoring: Adaptive CUSUM control chart with hybrid score functions

Abstract

The Cumulative Sum (CUSUM) Control Chart (CC) is a powerful tool for detecting small to moderate shifts in process parameters. While the traditional CUSUM CC determines the shift magnitude, it may not effectively handle a wide range of shifts encountered in real-world applications. To address this, an adaptive CUSUM (ACUSUM) CC has been developed. This study introduces a novel ACUSUM CC by integrating Huber and Bi-square score functions, which possess unique attributes such as monotonicity and redescending properties. Despite their individual advantages, limited research has explored their combined use in ACUSUM CC design. By amalgamating these functions into a unified formulation, we propose an innovative ACUSUM CC capable of effectively monitoring shifts of varying magnitudes in the process location parameter. The proposed CC is assessed through Monte Carlo simulations under both zero-state and steady-state conditions. Key performance metrics, including Average Run Length (ARL), median run length (MDRL), and Standard Deviation of Run Length (SDRL), are used to evaluate the ability of the proposed CC to detect individual shifts. Additionally, relative ARL, extra quadratic loss, and the process capability index are utilized to measure efficiency across a range of shifts, ensuring a comprehensive performance evaluation. A comparative analysis based on performance metrics and visual representations highlights the superior performance of the proposed CC over conventional methods. Furthermore, its application in energy usage analysis demonstrates its effectiveness in detecting anomalies, supporting proactive decision-making for optimizing energy consumption and resource allocation. These findings confirm the practicality, reliability, and enhanced monitoring capabilities of the proposed ACUSUM CC in real-world industrial and environmental scenarios.