Adaptive CUSUM control charts for efficient monitoring of process dispersion

An adaptive cumulative sum (ACUSUM) control chart is an advance form of the classical CUSUM control chart to identify different sizes of shift in the process parameters (location and/or dispersion). In the continuation of the ACUSUM control chart, this study also proposed ACUSUM control charts to enhance the performance of the process dispersion for a broad range of shift. The proposed ACUSUM control charts methodologies are based on the dispersion CUSUM statistic, score (Huber and Bi-square) functions, generalized likelihood ratio test, and nonlinear optimization technique. The use of dispersion CUSUM statistic helps to distinguish a specific shift as the classical CUSUM statistic does, the score functions, the nonlinear optimization technique and generalized likelihood ratio test enhance the ability of the proposed ACUSUM control charts to distinguish a shift of different size. For the assessment of control charts, run length (RL) measure is used, and it is generated by developing an algorithm in MATLAB through Monte Carlo simulation method. Further, average of RL is utilized to carry out comparative analysis of control charts for a single shift, while for a certain range of shift (comprehensive analysis), extra quadratic loss (EQL), relative average run length (ARL), and performance comparison index (PCI) measures are used. Findings based on numerical results and visual presentations reveal the superiority of the proposed control charts against some existing control charts. Moreover, for real-world point of assessment, the proposed control chart is implemented with numerical data to show the worth over other control charts.