A Novel S 2 ‐EWMA M Control Chart for Enhanced Process Dispersion Monitoring Using Möbius Transformation: Application to the Human Development Index

ABSTRACT Process location parameter shifts are commonly detected using conventional cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts (CCs). However, monitoring shifts in the process dispersion parameter is equally important. To detect shifts in the process dispersion parameter, traditional CUSUM and EWMA CCs are typically used with transformations such as the logarithmic transformation. To monitor the process dispersion parameter effectively, this study proposes a novel method that combines the classical EWMA CC with the Möbius transformation, which has not previously been used in CCs. This study addresses a gap in the literature by investigating the unrealized potential of the Möbius transformation in process monitoring. The resulting CC, denoted by , provides a new way to increase sensitivity to small shifts in the dispersion parameter. The average run length is used as the primary performance metric to assess the proposed CC for a single shift. A Monte Carlo simulation‐based Python algorithm is developed to compute this performance measure. Numerical results and graphical analysis show that the proposed CC performs better than some existing CCs. Real‐world human development index data are used to demonstrate its practical relevance and effectiveness.