Statistical design and simulation of a recursive auxiliary variable based EWMA monitoring scheme

This paper introduces a recursive auxiliary variable based EWMA statistic that adaptively updates auxiliary variables, with distributional derivations, simulation based calibration, and real process validation in one unified monitoring design. In modern industrial processes, incorporating information from auxiliary variables is essential for improving the sensitivity and reliability of process monitoring schemes. This study proposes an auxiliary variable based exponentially weighted moving average monitoring scheme for detecting changes in the mean of a study variable observed with two auxiliary variables. The proposed statistic replaces fixed reference means of these variables with recursive exponentially weighted estimates, so the monitoring rule can adapt when their behaviour changes during Phase II operation. This structure uses correlation information more effectively and reduces false signals caused by shifts in the auxiliary variables. The study derives the mean, variance, and distributional form of the statistic under the tri-variate normal model and under simultaneous shifts in the study and auxiliary variables. The roles of charting parameters are examined, and several existing monitoring charts arise as special cases. Since the control limit coefficient is not available in closed form, a stochastic approximation algorithm is used to calibrate limits for a target in control average run length (ARL). Extensive Monte Carlo experiments compare performance across correlation patterns, smoothing constants, updating weights, and shift configurations using ARL, standard deviation of run length, percentiles, and global measures. The results show that the proposed chart gives a balanced response when the auxiliary variables are stable or shifted. A continuous stirred tank reactor example further confirms its value for dynamic process monitoring. The method offers a useful computational framework for auxiliary variable sensitive sequential surveillance.