On the monitoring of linear mixed Berkson profiles in the presence of within-profile correlation

This article develops a Phase II monitoring framework for linear mixed Berkson profiles with within-profile correlation. The proposed model jointly accounts for Berkson-type covariate measurement error, random effects, and correlated within-profile errors, from which the induced covariance matrix of the response vector is derived. Based on this structure, the generalized least squares (GLS) estimator of the fixed-effect vector and its covariance matrix are obtained. Four existing multivariate exponentially weighted moving average (MEWMA)-type schemes, namely MEWMA, dMEWMA, MEC, and AMEWMA, are adapted to the proposed framework by using the GLS estimator and the model-corrected covariance matrix. Monte Carlo simulations are conducted under both known-parameter and Phase-I-estimated settings. The known-parameter study provides a baseline comparison of zero-state detection performance and overall performance over a range of shifts, whereas the Phase-I-estimated study examines the effect of parameter estimation on control-limit calibration and recalibrated Phase II monitoring. The results show that AMEWMA has the most stable overall performance, while MEC is mainly advantageous for very small shifts in the regression parameters.