On the effect of measurement errors in regression-adjusted monitoring of multistage manufacturing processes

• We investigate effect of measurement errors in regression-adjusted process monitoring.
• We compare performance of the OLS estimator and the TLS estimator.
• Measurement errors lead to bias in model estimation.
• The TLS estimator performs better when similar and large measurement errors exist.

A critical challenge in multistage process monitoring is the complex relationships between quality characteristics at different stages. A popular method to deal with this problem is regression adjustment in which each quality characteristic is regressed on its preceding quality characteristics and the resulting residual is monitored to detect changes in local variations. However, the performance of this method depends on the accuracy of the regression coefficient estimation. One source of the estimation errors is measurement errors which commonly exist in practice. To provide guidance on the use of regression-adjusted monitoring methods, this study investigates the effect of measurement errors on the bias of regression estimation theoretically and numerically. Two estimators, the ordinary least squares (OLS) estimator and the total least squares (TLS) estimator, are compared, and insights regarding their performance are obtained.