Two new approaches are presented for improved identification of measurement biases in linear pseudo steady-state processes. Both are designed to detect a change in the mean of a measured variable leading to an inference regarding the presence of a biased measurement. The first method is based on a likelihood ratio test for the presence of a mean shift. The second is based on a Bayesian decision rule (relying on prior distributions for unknown parameters) for the detection of a mean shift. The performance of these two methods is compared with that of a method given by Devanathan et al. (2000). For the process studied, both techniques were found to have higher identification power than the method of Devanathan et al. and appears to have excellent but sightly lower type I error performance than the Devanathan et al. method.