Imprecision of sensors is one of the main causes of poor control and process performance. Often, instrument measurement bias and variance change over the time and online calibration/re-estimation is necessary. Originated from a real industrial application problem, this paper proposed a Bayesian approach to determine the inconsistency of sensors, based on mass-balance principles. A mass-balance factor model is then introduced, where the factor analysis method is used to determine initial values for estimating instrument noise and process disturbance variance. Because of the structural constraint of mass-balance equations, a gray-box estimation procedure must be adopted for which Bayesian network estimation via the expectation-maximization (EM) algorithm is a very suitable method. Therefore, this paper uses factor analysis to determine the initial values, and, afterward, estimates process and sensor variance by means of Bayesian estimation. After estimating the process and instrument variance, the process steady state and instrument bias can be similarly estimated.