Detection of Gross Errors in Process Data

Process data reconciliation and rectification and their relationship to process performance monitoring functions have been the subject of many recent publications. [See, for instance, Mah (1981) for a review of these publications.] In this note we shall confine our attention to process data reconciliation subject to linear constraints, and more specifically, to the problem of detecting and identifying the presence of one or more gross errors in the process data. Generally speaking, process measurements are corrupted by two types of errors: Random errors which are commonly assumed to be independently and normally distributed with zero mean, and gross errors which are caused by non-random events such as instrument biases, malfunctioning measuring devices, incomplete or inaccurate process models. Let y be an (n X 1) vector of measured variables, b be a (p X l) vector of unknown parameters, D be an (n x p) matrix of known constants, for which rank (D) = p 5 n, and E be an (n X 1) vector of errors distributed normally with a zero mean vector and a known variance-covariance matrix Q. Then in the absence of gross errors, the basic model is