Equations introduced here identify measurement biases and process leaks, when gross errors exist in measured process variables and the variance-covariance matrix of the measurements, Σ, is unknown. Σ is estimated by the sample variance, S, using process data.

For an unknown Σ, the global test statistic is the well-known Hotelling T2 statistic. Its power function has a noncentral F-distribution. For component tests used for specific identification of measurement biases and nodal leaks, two tests are presented with Σ unknown. The first test is independent of the number of component tests, k, and is given by a statistic with an F-distribution. The second test depends on k and has a student t-distribution. The power functions for both component tests are provided. Process examples and a Monte Carlo simulation study presented demonstrate the use and performance of these statistical equations in identifying biases and process leaks.