GROSS ERROR-DETECTION WHEN VARIANCE-COVARIANCE MATRICES ARE UNKNOWN

Equations introduced here identify measurement biases and process leak s, when gross errors exist in measured process variables and the varia nce-covariance matrix of the measurements, SIGMA, is unknown. SIGMA is estimated by the sample variance, S, using process data. For an unkno wn SIGMA, the global test statistic is the well-known Hotelling T2 sta tistic. Its power function has a noncentral F-distribution. For compon ent tests used for specific identification of measurement biases and n odal leaks, two tests are presented with SIGMA 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 ha s a student t-distribution. The power functions for both component tes ts are provided. Process examples and a Monte Carlo simulation study p resented demonstrate the use and performance of these statistical equa tions in identifying biases and process leaks.