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Gross error detection when variance‐covariance matrices are unknown
Author(s) -
Rollins D. K.,
Davis J. F.
Publication year - 1993
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690390810
Subject(s) - statistic , mathematics , statistics , covariance matrix , covariance , monte carlo method , test statistic , variance (accounting) , sampling distribution , sample variance , statistical hypothesis testing , accounting , business
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 T 2 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.