Gross error detection when variance-covariance matrices are unknown

Authors

  • D. K. Rollins,

    1. Dept. of Chemical Engineering, The Ohio State University, Columbus, OH 43210
    Current affiliation:
    1. Depts. of Chemical Engineering and Statistics, lowa State University, Ames, IA 50011
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  • J. F. Davis

    Corresponding author
    1. Dept. of Chemical Engineering, The Ohio State University, Columbus, OH 43210
    • Dept. of Chemical Engineering, The Ohio State University, Columbus, OH 43210
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Abstract

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.

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