The maximum‐power test for gross errors in the original constraints in data reconciliation

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Abstract
The detection of gross errors in the reconciliation of process measurement data is an important step in removing their distorting effects on the corrected data. Tests of maximum power (MP), based on the normal distribution, are known for the detection of gross errors in the measurements and for the constraints, but only for those remaining after the removal of unmeasured flows. Here, the MP tests are derived for the original constraints, which allows the direct detection of gross errors in species balances around individual process units. It is shown that the square of the MP test statistic is precisely equal to the reduction in the weighted sum of squares of the adjustments which results from the deletion of that constraint. The test is illustrated with two examples.