On the definition of software accuracy in redundant measurement systems

Abstract

Accuracy of measurements is defined as the sum of precision (standard deviation) and bias. Unfortunately, this definition is of little use unless bias is independently assessed. In this article, we extend this classical definition of accuracy of measurements to one of estimators obtained through data reconciliation techniques. Connection to gross error robustness measures, defined earlier by the author, is studied. © 2005 American Institute of Chemical Engineers AIChE J, 2005

Downside financial loss of sensor networks in the presence of gross errors

“…This argument can be verified by looking at the absolute value of the coefficient ␣ i in the expression ␦ p i ( i ) ϭ ␣ i i for the induced bias in stream S 7 caused by an undetected gross error anywhere in the system: stream S 1 has the largest absolute value of ␣ i (0.3774), followed by streams S 6 and S 5 (Ϫ0.2453 and 0.1321, respectively). Note that because streams S 1 and S 7 are part of an equivalent set, 8 the results for biases in streams (1,5), (1,6), and (1, 2, 3) are the same as results for biases in streams (7,5), (7,6), and (7,2,3). In other words, if stream S 1 is replaced by stream S 7 , the results are the same.…”

“…Table 2 also shows that, when two gross errors are present, the two largest financial losses are incurred at locations of biases (1,6) and (1,5). This can be explained by the fact that an undetected gross error in stream S 1 causes the largest induced bias in stream S 7 (output stream or product stream), which then follow stream S 6 and S 5 .…”

“…Bagajewicz 5 also used Monte Carlo sampling to determine the software accuracy more efficiently. In this latter case, the expected software accuracy is introduced and calculated, whereas in the former 1 accuracy is defined more conservatively using an upper bound. Both definitions are valid and they are of importance for designers in different setups.…”

“…1 In addition, a new approach to assess the economic value of precision was presented. 2,3 In a follow-up article, the economic value of accuracy was discussed.…”

“…They argued that the probability of making the wrong decision is given by the conditional probability P{m p Յ m * p ͉ m p Ն m * p }, that is, the probability of having missed the target given that the estimator is larger than the target. A statistical analysis was performed to derive the following expression: (1) where g M (, m p , p ) and g p (m p , m * p , p ) are the measurement and true value distribution around their means, with standard deviations p and p , respectively. The downside expected financial loss (DEFL, loss incurred for not meeting the production target) was derived as follows:…”