Economic value of precision in the monitoring of linear systems

An economic value of precision in the monitoring of linear systems, that include provision of means to calculate the associated probability of loss when process variability is considered, is studied. It generalizes the probability and the associated expected downside financial loss to consider finite deviations from the targeted production values. The analysis concentrates on one of the product rates, and the downside financial losses obtained can be added up for all products. An assumption was made that the operator will not introduce corrective actions when the measurement is above the target. A given set of instrument provides both the level of confidence and its corresponding expected financial loss, under almost no process variations. To incorporate the notion that an estimator is being obtained and therefore some information is added that allows the operator to make corrections during the time of operations, the proper integral over all possible values of the true flow rate below the target that needs to be used to obtain the downside expected financial loss is represented by a relevant mathematical equation. The effect of adding an instrument of 1.5% standard deviation to some streams is finally illustrated.