This technical note presents a screening technique for using chance-constrained programming to achieve overall system (i.e., joint) reliability when there is statistical dependence between constraints representing an ambient air-quality requirement at different geographical locations. The technique is intended to determine whether the full analysis of row interdependence, which requires more intensive programming and larger computational effort, is warranted, by examining a possible spectrum of solutions at three extreme cases of row dependence. The technique is illustrated for airborne particulate emissions control, in which the overall cost of controlling particulate emissions from two electrostatic precipitators is minimized in a manner that maintains ground-level particulate concentration at all receptors with a prescribed reliability.In accordance with the theory presented here, such screening is achieved by setting the required reliability values of individual constraints according to assumptions of complete codependence, zero codependence, and complete negative codependence. In application, these reliability values represent the probability of achieving the ambient concentration standard at several receptor locations. The results of the screening technique are compared to those of two more computationally intensive methods for achieving overall system reliability. It is found that, for a given example, the screening technique brackets the results of those full-analysis methods for row dependence, as expected.

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[1] Under permit programs stemming from regulated riparian systems of water withdrawal control, significant quantities of water cannot be withdrawn from the stream without a withdrawal-constraining permit. There are two versions of such a permit system, one of which fixes the allowable withdrawal, the other of which allows withdrawals to vary directly with streamflows. However, both tie allowable withdrawal to streamflow at some level, the former simply shutting off all withdrawals when the streamflow breaches a low flow standard. Simple logic and the simulation of such systems with hydrologic models predict, in cases where the indexing gauge is downstream of the withdrawal point, the possibility of unstable feedback, leading to severe variability of both streamflow and allowable withdrawal. In this paper we characterize the streamflow variability with three indices, namely, flow crossing, flow reversal, and standard deviation, and compare the difference in those indices to represent the degree of the streamflow variability under the fixed flow and fractional flow withdrawal permit programs. Techniques based on control theory are proposed for modifying the fractional flow withdrawal program to reduce the streamflow variability. It is concluded that regulatory programs modified by inclusion of a first-order filter are able to reduce streamflow variability without significant sacrifice in net benefit or low flow frequency.