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The problem of designing a water quality monitoring network for river systems is to find the optimal location of a finite number of monitoring devices that minimizes the expected detection time of a contaminant spill event with good detection reliability. We formulate this problem as an optimization problem with a stochastic constraint on a secondary performance measure where the primary performance measure is the expected detection time and the secondary performance measure is detection reliability. We propose a new objective function that integrates the stochastic constraint into the original objective function in a way that existing Optimization via Simulation (OvS) algorithms originally developed for an optimization problem without any stochastic constraint can be applicable to our problem. The performance of an OvS algorithm, namely the nested partitions method, with the new objective is tested on a hypothetical river.