The use of random-model tolerance intervals in environmental monitoring and regulation

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When appropriate data from regional reference locations are available, tolerance-interval bounds can be computed to provide criteria or limits distinguishing reference from nonreference conditions. If the limits are to be to applied to locations and times beyond the original data, the data should include temporal and spatial variation and the tolerance interval calculations should utilize a random crossed or nested ANOVA statistical design. Two computational methods for such designs are discussed and evaluated with simulations. Both methods are shown to perform well, and the adverse effect of using an improper design model is demonstrated. Three real-world applications are shown, where tolerance intervals are used to (1) establish a reference threshold for a benthic community pollution index, (2) set criteria for chemicals in sediments, and (3) establish background thresholds for survival rates in sediment bioassay tests. Some practical considerations in the use of the tolerance intervals are discussed.