Abstract Surveying species that are present in low numbers is difficult because often the survey fails to locate any individuals. One strategy to improve the sample design is to survey the site repeatedly. With repeat surveys the abundance of the target species, and hence likelihood of detection, may change between visits. We present a model for deciding on the maximum surveillance interval between repeat surveys so that there is a high probability of detecting the species. We use as an example surveys for new weed infestations and model the chance of detecting the weed before control costs reach a threshold. The maximum surveillance interval depends on the rate of weed growth, the ability to detect the weed, and the cost of controlling the weed. Typically weed growth rates are high. Fast growing plants need to be detected early before they spread, but often weeds are difficult to detect when young and still comparatively cheap to control. Results from the model to determine maximum surveillance intervals are given for five broad habitat types and seven weed types. Surveillance intervals ranged from 1 to 10 years. Longer intervals are appropriate when searching for weeds with slower growth rates, that are easier to detect, and those that can be controlled cheaply.