Ecological processes often exhibit time lags. For plant invasions, lags of decades to centuries between species’ introduction and establishment in the wild (naturalisation) are common, leading to the idea of an invasion debt: accelerating rates of introduction result in an expanding pool of introduced species that will naturalise in the future. Here, I show how a concept from survival analysis, the hazard function, provides an intuitive way to understand and forecast time lags. For plant naturalisation, theoretical arguments predict that lags between introduction and naturalisation will have a unimodal distribution, and that increasing horticultural activity will cause the mean and variance of lag times to decline over time. These predictions were supported by data on introduction and naturalisation dates for plant species introduced to Britain. While increasing trade and horticultural activity can generate an invasion debt by accelerating introductions, the same processes could lower that debt by reducing lag times.