The signal crayfish Pacifastacus leniusculus is an invasive species in Sweden, threatening the red-listed nobel crayfish Astacus astacus through spreading the crayfish plague. Time-to-event models can handle censored data on such introduced populations for which the state (successful or not) is only partially known at the last observation, but even though data on introduced populations most often are censored, this type of model is usually not used for likelihood-based inference and predictions of the dynamics of establishing populations. 2. We specified and fitted a probabilistic time-to-event model to be used to predict the time to successful establishment of signal crayfish populations introduced into Sweden. Important covariates of establishment success were found by the methods of 'model averaging' and 'hierarchical partitioning', considering model uncertainty and multi-colinearity, respectively. 3. The hazard function that received the highest evidence based on the empirical data showed that the chances of establishment were highest in the time periods immediately following the first introduction. The model predicts establishment success to be < 50% within 5 years after first introduction over the current distributional range of signal crayfish in Sweden today. 4. Among covariates related to temperature, fish species and physical properties of the habitat, the length of the growing season was the most important and consistent covariate of establishment success. We found that establishment success of signal crayfish is expected to increase with the number of days when growth is possible, and decrease with the number of days with extremely high temperatures, which can be seen to approximate conditions of stress. 5. Synthesis and applications. The results demonstrate lower establishment success of signal crayfish further north in Sweden, which may decrease the incentives of additional illegal introductions that may threaten the red-listed noble crayfish Astacus astacus. We provide a fully probabilistic statistical evaluation that quantifies uncertainty in the duration of the establishment stage that is useful for management decisions of invasive species. The combination of model averaging and hierarchical partitioning provides a comprehensive method to address multi-colinearity common to retrospective data on establishment success of invasive species.