Reliability of wind turbines is analyzed with the use of an easily interpretable mathematical model based on a Poisson process, which takes into account jointly observable differences between turbines described by covariates (type of turbine, size of turbine, harshness of environment, installation date and seasonal effects) as well as unobservable differences modeled by a standard frailty approach known from survival analysis. The introduced model is applied to failure data from the WMEP database, and the fit of the model is checked. The paper demonstrates the usefulness of the model for determination of critical factors of wind turbine reliability, with potential for prediction for future installations. In particular, the model's ability to take into account unobserved heterogeneity is demonstrated. The model can easily be adapted for use with different datasets or for analysis of other repairable systems than wind turbines. Copyright © 2016 John Wiley & Sons, Ltd.