Discrete-time survival models are mostly used in modelling time to event data with discrete time intervals in social sciences. In this study this approach is used for modelling non-life insurance data which covers 386200 customers belongs to a local insurance company in Turkey. We use no-claim discount level as the survival time where the interested event is defined as having a damage. Customers who have still no damage at the end of the follow-up period were treated as censored observations, whereas the others were treated as failed observations. The classical survival models and also discrete-time survival models were applied to the data. Age, sex, age of the car and the city were taken into consideration to model the failure times. As we use the no-claim discount level as the survival time, the discrete-time survival model with complementary log-log function is chosen as a better approach for our data set.