The stepped wedge design is a unique clinical trial design that allows for a sequential introduction of an intervention. However, the statistical analysis is unclear when this design is applied in survival data. The time‐dependent introduction of the intervention in combination with terminal endpoints and interval censoring makes the analysis more complicated. In this paper, a time‐on‐study scale discrete survival model was constructed. Simulations were conducted primarily to study the performance of our model for different settings of the stepped wedge design. Secondary, we compared our approach to continuous Cox proportional hazard model. The results show that the discrete survival model estimates the intervention effects unbiasedly. If the length of the censoring interval is increased, the precision of the estimates is decreased. Without left truncation and late entry, the number of steps improves the precision of the estimates, whereas in combination of left truncation and late entry, the number of steps decreases the precision. Given the same number of participants and clusters, a parallel group design has higher precision than a stepped wedge design. Copyright © 2016 John Wiley & Sons, Ltd.