4D treatment plans are optimized to compensates for a patient's individual respiratory motion. However, changes in the time spent in the each respiratory state may render a 4D plan invalid. We introduced and evaluate two robust treatment planning approaches to compensate for respiratory motion variations. Robust 4D plans can be designed either using an average pdf approach or a worst case pdf approach. We tested these approaches on two motion variation scenarios and compared them with nominal 4D optimization and ITV plans. The nominal 4D plans were very sensitive to the variation in respiration pattern while the average pdf and worst case pdf plans were less sensitive under the similar variations. The average and worst case pdf plans were not as robust as the ITV plans but had better healthy tissue sparing. The worst case pdf approach was found to be the most promising for robust 4D plan optimization.