Reliability of bus travel time is an objective of major concern for bus operators and users. However, due to traffic conditions and variability in bus demand, deviations from schedules are unavoidable, leading to an overall decrease in level of service and capacity. The ability to accurately and effectively analyze various performance measures is fundamental to determining how well the bus service is adhering to its service standards. Understanding and developing methods to assess transit operations performance is not only valuable in identifying potential problem areas along a route; it is also constructive in proposing effective strategies to improve service reliability. After a state-of-the-art and a state-of-practice studies of the service regularity measures for high-frequency buses, we propose in this paper the use of the Lorenz curve as a tool for the analysis of bus regularity. We show that the Lorenz curve, if drawn for the scheduled headways, allows analysis of the regularity of the waiting time of all riders of the bus line and is a good measure from the users' point of view. The Lorenz curve drawn for the ratio of the observed to the scheduled headway allows analysis of the regularity of the bus service with regard to the scheduled headways and is therefore an effective measure, mainly from the operator's point of view.