Rapid tranit systems are the most important public transportation service modes in many large cities around the world. Hence, its service reliability is of high importance for government and transit agencies. Despite taking all the necessary precautions, disruptions cannot be entirely prevented but what transit agencies can do is to prepare to respond to failure in a timely and effective manner. To this end, information about daily travel demand patterns are crucial to develop efficient failure response strategies. To the extent of urban computing, smart card data offers us the opportunity to investigate and understand the demand pattern of passengers and service level from transit operators. In this present study, we present a methodology to analyze smart card data collected in Singapore, to describe dynamic demand characteristics of one case mass rapid transit (MRT) service. The smart card reader registers passengers when they enter and leave an MRT station. Between tapping in and out of MRT stations, passengers are either walking to and fro the platform as they alight and board on the trains or they are traveling in the train. To reveal the effective position of the passengers, a regression model based on the observations from the fastest passengers for each origin destination pair has been developed. By applying this model to all other observations, the model allows us to divide passengers in the MRT system into two groups, passengers on the trains and passengers waiting in the stations. The estimation model provides the spatio-temporal density of passengers. From the density plots, trains' trajectories can be identified and passengers can be assigned to single trains according to the estimated location. Thus, with this model, the location of a certain train and the number of onboard passengers can be estimated, which can further enable transit agencies to improve their response to service disruptions. Since the respective final destination can also be derived from the data set, one can develop effective failure response scenarios such as the planning of contingency buses that bring passengers directly to their final destinations and thus relieves the bridging buses that are typically made available in such situations.