Traditional reliability analysis techniques assume behavior of the components as binary-state while evaluating reliability of system. These components have two states only: complete failure and perfect functioning. But reliability analysis is often focused on a component, which has multi-state functioning. Such components are able to perform its task with partial performance and hence can fail at any intermediate state as well. The time to failure for these intermediate states of a component can have different probability distribution which does vary from one state to another. In addition, it is also possible that the fault may increase/decrease in a particular direction with respect to time. In this paper, a methodology is developed for reliability estimation of the dynamic systems considering (a) multi-state failure; (b) probability distribution for time to failure for these multi-states and (c) fault increment of components during the system evolution. The methodology uses Monte Carlo simulation and next transition time sampling technique. The methodology was applied to a level control system of a hold up tank with continuous inlet and outlet flows as a benchmark exercise. With the help of results, it has been shown that there is a significant over and underestimation of probability of failure as compared to that of binary mode of failure and hence reliability of the system. It is suggested that one should take care of these dynamic characteristics while estimating the system reliability.