We study how to combine the censoring technique for Markov chains and the strong stochastic comparison to perform model checking of discrete-time Markov chains. Our goal is to reduce the complexity of the model checking in order to be able to consider numerically intractable models. In model checking we do not need the exact values but we must decide if the required guarantees are satisfied or not. Thus bounding methods are suitable in this context : if the bounds meet the threshold we can decide for the satisfaction of the formula. In the case when it is not possible to decide the satisfaction of the underlying formula through the bounds, we can refine the bounds by considering a larger set of states.