This paper develops a warranty cost model for complex systems with imperfect repair within a warranty period by addressing a practical case that the first inter-failure interval is longer than any other inter-failure intervals. The product is in its best condition before the first failure if repair is imperfect. After the imperfect repair, other inter-failure intervals which are explained by renewal processes, are stochastically smaller than the first inter-failure interval. Based on this idea, we suggest the failure-interval-failure-criterion model. In this model, we consider two random variables, X and Y where X represents failure intervals and Y represents failure criterion. We also obtain the distribution of the number of failures and conduct the warranty cost analysis. We investigate different types of warranty cost models, reliabilities and other measures for various systems including series-parallel configurations. Several numerical examples are discussed to demonstrate the applicability of the methodologies derived in the paper.