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Kijima I and Kijima II models are two important imperfect repair models in literature. These two models use one constant parameter to represent the degree of repair, which is called Repair Effectiveness (RE) in this paper. We developed a more general imperfect repair model by extending the constant RE to a time-dependent function based on the virtual age process, where the Kijima models are special cases of the new model. A simulation method is developed to estimate the cumulative number of failures for the new model, and a Bayesian inference method is proposed to select the best imperfect repair model. Finally, to demonstrate the new model, a numerical example is provided. From this example, the new model shows a more accurate mean and a narrower confidence interval than that of the Non-Homogeneous Poisson Processes, and Kijima I and Kijima II models.