Based on some practical problems in maintenance, a new model for K-out-of-N Markov repairable systems is introduced in this paper. The model focuses on that repair times that are sufficiently short (less than some threshold value) do not affect the system operation. We can say that such a repair time is omitted from the downtime record, and the system can be considered as being operating during this repair time. A model is built in which the threshold value is regarded as a constant at first. And then the model is generalized to allow the threshold value to be a non-negative random variable. Both instantaneous availability and steady-state availability are calculated for these new models as reliability indices. Some numerical examples are presented to verify the validity of these models.