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A new system is defined based on a series Markov repairable system. In this new system, if a repair time of the system failure is too short (less than a given critical value) to cause the system to fail, then the repair interval may be omitted from the downtime record, i.e., the failure effect could be neglected. Otherwise, if a repair time is longer than the given critical value, then the system remains operating from the beginning of this repair until this repair time exceeding the critical value, i.e., the failure effect could be delayed. In Ion-Channel modeling, we call this situation the time interval omission problem. Incorporating this situation, the availability indices are presented as a measure of reliability. Some numerical examples are shown to illustrate the results obtained in the paper.