In artificial immune systems, the detectors in the nonself space are often adopted to detect anomaly changes, such as the negative selection algorithm and its improvements. Since the detectors in the self space can also be used to detect anomaly changes, a frequently asked question is which kind of detector sets is more efficient for a specific problem. In this paper, firstly, the advantages and disadvantages of the self detector set and the nonself detector set are briefly reviewed. Secondly, when the complete matching rule is adopted, the average time costs of employing the nonself detector set and the self detector set for anomaly detection are compared theoretically. Thirdly, simulated experiments are done, and experimental results demonstrate that the theoretical conclusion is essentially correct.