This paper presents a comprehensive method for evaluating intrusion detection systems (IDSs). It integrates and extends ROC (receiver operating characteristic) and cost analysis methods to provide an expected cost metric. Results are given for determining the optimal operation of an IDS based on this expected cost metric. Results are given for the operation of a single IDS and for a combination of two IDSs. The method is illustrated for: 1) determining the best operating point for a single and double IDS based on the costs of mistakes and the hostility of the operating environment as represented in the prior probability of intrusion and 2) evaluating single and double IDSs on the basis of expected cost. A method is also described for representing a compound IDS as an equivalent single IDS. Results are presented from the point of view of a system administrator, but they apply equally to designers of IDSs.