I. Introduction
The need to identify a subset of anomalous or outlying processes arises in various contexts. For example, in economics the processes may refer to prices in stock market [9], while in fraud prevention security systems, they may refer to e-commerce activity [8]. In large scale systems, the practitioner may be willing to tolerate a small number of errors in the final decision in order to reach a conclusion faster. This tolerance to error can be expressed as a requirement to control the probabilities of at least k1 false alarms and at least k2 missed detections, or alternatively the probability of at least k errors, of any kind. We will refer to the former as control of generalized familywise error rates when either k1 > 1 or k2 > 1, and to the second as control of the generalized misclassification rate when k > 1.