Person-fit research in the context of paper-and-pencil tests is reviewed, and some specific problems regarding person fit in the context of computerized adaptive testing (CAT) are discussed. Some new methods are proposed to investigate person fit in a CAT environment. These statistics are based on Statistical Process Control (SPC) theory. A technique from SPC that is effective in detecting small shifts in the mean of the variable being measured is the cumulative sum (CUSUM) procedure. How CUSUM is applied to CATs is outlined, and eight statistics are proposed to investigate the sum of consecutive negative or positive residuals. Two simulation studies evaluated the use of these eight statistics. Results show that the detection rates of these statistics are dependent on the type of aberrance simulated. Conditions under which the statistics can be used or should not be used are discussed. (Contains 2 tables and 26 references.) (SLD)