If the phases of a decomposed alloy show no contrast in field ion images, only random area atom probe (AP) analyses are possible. The AP data, have to be evaluated by statistical methods to obtain the decomposition parameters. Especially, the autocorrelation analysis of AP concentration profiles has often been used. We have studied the applicability of this statistical method using computer simulated concentration profiles. The limits of the reliability of autocorrelation analysis are tested by varying the input values for the mean concentration of the precipitate and matrix, the aperture diameter and mean diameter of an assumed particle distribution and its standard deviation. Furthermore, the conditions for a successful use of this statistical method are discussed.