This study examined scaling properties of an increment series from rotating machinery. Moreover, two fluctuation parameters for the smallest and largest time scales of a scaling range served as a pair of fluctuation parameters to describe system conditions. Therefore, an interesting phenomenon is observed: the data points, each representing a pair of fluctuation parameters, for fault conditions almost form a straight line, while those for normal clearly depart from the straight line. To describe the phenomenon, a novel concept termed the diagnostic line was introduced. Subsequently, properties of the diagnostic line were carefully investigated theoretically and numerically. Consequently, a decisive role of noise in forming the diagnostic line was determined. Accordingly, this study develops a novel criterion for condition monitoring of rotating machinery.