Bull's algorithm has been evaluated by computer simulation studies. Varying amounts of systematic analytic error were simulated in either hemoglobin (Hgb), red blood cell count (RBC), or mean corpuscular volume (MCV) with the resulting red blood cell indices averaged in batches of 20 using Bull's algorithm. The number of average indices outside the limits of 0.97 means and 1.03 means (means = stable patient mean index) was tabulated and plotted against the size of the systematic shift, expressed in multiples of the long-term analytic standard deviation (SD). The resulting plots, called power functions, show that Bull's algorithm can detect large shifts effectively and that its power increases with increasing batch number. Shifts less than 2 SD rarely are detected. The minimum error that is detected 50% of the time after nine consecutive batches is shown below: (Formula: see text) The simulation of populations with outlying indices, e.g., neonates and oncology patients, resulted in both decreased and increased power, depending on the proportion of outliers averaged, the index averaged, and the direction of the shift.