A new failure criterion for discriminating good and bad (overheated) railroad car wheels is proposed using X-ray residual stress data. The procedure for the new discrimination criterion is based on the fluctuations of the azimuthal residual stress in the tread of the wheel. This criterion is based on a maximum likelihood statistical analysis of stress data obtained from six different wheels as determined by x-ray diffraction. Of these locations, the analysis showed the tread, and perhaps a critical point on the top of the flange, to be the most sensitive to residual stress. The variance analysis showed that fluctuations in stress a.l the most sensitive location in the tread to be related to the service history. The residual stresses showed an oscillatory pattern in the hoop direction around the wheels. Extension of the measurement technology to the use of faster residual stress measurements is proposed. To validate our x-ray residual stress data, residual stresses were also measured by hole drilling. Excellent agreement between two techniques was found.