A new failure criterion for discriminating good and bad (overheated) railroad car wheels is proposed. This criterion can replace the conventional “four inch" discoloration rule. 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 data obtained from six different wheels as deterrmined 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 at the most sensitive location in the tread appeared 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 magnetoelastic stress measurement is proposed. To evaluate the inaccuracy in stress data possible from a large sample with curved surface, corrections for a deliberate tilt of the plane of the x-ray diffractometer from the normal to the sample surface have been developed. Analysis of different misalignments are discussed. To validate our x-ray residual stress data, residual stresses were also measured by hole drilling. Excellent agreement between two techniques was found. Finally, stress variation with depth below surface was determined by the hole drilling technique. / Ph. D.