The confidence limits of stress values measured by X-ray diffraction are usually determined from the equation of the t distribution for the linear regression analysis. Experimentation has shown that not all of the four assumptions on which the equation is based hold for X-ray stress measurement. X-ray residual stress measurement on a quenched structural steel was repeated 65 times. A slight failure of the assumption of linearity of the sin2ψ diagram gives confidence limits of the stress determined from the equation 1.5 to 6 times larger than the actual values depending on the preset times used. However, the confidence limits of the stress determined from the equation derived analytically from X-ray counting statistics agree very closely with the actual values. The standard error of the confidence limits determined from this equation is much smaller than that determined from the equation of the t distribution by a factor of
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