A Statistical Analysis of the Precision of the X-Ray Stress Measurement for the Counter Method - Theory

Abstract

Many investigations have been performed on the accuracy of the X-ray stress measurements from a physical point of view. However, in the X-ray stress measurements the individual stress values exhibit an intrinsic variability. The variability of the X-ray stress value and a precise estimation of the accurate stress value must be dealt with from a statistical point of view. The error distribution of stress values is expressed in terms of that of 2θ_i. And the statistical meanings of the X-ray stress values by various methods are clarified. Furthermore, it is proved mathematically that the stress by the double 0°-45° method proposed by the author, which can be obtained by four measured values like the most commonly used sin²Ψ method, has the least variance of stress for arbitrary value of variance σ_i² of 2θ_i among stresses by four methods described in this paper.