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Nickel aluminium bronze is the main material of the controllable pitch propeller in the dynamic positioning system of an ocean-going vessel. When using an X-ray stress measuring instrument to measure the residual stress in this material, measurement failure phenomena often appear since the X-ray diffraction profile of nickel aluminium bronze has a low signal-to-noise ratio. Therefore, the Bragg diffraction angle identified by the traditional method has a large uncertainty, which could cause a large random disturbance of the X-ray stress measurement. Considering the measurement noise and model error, a new approach based on the Bayesian model class framework is proposed to improve the performance of current X-ray stress measurement analysis. For model classes with different peak shape functions, the posterior distributions of the Bragg diffraction angle 2θB are identified first, the posterior probabilities of each model class are computed, a hyper-robust value of 2θB is obtained and finally the residual stress is calculated. Using the confidence intervals of 2θB, the uncertainty of the X-ray stress measuring instrument at each measurement can be determined. Several experiments show that the performance of the proposed method is better than that of the current instrumental method. Of course, the proposed method is also suitable for the residual stress measurement of other new materials and is not limited to nickel aluminium bronze.