A Bayesian framework-based approach is proposed for the quantitative validation and calibration of the kriging metamodel established by simulation and experimental training samples of the injection mechanism in squeeze casting. The temperature data uncertainty and non-normal distribution are considered in the approach. The normality of the sample data is tested by the Anderson–Darling method. The test results show that the original difference data require transformation for Bayesian testing due to the non-normal distribution. The Box–Cox method is employed for the non-normal transformation. The hypothesis test results of the calibrated kriging model are more reliable after data transformation. The reliability of the kriging metamodel is quantitatively assessed by the calculated Bayes factor and confidence. The Bayesian factor and the confidence level results indicate that the kriging model demonstrates improved accuracy and is acceptable after data transformation. The influence of the threshold ε on both the non-normally and normally distributed data in the model is quantitatively evaluated. The threshold ε has a greater influence and higher sensitivity when applied to the normal data results, based on the rapid increase within a small range of the Bayes factors and confidence levels.