Combining Model and Test Data for Optimal Determination of Percentiles and Allowables: CVaR Regression Approach, Part I

Summary

We propose a coherent methodology for integrating various sources of variability on properties of materials in order to accurately predict percentiles of their failure load distribution. The approach involves the linear combination of factors that are associated with failure load, into a statistical factor model. This model directly estimates percentiles of the failure load distribution (rather than mean values as in ordinary least squares regression). A regression framework with CVaR deviation as the measure of optimality, is used in constructing the estimates. We consider estimates of confidence intervals for the estimates of percentiles, and adopt the most promising of these to compute A-Basis and B-Basis values. Numerical experiments with the available dataset show that the approach is quite robust, and can lead to a significant savings in number of actual testings. The approach pools together information from earlier experiments and model runs, with new experiments and model predictions, resulting in accurate inferences even in the presence of relatively small datasets.