Improved Tolerance Limits by Combining Analytical and Experimental Data: An Information Integration Methodology

We propose a coherent methodology for integrating different sources of information on a response variable of interest, in order to accurately predict percentiles of its distribution. Under the assumption that one of the sources is more reliable than the other(s), the approach combines factors formed from the data into an additive linear regression model. Quantile regression, designed for quantifying the goodness of fit precisely at a desired quantile, is used as the optimality criterion in model-fitting. Asymptotic confidence interval construction methods for the percentiles are adopted to compute statistical tolerance limits for the response. The approach is demonstrated on a materials science case study that pools together information on failure load from physical tests and computer model predictions. A small simulation study assesses the precision of the inferences. The methodology gives plausible percentile estimates. Resulting tolerance limits are close to nominal coverage probability levels.