Simultaneous tolerance intervals for linear regression models using an adjusted product set method

Pointwise tolerance intervals for linear regression models are well established in the literature, however, there is no gold standard for a procedure to construct simultaneous tolerance intervals for linear regression models. The existing methods vary considerably with respect to their finite sample performance in terms of coverage probabilities. Moreover, the numerical investigations into their coverage performance have only been conducted under very limited settings. In this work, we investigate the coverage performance for the major procedures available for the construction of simultaneous tolerance intervals for linear regression models, with increasing complexity in the structure of the models considered. We further show that an adjustment made to the confidence level for a product-set-based method provides coverages close to nominal for the majority of models considered, and this adjusted method is nearly always better than each of the other existing methods. Simultaneous tolerance intervals are then constructed and interpreted for a chemical oxygen demand regression model and two models for the strength of polymer-modified cement mortar.

Automated summary

This study investigates the coverage performance of major procedures for constructing simultaneous tolerance intervals for linear regression models, finding that adjusting the confidence level using a product-set-based method provides close to nominal coverage for the majority of models, and this adjusted method is generally better than other methods. Simultaneous tolerance intervals are then constructed and interpreted for a chemical oxygen demand regression model and two models for the strength of polymer-modified cement mortar.