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

A Alexandre Trindade,Stan Uryasev

doi:10.6339/jds.2006.04(3).271

Abstract

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.

Highlights

The aim of this paper is to propose a method for integrating different sources of information on a response variable of interest, in order to make inferences on the percentiles of its distribution
We have shown how predictions on material strength from computer or analytical models can be coherently integrated with physical test data, in order to improve the accuracy of estimates for percentiles of the failure load distribution
The information integration is accomplished in the farmework of a regression model, the parameters of which can be estimated via weighted quantile regression, a criterion designed to achieve a good fit at a chosen percentile

Summary

Introduction

The aim of this paper is to propose a method for integrating different sources of information on a response variable of interest, in order to make inferences on the percentiles of its distribution. A comprehensive methodology has been advanced by Reese et al (2004), who show how information from computer models, expert opinions, and physical experiments, can be integrated via a multi-stage hierarchical Bayesian regression framework. By their very nature, Bayesian approaches tend to suffer from prior sensitivity problems. Our method is motivated by the need to analyze a specific setup where only test data and computer prediction data in the form of a range of values are available In this context we seek to make inferences on specific extreme percentiles of the response.

The Modeling Framework

Model Fitting

Assessing the Precision of the Inferences on Simulated Data

Findings

Summary