Hierarchical Bayes Statistical Analyses for a Calibration Experiment

Abstract

We consider hierarchical Bayes analyses of an experiment conducted to enable calibration of a set of mass-produced resistance temperature devices (RTDs). These were placed in batches into a liquid bath with a precise NIST-approved thermometer, and resistances and temperatures were recorded approximately every 30 seconds. Under the assumptions that the thermometer is accurate and each RTD responds linearly to temperature change, we use hierarchical Bayes methods to estimate the parameters of the linear calibration equations. Predictions of the parameters for an untested RTD of the same type, and interval estimates of temperature based on a realized resistance reading are also available (both for the tested RTDs and for an untested one produced under the same production process conditions).