We present an overview of consensus values and reference values for various situations and apply the computational methods to data from the Charpy machine certification program administered by the National Institute of Standards and Technology. Candidate Charpy machines are certified by comparing a reference value to the average of a set of verification specimens measured by the candidate machine. Currently, the reference value is the average of three averages observed for measurements taken using three Charpy reference machines. However, the simple average, which does not account for differences among reference machines, may not be the optimal method of computing the reference value for every situation. We describe four different methods based on the simple average, the average weighted by sample size, the weighted average that takes into account machine differences, and the weighted average when machine biases are known, for computing the consensus value and its uncertainty. We also present two methods for computing reference values using weighted and unweighted averages. The techniques and recommendations described in the paper are applicable to consensus value and reference value problems in general.
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