Statistical Methods for Materials Testing
Diwakar Gupta, Amy Peterson
Report no. Mn/DOT 2009-41
Mn/DOT provides incentives to contractors who achieve high relative density via a pay factor applied to each unit of work. To determine the pay factor, Mn/DOT divides each day of a contractor?s work into a small number of lots. Then, core samples are taken from two locations within each lot and the relative densities of the cores are calculated by performing standardized tests in materials testing laboratories. The average of these two values is used as an estimate of the lot's relative density, which determines the pay factor.
This research develops two Bayesian procedures (encapsulated in computer programs) for determining the required number of samples that should be tested based on user-specified reliability metrices. The first procedure works in an offline environment where the number of tests must be known before any samples are obtained. The second procedure works in the field where the decision to continue testing is made after knowing the result of each test. The report also provides guidelines for estimating key parameters needed to implement our protocol.
A comparison of the current and proposed sampling procedures showed that the recommended procedure resulted in more accurate pay factor calculations. Specifically, in an example based on historical data, the accuracy increased from 47.0% to 70.6%, where accuracy is measured by the proportion of times that the correct pay factor is identified. In monetary terms, this amounted to a change from average over and under payment of $109.60 and $287.33 per lot, to $44.50 and $90.74 per lot, respectively.