Use of the Fréchet distribution for UPV measurements in concrete

Ultrasonic pulse velocity (UPV) measurements are routinely used to assess the health of concrete structures. In applications where many measurements are envisaged, the underlying probability distribution of multiple UPV measurements is of interest. We observe empirically in several cases, where multiple UPV measurements can be treated as identically distributed, that the Fréchet distribution fits the reciprocal of the UPV quite well. We also present a physically motivated statistical model that, through Monte Carlo simulations, validates the Fréchet distribution approximation. Our observation may have practical applications in both nondestructive testing (NDT) and statistical quality control.