Underground storage tanks (UST): A closer investigation statistical implications to changing the shape of a UST

Gasoline service stations that use underground storage tanks (UST) assume that the manufactured tank is an ideal cylindrical shape. This cross-sectional shape plays a crucial role in determining a functional form for the volume of liquid that remains inside the tank. In industry, these formulas are used to compute strapping charts. But realistically, the manufacture, assembly, and installation of a tank may have deviation from the actual tank design (for which strapping charts had been developed). A theoretical volume function (based on tank dimensions) is used alongside of statistical methodology to reconcile volume differences in gasoline dispensed at the pump meters versus that displaced inside the tank. Statistical inventory reconciliation of this nature falls within the family of leak detection methods approved by the EPA (Environmental Protection Agency) and the California Water Resources Board. This methodology can also be used to assess deformation of the cross-sectional shape of the tank. We consider a deformation to an ellipse. Through simulation, we estimate the tank dimensions based on a nonlinear model with normal errors. The use of normal errors naturally facilitates a likelihood ratio test. Through this exploration, an approximation function is developed to help improve the power of the likelihood ratio test.