Some contributions to underground storage tank calibration models, leak detection and shape deformation

The Environmental Protection Agency's Federal Register provides strict mandates and protocol for Underground Storage Tank reconciliation and maintenance. Keating and Dunn expanded upon this with a patented proprietary statistical model for leak detection. Leak detection modeling is an important asset for not only detecting leaks but also saving millions of dollars in governmental fines. The cornerstone of most statistical leak detection is applying regression theory and methodology to estimate leaks. However, this thesis builds on the problem from another perspective: estimating tank dimensions. Correct tank dimensions are essential to provide correct theoretical volume estimates. Deformation in the tank or, tanks not built to manufacturer specifications can cause major inconsistencies between measured and theoretical volumes. In the third chapter, we present Keating's cylindrical volume functions with hemispherical end caps and then expand it to a general shape of an ellipse and deformed hemispherical end cap. In the derivation with elliptical cross-section two functions are found through "calculus and geometric approaches." Using these functions, we adapt normal, uniform and normal and uniform mixed models with independent and correlated errors. The Normal model also provides a likelihood ratio test for testing cylinder versus ellipse tank shape. We will also consider correlated errors in order to use in comparison to independent errors within the imputation section. Imputation is equally important in a practical sense in the field (to track gasoline deliveries), so we compare common imputation methods with the previously mentioned models.