Date of Award

9-2023

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Mathematics and Statistics

First Advisor

Christine M. Schubert Kabban, PhD

Abstract

Probability of detection (POD) is an invaluable part of the calculations used by the USAF to validate the capabilities of nondestructive inspection systems for detecting defects in critical structural components on aircraft. A POD study consists of a designed experiment, linear modeling, and a probability of detection verses defect size curve. This curve is useful for determining how often an aircraft should be re-inspected. Some POD studies are unsuccessful in creating realistic POD curves because the statistical modeling used has two common limitations: (1) a lack of convergence leading to no solution and, (2) violated assumptions leading to incorrect solutions. In this dissertation, new statistical methodology for POD is developed to overcome several complexities introduced by these limitations. For categorical responses, 3 additional models will be introduced which aid in convergence, and more accurate confidence intervals will be developed. For continuous independent responses, extensions to the simple linear model will be developed. For continuous dependent responses, mixed linear models will be developed. These developments extend accepted POD methodologies in order to appropriately create statistical models in contemporary data structures.

AFIT Designator

AFIT-ENC-DS-23-S-002

Comments

A 12-month embargo was observed for posting this dissertation on AFIT Scholar.

Approved for public release. PA case number on file.

Additional Files
4. SF 298 - Knott.pdf (90 kB)
SF298 for AFIT-ENC-DS-23-S-002
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