Statistical methods have a long history of applications in physical sciences and engineering for design of experiments and data analyses. In nondestructive evaluation (NDE) studies, standard statistical methods are described in Military Handbook 1823A as guidelines to analyze the experimental NDE data both in carefully controlled laboratory setup and field studies. However complicated data structures often demand non-traditional statistical approaches. In this dissertation, with the inspiration and needs from actual NDE data applications, we introduced several statistical methods for better description of the problem and more appropriate modeling of the data. We also discussed the potential applications of those statistical methods to other research areas.

The dissertation is organized as following. First a brief background introduction and overview are presented at Chapter 1. Then the complementary risk noise-interference model is discussed in Chapter 2 to better describe the noise and signal relation. In Chapter 3, a direct application of the noise interference model to vibrothermography NDE experiment scalar data is presented. In Chapter 4, the matched filter technique is used to increase signal-to-noise ratio for sequence of image analysis. In Chapter 5, the physical model assisted probability of detection analyses are introduced where the underlying physical mechanism plays an important role in the data interpretation. In Chapter 6, a bivariate normal Bayesian approach is studied to efficiently handle missing information. Finally we summarize these recent NDE developments at Chapter 7.