Nondestructive Evaluation (NDE) is a scientific/engineering discipline involved in the development of methods to nondestructively interrogate physical items (e.g., aircraft engine components or structures) for flaws such as material defects or cracks. A variety of methods exist for performing NDE to detect such flaws. NDE inspection capability is usually quantified by the probability of detection (POD). Typically, in a new application of NDE, there will be a POD study to estimate the POD for the application. NDE inspection data are either binary (hit-miss) or signal-response (on a continuous scale). First, this thesis develops an appropriate method for analyzing repeated-measures NDE hit-miss data. To this end, a well-known binary NDE dataset - commonly called the "Have Cracks, Will Travel" dataset - is used to demonstrate how unbalanced, repeated measures, hit-miss data can be modeled probabilistically by considering the POD as a random variable. Then, a commonly used metric for NDE performance evaluation, the Mean POD, is derived and we introduce the concept of a quantile POD and show that mean POD and quantile POD can differ considerably and emphasize that both metrics serve to answer different questions about inspection capability. Next, the thesis develops statistically-based methods for planning POD studies of various types. We look at finding optimum test plans which maximize estimation precision for hit-miss as well as signal-response data. We use a Bayesian framework which allows the probabilistic incorporation of information regarding model parameters. These optimum plans are used as a benchmark to compare proposed compromise plans which may be sub-optimal but are more practical for implementation. Finally, we look at the effect that different sources of variability have on estimation precision when a particular, specified POD study design is used. We make available a tool for experimenters who wish to gauge the trade-offs/benefits of implementing such designs under different test conditions.