Vibrothermography is a nondestructive evaluation method that can be

used to detect cracks in specimens and it is the main engineering

technique we focused in this thesis. This study can be separated into

three parts. In the first part, we develop a systematic statistical

method to provide a detection algorithm to automatically analyze the

data generated in Sonic IR inspections. Principal components analysis

(PCA) was used for dimension reduction. Robust regression and cluster

analysis are used to find the maximum studentized residual (MSD) for

crack detection. The procedure proved to be both more efficient and

more accurate than human inspection. A simulation tool was developed

in the second part of the study by simulating background noise and the

crack signal. The new simulated sonic IR movie data sets can be used

to evaluate existing detection algorithm and testing and developing

new algorithms. The last part of the study analyze the data from sonic

IR inspections on turbine blades. Separate but similar analysis were

done for two different purposes. In the first analysis, the purpose of

the study was to find Sonic IR equipment settings that will provide

good crack detection capability over the population of similar cracks

in the particular kind of jet engine turbine blades that were

inspected. In our second analysis, crack size information was added

and a similar model in the first analysis was fit. Both models are

random mixed effect models and are used to estimate probability of

detection (POD) in certain conditions. The relationship between the

POD and the crack size are calculated based on the second analysis and

the confidence interval on POD estimate are studied using

bootstrap.