Non-destructive inspections are a cornerstone of a wide range of safety critical industries in which the assurance of the integrity of equipment is essential. Prior to any technique being used in service, it is necessary to qualify the inspection by demonstrating that it is capable of detecting defects of interest. Traditionally, this has been achieved using expensive and time-consuming experimental trials. Within the Ministry of Defence (MOD), this has proved to be a significant barrier and an alternative methodology is needed. This project was instigated by the Defence Science \& Technology Laboratory (DSTL) to develop a methodology which will allow this barrier to be overcome.
The use of numerical models to simulate inspections has become increasingly common over the past few decades with the advent of cheaper and more powerful computing resources. This presents the opportunity to replace a significant proportion of experimental trials with faster and cheaper numerical simulations. This thesis presents a general approach to achieving this as well as demonstrating other useful information that a model-based approach can yield. A generalised method of calculating metrics of inspection capability is demonstrated, making no assumptions as to the nature of underlying probability distributions or the response of the inspection. Appropriate sampling and interpolation methodologies provide tools to accurately and rapidly map the inspection's response. Sensitivity analysis is shown to be a suitable tool for quantitatively assessing which parameters can be ignored due to having little impact on the response of the inspection. These methods are applied to a canonical example inspection in the aerospace industry, demonstrating that the reliability of an inspection can be quantified using a range of metrics in a time frame suitable for the MOD.