In his invitation to me to present this Keynote Lecture, Dr. Don Thompson suggested that I focus on some experimental and theoretical developments supporting our intended ultrasonic examination of the Pressurized water Reactor. The Central Electricity Generating Board (CEGB) is proposing to introduce the PWR into Britain and an official Public Inquiry is currently being held into all aspects of this proposal. In the Inquiry quantitative NDE has an important function in the crucial area of establishing reactor pressure vessel integrity. Now I recognise that the interest of many conference participants is in the application of NDE to aircraft components. However, despite the differences in scale and geometry between aircraft and nuclear pressure vessels, I believe you will see strong similarites in our methods and approach. I trust, therefore, that my talk will illustrate by example some important general aspects of the application of quantitative NDE to inspection reliability, and so introduce a broad discussion of the Conference’s themes.