Bayesian analysis in manufacturing instrumentation for test and evaluation

In many test situations, a known measurement is expected or a type of defect can be anticipated. A knowledge of the expected results (a template) allows asking the pertinent question: given the data taken, and given knowledge of the template, what is the probability that the expected object (or event) is present? Two examples of the usefulness of this approach are presented. The first is a test for the presence of wires in tire belting (based on the knowledge of how single wire behaves under the given test). The instrumentation is an eddy current bridge. The second example is testing for a known type of defect in a steel bar. The magnetic field surrounding the bar, when direct current is passed through the bar, is used as the tested quantity; the template is the magnetic field normal to the bar surface, computed by the finite element method (FEM). In both cases, the expected location of the object is identified, along with related information on the tested object. In both cases, the Bayesian approach focuses attention on the question of interest: what is the probability that the test hypothesis is true?.<>