Conditional Probability of Failure and Accept/Reject Criteria

A discussion is given of a general probabilistic approach to the derivation of the failure probability conditioned by nondestructive (ND) measurements and of an optimal accept/reject procedure. This approach involves the use of explicit stochastic models of both the ND measurement process and the failure process (including a postulated stress environment). The overall decision logic involves a number of online and off-line inputs and outputs which will be described in detail with some indications of the kinds that are of interest to various categories of users. Particular emphasis will be placed upon the operating characteristic curve (i.e., the false-rejection probability vs. the false-acceptance probability representing a broad spectrum of optimal decision procedures) and its significance as a measure of the performance and cost-effectiveness of NDE systems. Explicit results will be given for the case o ceramic NDE with acoustical scattering measurements and two alternative failure models. The first is one in which the fracture process originates at a void surrounded by peripheral microcracks and the second involves fracture originating in a subcritical inclusion. Particular attention will be devoted to limiting situations in which the unconditional failure probability is small and/or in which the ND measurements are accurate and sufficiently diverse.