Accept-Reject Decisions and Probabilistic Failure Prediction

The purpose of this paper is to discuss recent progress in the development of an NDE decision formalism applied to the case of brittle fracture in ceramics. The on-line input into the formalism is a set of nondestructive (ND) measurements and the on-line output is the probability of failure conditioned on the above measurements. The final accept-reject decision depends only upon the comparison of the above output with a threshold related to the concerns of the user. The formalism involves stochastic physical models of the ND measurement process, the failure process (assuming a given stress environment), and the a priori statistics of defects. The present formalism goes beyond that reported at the previous meeting in several respects: (a) a greater variety of possible defect types are included, (b) a correspondingly grater variety of competing failure processes are considered, and (c) a more diverse set of ND measurements are incorporated. An important general modification of the total formalism has been introduced: namely, the earlier formalism involving a single most significant defect concept has been replaced by a more realistic formalism in which all possible combinations of defects are taken into account. The model of a priori statistics of defects has been accordingly modified with the removal of the extreme value feature. We will present false-rejection false-acceptance probability curves for various sets of synthetic test data and various values of model parameters.