Accept-Reject Decisions and Probabilistic Failure Prediction
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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 non-destructive (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formalism has been introduced: namely, the earlier formalism involving a single most significant defect concept has been replaced by a more realistic formalism in which all possible combinations of defects are taken into account.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.