Abstract
We have obtained a mathematical expression for the probability of flaw nondetection in pressure vessels. Also we have derived the distribution function of the largest undetected flaw. Specifically we can now estimate the probability that at least one flaw of a size a or more is left undetected after a sequence of flaw inspection procedures is carried out. This solution takes into account (i) the number of flaws initially present in the vessel, (ii) the sizes of these flaws, and (iii) the detection capability of the inspection procedures. The result given here can be used in assessing the effectiveness of various inspection sequences and in obtaining an estimate of the unconditional probability of brittle fracture.
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