Statistics of defects in one-dimensional components

Equations related to spatial statistics of defects and probability of detecting defects in one-dimensional components have been derived. The equations related to spatial statistics of defects allow to estimate the probability of existence of safe, defect-free zones between the defects in one-dimensional components. It is demonstrated that even for a moderate defect number densities, the probability of existence of clusters of two or more defects at a critically small distance is substantial and should not be neglected in calculations related to risks of failure. The formulae derived have also important application in reliability and risk assessment studies related to calculation of the probability of clustering of evens on a given time interval. It is demonstrated that while for large tested fractions from one-dimensional components, the failures are almost entirely caused by a small part of the largest defects, for small tested fractions almost all defects participate as initiators of failure. The problem of non-destructive defect inspection of one-dimensional components has also been addressed. A general equation has been derived regarding the probability of detecting at least a single defect when only a fraction of the component is examined.