On Coolen’s comments related to statistics of defects in one-dimensional components

An answer is provided to Coolen’s comments on the article ‘Statistics of defects in one-dimensional components’ published in the journal Computational Materials Science. It is demonstrated on a number of examples that (i) a Poisson process conditioned on the number of events in a finite interval can be of substantial practical importance; (ii) a probabilistic analysis based on conditioning on the number of events following a homogeneous Poisson process is a powerful tool for deriving new results; (iii) the equation dealing with a Poisson process conditioned on the number of random variables in a finite interval is an important result. It is demonstrated how this result can be used to derive a new equation dealing with the case where the number of defects in a finite length is a random variable.