Determining the optimal sample size in forensic casework - with application to fibres

This paper addresses the question of the number of recovered microtraces (hairs, fibres, glass, paint, etc.) to be measured in forensic casework. If the measurement method allows for identification with absolute certainty, the appropriate probability model is identified as sampling without replacement from an urn containing balls of two colours, associated with a hypergeometric probability distribution. For the general situation, where certainty is less than 100%, an adaptation of the classical urn model is proposed and solved. The paper specifically concentrates on fibres to illustrate the practical implementation of theoretical ideas.