Problems of asbestos fibre counting in the presence of fibre-fibre and particle-fibre overlap

Evaluation ‘errors’ arising from chance overlaps among fibres and particles in microscopical samples when using different counting criteria are examined statistically and simplified expressions for their magnitudes are derived. The density of fibre-fibre overlaps is shown to depend on the fibre density and mean fibre length, and the density of the fibre-particle overlaps depends on mean fibre length and particle diameter and the fibre and particle density. Good agreement is shown between the fibre-particle overlap probability as computed by numerical integration over the size distributions and by this analysis using the mean sizes. We show from these calculations how, starting from an ‘entity’ count of particle-free fibre groups, the count of the number of individual airborne entities can be calculated and that the difference between these two counts is generally less than 30% for ‘countable’ filters. We also discuss how this difference could be contained within an acceptable limit by controlling sampling conditions in environments surrounding routine operations. Some laboratory experiments are described where the intention was to check the level of agreement between the actual and expected numbers of overlaps. Any gross disagreement would suggest contributions from some other clumping process occurring during sampling or mounting. None was observed. Some factory samples have also been counted, with particular reference to the overlap frequency, to demonstrate typical magnitudes of the count discrepancies arising from the use of different treatments of clumps as specified by various counting rules