Error propagation at the conversion of particle size distributions
- Theoretical analysis of error propagation when converting size distributions
- Introducing a new parameter in data analysis: the total error propagation factor
- Examination of error propagation for different kinds of conversion tasks
- Low reliability of converted size distributions if total EPF > > 10
Particle size distributions quantify the amount of particles of a characteristic length or equivalent diameter by a certain type of quantity (TOQ). A particle system can be thus characterised by different kinds of size distributions. The conversion of one kind into the other is frequently required in practice and therefore typically employed in data evaluation software. Such a conversion is a rather straightforward mathematical procedure, but it can considerably amplify measurement uncertainties. The degree of this error magnification depends on the differences in TOQ and on the shape of original distribution function. In this study, error propagation is analysed for the general case. A new parameter is introduced, which quantifies the overall impact of conversion on uncertainty: the total error propagation factor. It is applied to the conversion of simulated and measured size distributions which leads to a recommendation for its use in practice.
Frank Babick, Christian Ullmann