Five-parameter logistic functions for partition curves

A five-parameter logistic function (5PL) and a five-parameter generalised logistic function (5PGL) for partition generating symmetric and asymmetric partition curves are presented. For symmetric curves Whiten and Modified Whiten functions are routinely used in Coal Preparation to fit curves to partition data from laboratory and density tracer test results. The functions are also used in process simulations. Whiten functions produce curves that are rotationally symmetric about an inflection point. They cannot produce asymmetric curves that are skewed to product or rejects. The International Standard for density tracer testing (ISO 5146) introduced the 5PL function to cater for asymmetry that had been found in sets of partition data. However, it required modification for use in process simulations to prevent unintended changes in Epm when the cutpoint is changed. A 5PGL function has since been identified that can also manage asymmetry and be used in process simulations without modification. For both the 5PL and 5PGL functions the relative values of parameters need to be considered depending on if the partition is to rejects or to product, and if skewness is to rejects or to product. Process performance indicators derived from the functions are also presented.