Unreliability of Performance Comparisons for Density Separators

Partition curve determinations based on coal sampling and float/sink analyses are subject to a wide range of errors arising from sampling, particle breakage and problems inherent in float/sink analyses. This study focussed on errors which arise from considerations of particle statistics. It tended to concentrate on results derived using density tracers because that technique almost completely avoids the other error mechanisms and because it allows much better definition of statistical criteria.

The original objective was to use Bernoulli statistics and Monte Carlo simulation techniques to develop a broad-brush guide to the likely range of Ep results which may arise from defined tests of a specified true or underlying separation. However, as the project developed it became evident that it is not appropriate to work with distributions of simulated cutpoints and distributions of simulated Ep values. If that approach is taken, many of the partition curves (cutpoint and Ep combinations) which may be predicted are simply not allowed by the statistical processes which govern partitioning. Thus it is important to maintain the ability to identify the cutpoint and Ep combinations generated by simulation.

With programming assistance from Queensland University of Technology personnel, the simulation procedures were refined and largely automated to generate extensive data bases which were then incorporated into an Excel workbook. The databases store likely test outcomes (cutpoint and Ep) from 100 simulations of each of a very large number of underlying partition curves (combinations of True Cutpoint and True Ep from an extensive discretised grid).

Scott Mine Consulting Services were commissioned to implement, within the workbook or "Error Estimator", the following procedures:

1. Prompt and accept user input on the structure, conduct and results of a density tracer test.
2. Identify which (if any) database is compatible with the test strategy which was used.
3. Find the 100 simulation outcomes closest to the actual test result of the user.
4. List the True Cutpoint and True Ep combinations which generated those simulation results.
5. Plot the true Ep values in a way that will facilitate simple statistical assessment of the range of True Ep values which may have generated the test result.

The databases and workbook are rather large at around 30 megabytes. They have been made available to the ACARP project monitor but they, and the concepts behind, them have not been rigorously assessed or reviewed and there is no plan to support the workbook or to release it for general circulation. Nevertheless, it has been used to prepare a set of 36 charts which will allow a user to draw conclusions such as

"My test Ep was 0.012 RD units. I used 40 tracers at each nominal density and the interval between densities was 0.02 RD units. The most relevant charts met those conditions except that the test Ep was 0.01 RD units. In that case the 90% confidence interval was less than +/-0.002 RD units, so I can be at least 90 % confident that the true Ep of my separation was in the range 0.010 to 0.014."

Confidence intervals such as these are considerably better than the author had expected. Like earlier workers he had previously misled himself by considering cutpoint distributions and Ep distributions to be independent of each other. The recognition that they can occur only in specific combinations, and the use of databases of possible test outcomes has allowed better definition of the accuracy of test determinations of cutpoint and Ep values.

A similar approach is applied to assessment of errors which arise from particle statistics issues in respect of partition curves generated by sampling and float/sink analyses. Subject to the proportion of near-gravity material, particle statistics usually favour tracers at coarse particle sizes and sampling and analysis at small sizes (because of the abundance of particles). Tracers avoid the other forms of errors associated with partition data developed from sampling and float/sink analyses.