‘Little Jack Horner, sat in a corner, eating his Christmas pie He put in his thumb, and pulled out a plum, and said what a good boy am I’ Hilaire Belloc (1870–1953)

Through the ages, mining has been the gambler’s happy hunting ground. More so in South Africa than in any other part of the world. One has only to recall the the discovery of diamonds, the Witwatersrand gold fields, Barney Barnato, Hans Merenski and the platinum riches of the Bushveld Igneous Complex and the Phalaborwa carbonitite to recognize that we have had more than our fair share of plums in the pudding and the magnate millionaires to pull them out. This gambling addiction continues.

We are a global gambling paradise, and our casinos and state lottery are, I understand, the most lucrative in the world. Less palatable are our road accident statistics and the ups and downs of the metal prices and the JSE share oscillations. However, in spite of this gambling predilection, our scientists in the mining and minerals have been in the fore-front of reducing the gambling aspects of this industry. In the early part of the last century the geophysicists pointed the way to avoiding the ‘pot luck’ approach to sinking boreholes with amazing success in identifying the extensions of the goldfields in the western Transvaal and the Orange Free State.

Similarly, we have witnessed the development of geo-mineralogy in the prospecting for diamonds and of geochemistry for locating promising areas for base metals and other mobile metal deposits. Once deposits of minerals have been located, the uncertainty of deciding how much payable material exists from a limited number of boreholes has been dramatically improved by the pioneering work of the many geo-statisticians, such as Dr Danie Krige, who have evolved the methodology of the evaluation of ore resources and reserves to satisfy the assurances needed by the investors. Slowly but surely the gambling aspect of mining has been not eliminated, but reduced to the computer calculation of the risk factors in achieving a return on investment within prescribed norms. Have all these advances taken the fun and excitement out of mining?
Are there still bonanzas to be discovered in mineral exploration in say, Southern Africa? Hardly likely. Or in the language of the statistician, a low probability. (But not impossible. The impossible can still happen as was the case of a recent cricket match between Australia and South Africa!) There is much fun and excitement still to come. Maybe not in the true gambling spirit, but more in the generation of superior technical and management skills to squeeze out the highest recovery and the optimization of mining and processing costs so as to beat the global competition. Indeed it is now the challenge to take the gamble out of mining metallurgy and mineral processing. For many decades mineral processing was an art rather than a science and there are papers in this issue to indicate the common-sense approach to operations such as smelting, for example. However, to a very large extent this is also going to depend on statistical methods.
There is no orebody that is homogenous so as to provide a constant feed to the processing plant. Deposits are heterogeneous and the feed can vary considerably so the optimum operation parameters change from moment to moment and so does the cost and efficiency. One way to reduce this cost factor is to attempt to mix the incoming feed material so as to obtain a blend over several weeks, which has more uniformity in the daily feed characteristics.

This is easy to do in a laboratory using the wellknown ‘cone and quartering’ methods, which were fine for small laboratory quantities. However, to do this blending with, say, 100 thousand tons a month is another matter. Not only does this incur a cost factor because of the increased pipeline time before the product appears in the market, but one must know the magnitude of the variance within the orebody and whether it is a normal or lognormal or some other statistical distribution, and this determines at what particle size is this mixing most beneficial. A paper presented in this issue is another step in providing the computer model to suit specific situations to help the management make cost-wise decisions.

There has been a wealth of work done on the statistical variations that can be experienced in milling and the impact on processes such as flotation. Slowly but steadily we are moving towards a complete integration of statistical models from mine to final product. But there is more to holistic management than the physical and chemical aspects of the mine to product operation. The final products can change in value as world prices oscillate with short and long cycles. (I have seen the price of cobalt vary from $5/lb to $60/lb in the course of a few years). Suddenly a waste heap can become valuable and underground pay limits change rapidly. So once again statistical methods have to be used to attempt to predict the future periods of shortage and oversupply in advance and the impact on the sales price of the products. These variables are challenging enough when the ore deposit to final product sales affect only one company. In another paper in this issue, the very much more complex problem of a toll smelter, which smelts several concentrates from different mines and has to account for the efficiencies and recoveries for each of the clients, is considered.

Once again the variances in the feed material to the smelter and all the process variables have to be taken into account. There is a lot more work to be done before a reasonable model can be developed. The point that I wish to make is that we can never be free of statistical methods and increasingly sophisticated modelling techniques. To a considerable extent the gambling component of mining has been reduced. But uncertainties in the management of mineral resources will be with us for a long time and are becoming more important as grades decrease and global competition increases. Management metrics is the latest buzzword. Great emphasis is placed on mathematics in the education of engineers, geologists and other technical people and probably the branch of mathematics that will prove most useful in careers after leaving university is that of statistics.

Come to think of it, the same applies to most school-leavers. In normal life we are never endingly bombarded with statistics. Every new drug is associated with a statistic on efficacy. There are economic statistics, unemployment statistics, weather forecast statistics, environmental statistics on decline of species, global warming statistics, accident statistics, inflation growth rates, obesity and matriculation results are all manipulated by statistical methods. There are good stats, bad stats, fraudulent stats and meaningless stats and every now and then important-to-know stats. They have a language of their own, which few understand and therefore the public can be hoodwinked easily. One does not have to become involved in the higher levels of some complex mathematics. But the basic concepts are just as important as trigonometry, calculus or geometry. About the only activity where statistics has a very simple relevance, is in casinos and the lottery. The more you play the more you lose!

R.E. Robinson   March 2006