Testing for heterogeneity in complex mining environments

Abstract

Heterogeneity refers to a state or quality of being variable/diverse and comprising different non-compatible elements or parts. In statistical terms a heterogeneous population can refer to a population comprising different non-compatible sub-populations or a multipopulation environment. The latter is commonly found in natural environments such as geological environments (Bardossy and Fodor, 2001). The inherent heterogeneity of complex geological environments is also referred to as spatial heterogeneity. Heterogeneity or variability, however, also occurs over time at mining operations. A case in point is variable ore composition on a conveyance system feeding a processing plant or product stockpile.Heterogeneity associated with the mining environment can significantly influence key aspects of day-to-day mining operations such as sampling, the use of descriptive, probabilistic, and inference calculations, and an operation's ability to manage and control the mining value chain as a whole.The data generated from sampling campaigns forms the basis of nearly all decision-making at the operational, tactical, and strategic levels. As such, it can be argued that the quantity, quality, and correct use of sampling data greatly influence the sustainability of a mining operation.As far as sampling of heterogeneous environments is concerned, an attempt should be made to capture the variability (both spatial and in time) in all key value chain performance drivers through representative or random sampling. According to the theory of sampling developed by Pierre Gy (1983), sampling errors are induced mainly by high levels of heterogeneity of the population being sampled.Descriptive statistics are used on a daily basis in mining operations to calculate values such as the average, median, range, and standard deviation of a known data-set. Probabilistic and inference statistics are less frequently employed. Probabilistic statistics (based on probability theory) are used to determine the likelihood or degree of certainty/uncertainty of outcomes drawn from a known population, i.e. if the population is known, what can be deduced from the samples taken from it?Inference statistics are used to describe an unknown population if everything about the sample is known (random sampling required). Inference statistics involve tests of hypotheses, confidence intervals, and regression.Testing for heterogeneity in complex mining environments by J.O. Claassen* Homogeneous populations are required to perform descriptive, probabilistic, and inference statistics and to support stable, predictable mining operations. The geological and downstream processing environments are, however, highly heterogeneous. The complex nature of mining environments requires means to identify and define multipopulation environments that could affect the performance of mining value chains. A study performed at several operating mines suggests that the impact of heterogeneous or variable geological, mining, and plant processing environments on overall mining value chain per...