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Universal Journal of Geoscience(CEASE PUBLICATION) Vol. 6(2), pp. 40 - 46
DOI: 10.13189/ujg.2018.060202
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Parametric Theory of Cutoff Grade Estimation in Mining

B.K. Sahu ^*
Professor Emeritus, Department of Earth Sciences, IIT BOMBAY, MUMBAI- 400076, India

ABSTRACT

Estimation of cutoff grade (fractional assay), x(C), in mining of mineral resources is crucial for profit maximization and sustainable growth [7, 8, 9]. It is very complex involving several geological and economic random variables which can be solved assuming the parameters are time-invariant (Static Models) or are time-varying (Dynamic Models). Parametric estimation of cutoff grade, x(C), involves modeling of the assay distribution of the ore (globally and locally) and of the economic random variables such as sale value of marketable ores (s/ton) and cost of production of mineral resource (c/ton). Fractional assay, x where 0< x < 1, of minerals/oxides/elements in rocks and ores is known to possess globally/locally log-normal pdf or some log function of assay is Normal/Gaussian [1,3,4,6] under proper geological/statistical sampling, with the two parameters: mean(渭) and variance(蟽²). However, estimation of cutoff grade, x(C), where(x(C) = inverse cdf, F^-1 (x(C))), is a very complex problem for both static and dynamic modeling. A high cutoff induces lower profits as less ore material can be extracted for sale whereas a low cutoff also induces lower profits as a much larger quantity of lower grade ore and waste materials having little sale value have to be handled which increase the cost of mining and processing. Since life of mine is about 15 years or more, all profits must be reduced to net present value (NPV) for economic comparisons and decisions [5]. Static model assumes time-invariant geological, spatial and economic random variables (rv.s) or random vectors needing simpler statistical analysis [4] to estimate the required parameters, whereas dynamic modeling though more realistic and desirable) requires rather complex time series analysis and forecasting procedure [3]. Forecasted values of the predictors from the concerned dynamic model parameters [3] are then used as inputs to the (linearized) regression equation in dynamic model situations. Optimal cutoff grade, x(CO), is therefore a time-step specific and/or block specific random variable which does not have a global value to be computed. Therefore, general solution to optimal grade, x(CO) , under dynamic model is not feasible and hence, not pursued further.

KEYWORDS
Cutoff Grade x(C), Optimal Cutoff Grade, x(CO), Break-even Grade with No Risk, x(B), Break-even Grade with Statistical Risk x(BR), Log-assay Statistical Parameters, Risk Analysis and Profit Optimization under Static/Dynamic Models

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] B.K. Sahu , "Parametric Theory of Cutoff Grade Estimation in Mining," Universal Journal of Geoscience(CEASE PUBLICATION), Vol. 6, No. 2, pp. 40 - 46, 2018. DOI: 10.13189/ujg.2018.060202.

(b). APA Format:
B.K. Sahu (2018). Parametric Theory of Cutoff Grade Estimation in Mining. Universal Journal of Geoscience(CEASE PUBLICATION), 6(2), 40 - 46. DOI: 10.13189/ujg.2018.060202.