Application of Taguchi’s Method to Uncertainty Assessment and Sensitivity Analysis for Mineral Processing Circuits

"While many classic mineral processing circuit design approaches rely on deterministic methods, numerous studies have shown that the uncertainty inherent to the various input parameters can significantly influence design decisions. In a separation circuit, many of the technical uncertainties can be mathematically represented as statistical distributions for the unit recovery and feed grade. These uncertainties are then propagated by the circuit design and reflected in the circuit performance indicators, such as product grade and global recovery. An effective design strategy entails identifying which units are most influential in this uncertainty propagation and thus merit further consideration. Unfortunately, few analytical tools provide this information, particularly those that rely solely on deterministic methods. However, one promising approach is through the application of Taguchi’s method, in a fashion similar to statistical tolerancing of manufactured products. Since the technical challenges are fundamentally similar, Taguchi’s method shows promise in evaluating the level of compounded uncertainty by various circuit designs while determining the role of each separation stage on the overall selectivity and variability of separation circuits. This paper demonstrates Taguchi’s method in several two and three unit circuit designs. INTRODUCTION AND METHOD DESCRIPTION Uncertainty in Mineral Processing Circuit Design Analysis and estimation of uncertainty propagation in mineral processing separation circuits is an essential and significant aspect of an optimal circuit design procedure. Most of the current circuit design methodologies have been constructed, implemented, and validated using a deterministic modeling approach. However, numerous studies have shown that the inherent uncertainty induced by uncertain design parameters can be a significant factor in many mineral processing applications (e.g. Kraslawski 1989; Xiao and Vien 2003; Ghaffari et al. 2012). Thus, an effective circuit design methodology must be able to quantify uncertainty in separation circuits with limited input data. This paper describes Taguchi’s method, as an experimental design technique, to approximate uncertainty in mineral processing applications, and then the similarity of results between Taguchi’s method and Monte Carlo Simulation is investigated. Monte Carlo Simulation The term “Monte Carlo Simulation” has been used to refer to a variety of stochastic simulation methods spanning a broad array of business, technical, and scientific domains. Most generally, Monte Carlo Simulation refers to numerical analysis which is based on (pseudo) random sampling from a domain of input parameters with a known statistical distribution. This methodology allows one to determine the distribution of expected results from a standard deterministic process model. Execution of a Monte Carlo simulation begins by identifying the domain of input parameters, statistical distributions for each parameter, and a deterministic process model which describes the anticipated result as a function of the inputs. Next, one discrete random sample is taken for each input parameter, considering the input distributions. The process model is then solved for this mix of input parameters, producing a single simulation result. This procedure is then repeated a “large” number of times, utilizing new randomly sampled input parameters for each simulation iteration. Once the desired number of iterations is reached, the results of each independent simulation are aggregated to produce descriptive statistics such as minimum, maximum, mean, standard deviation, kurtosis, and other distribution parameters. Given enough iterations, the Monte Carlo method fully explores potential synergies between the input parameters. The methodology does not require the process model to be differentiable, continuous, or even analytically defined. While the number of required iterations varies in relation to th"