Statistical reliability of the liberation distribution of ore particles with respect to number of particle measurements. (September 2018) - Ueda, Takao; Oki, Tatsuya; Koyanaka, Shigeki
Graphical abstract: Highlights: The statistical reliability of liberation assessment of ore particles is investigated. A correlation between statistical reliability and particle number is established. Numerical validation shows sufficient reliability for number-based liberation. Abstract: Automated mineral liberation analyzers, which have recently seen widespread use, enable us to obtain liberation distribution information based on sectional measurements of a great number of ore particles. A statistically based method was here developed, which correlates the confidence interval of each bin of the liberation distribution with the requisite minimum number of sectional particle measurements. Its primary feature is the estimation, by statistical means, of the required number of particle measurements from probabilities corresponding to the frequencies of the respective bins. The noteworthy feature of the method is that it determines the required number of particle measurements with respect to the specific needs of statistical reliability, such that the confidence interval for volumes over 90% content of the mineral of interest is less than 0.01, and so on. A series of numerical validation simulations was conducted, in which 100, 000 binary particles were modeled and sampling of the estimated required number of particles was conducted 1000 times. Three types of liberation distributions were investigated, based on the respective assessment of two-dimensional (2D) sectional area, 2D particle number, and three-dimensional particle number. If the measurement reliability of a given sampling satisfied the designated confidence level, it was considered to meet the required quantitative reliability for liberation distribution. However, the measurement reliability for 2D areal liberation distribution failed to satisfy the requirement, and the reason for this, as well as a possible solution, are also discussed.