RI 7177 A Multistage Probability Model Of Sample Reduction In The Mineral Industries

A multistage probability model for assessing the reliability of mineral samples following any number of stages of sample reduction is presented. Sample reduction is the process of alternately crushing or grinding and sampling mineral particles prior to assaying. The final multistage model developed accurately describes the ideal sample reduction practice. This model is based on previously developed and experimentally tested models for a single stage of sampling. The problem is approached through the probability distributions for the various stages of sampling. The probability distribution, moments, and moment relationships for a single stage of sampling are first reviewed, and the useful concept of unit moments is defined. In presenting the models for two stages of sampling, emphasis is placed on the physical description of the sample reduction process which leads quite naturally to its mathematical representation. In this representation, crushing or particle-size reduction between the stages of sampling is viewed as a random process with respect to the number and proportion of particles of the various kinds produced. The physical and mathematical description is extended to more than two stages of sample reduction, and the first three moments for any number of stages are developed. In common sample reduction practice the effects of a finite population (finite amount of material) at each stage of sampling appear to be important in describing the variance contribution of each stage. This is also true for the third moment about the mean. An example is cited in which the skewness increases by more than an order of magnitude when several stages of sampling are considered. This is largely due to the dependence of the multistage third moment about the mean on the variance. In general the model and results should be useful in helping to understand, control, and reduce the random errors that arise in the sample reduction process.