Sampling representative

Concept: The representativeness of a sample refers to the extent to which the sample or sample taken represents the location or ore body unit (or population) being sampled. Its quantitative representation is analog error or representative error. The representativeness of the sample is divided into three categories: total (or overall) representative, hierarchical or local representative, and individual representative.

  1. The overall representativeness refers to the degree of agreement between the average value of the sample and the overall average, that is, the degree of conformity of the average value of the ore body (or deposit) obtained from the sample to the average value of the ore body (or deposit).
  2. Hierarchical representation refers to the degree of conformity between the probability distribution of the sample and the overall probability distribution, that is, the degree of conformity between the proportion of the grades at each level and the actual proportion. The proportion of grades at all levels is one of the inherent characteristics of the deposit. If the sampling results can only satisfy the overall representativeness and cannot satisfy the representativeness of the grade, the representativeness of the sample cannot be considered good. In general, if each grade represents performance, the overall representativeness is generally satisfied.
  3. Individual representative refers to whether each specific sample can represent the actual situation of the affected range.
Sampling representativeness and reliability are undoubtedly the core issues of sampling. Economically and effectively obtaining samples with certain representativeness and reliability are the basis and criteria for selecting and evaluating sampling methods, sampling measures, and programs. Factors affecting the representativeness of sampling:
  1. The variability of the quality of the ore itself
  2. The exploration project for sampling is restricted.
  3. The number of samples is expressed as follows: the more samples are collected from the same ore body (mine section), the better the sampling representative. On the contrary, the smaller the number of samples, the worse the representativeness.
  4. The sample spacing is as follows: 1 When the grade change is random, if the sampling range is fixed and the sample spacing is denser, the more samples are, the better the representativeness is. Otherwise, the representative is worse; 2 The grade change For the directional change, the denser the sample spacing, the better the representativeness, that is, the more natural variability of the ore quality can be reflected. At this time, with sparse sampling engineering, interpolation and extrapolation can also achieve better representation.
  5. The geometric characteristics of the sample refer to the influence of the direction, scale, specification and shape of the sample arrangement on the sampling results. It is known from theory and practice that in general, a single sample is always arranged along the thickness direction of the ore body; the larger the volume of the sample, the smaller the dispersion of the sampling result, that is, the smaller the observed variability.
Figure 4-5-8 Sketch of the influence of the sample size on the grade change (according to А.Б. Kazindan, 1984) As can be seen from Figure 4-5-8, as the sample size (geometry) becomes smaller, the observation The variability will become larger, and conversely, the larger the sample size, the more uniform the change. Figure 4-5-9 Sketch of the influence of sample shape on grade change (According to АБ卡日丹, 1984) Under the conditions of mineralization characteristics, when the sample volume is the same and the geometry is different, the sampling results will be different. As can be seen in Fig. 4-5-9, for the mineralization of such features, the observation results of the "linear" samples are obviously more uniform than the observations of the square samples, and more reflect the overall variation characteristics of the ore quality. If the grade value is an independent random variable, then: Where: δ - absolute error of the mean;  σ - standard deviation grade observations;  τ - relative error of the mean; the number of observations of -; -  n Grade variation coefficient  V .分级 Graded representative evaluation can establish confidence intervals for grade frequencies at all levels. If the distribution law of the grade of the deposit is known, the distribution law can also be tested. Individual representative evaluations can be used for cryptographic sampling within the range of individual sample impacts, or for error assessment using the same or different sampling methods that are more reliable (eg, larger). Note: The Kriging method in geostatistics is based on a certain eigenvalue data (such as grade value) of several information samples inside and outside a block, and a linearity is made on a certain eigenvalue (grade) of the block. Estimation method for unbiased and minimum estimated variance (variation of estimation error). That is, after considering the geometric shape of the shape and size of the information sample and its spatial distribution position with the block to be estimated, and the spatial structure information of the grade (reflected by the variogram or covariance function), The method of linear, unbiased and minimum estimation error variance, and each sample value is given a certain weight coefficient, and then the weighted average class is used to estimate the average grade of the block. This method not only guarantees a most accurate estimate, avoids errors as much as possible, but also provides the concept of estimation error (accuracy). For the calculation of the variance of the overall and local average grade estimates and their estimation errors, as well as the specific methods and procedures for the grade estimation of the specific samples (points), please refer to the relevant information.

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