Sample Number Determination for Discrete Ore Particle Measurement
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Solution Overview
Problem
Current methods for determining the number of samples required for measuring physical amounts in discrete materials, such as ore particles, are impractical due to high costs and time consumption, and lack accuracy in estimating measurement reliability, especially for specific components or distributions.
Innovation Solution
A device and method that calculate the required sample number for each class based on the proportion of discrete materials using the equation Ni = (KPξi)^2 * P^i * (1 - P^i), where KP is a reliability constant, ξi is the accuracy constant, and Pi is the proportion of samples in each class, ensuring the sample number meets the desired reliability and accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If statistical data is created for all ore particles belonging to the population, then reliability of statistical data is improved, but cost and time consumption increase significantly
Solution Approach 1:
The patent applies partial action by determining the minimum required sample number needed to achieve the desired reliability level. Instead of measuring all particles in the population, the invention calculates and uses only the necessary subset of samples (Ni) required to obtain statistically reliable data, thereby reducing time consumption while maintaining the required reliability standard.
2Reliability
If statistical data is created for all ore particles belonging to the population, then reliability of statistical data is improved, but cost increases significantly
Solution Approach 1:
The invention implements partial action by measuring only the necessary number of samples (Ni) calculated through the required sample number determination unit, rather than processing the entire population. This approach achieves the desired reliability while significantly reducing the quantity of materials and resources required, thereby lowering overall measurement costs.
3Productivity
If bootstrap method is used to estimate liberation distribution, then practicality is improved, but accuracy of error prediction deteriorates
Solution Approach 1:
The patent applies preliminary action by pre-determining the required sample number (Ni) for each class before conducting measurements. The required sample number determination unit calculates the exact number of samples needed to achieve desired reliability and accuracy, allowing the measurement process to be planned and executed efficiently with the precise sample size required, thus maintaining both practicality and accuracy.
Solution Approach 2:
The invention implements feedback through the measurement accuracy estimation unit, which evaluates the reliability and accuracy of the obtained statistical data. This feedback mechanism allows users to assess whether the measured samples sufficiently represent the population and to determine if additional measurements are needed, thereby ensuring accurate error prediction while maintaining practical efficiency.
4Reliability
If high accuracy is required for overall liberation distribution, then reliability for all classes is improved, but number of samples required increases
Solution Approach 1:
The patent applies segmentation by dividing the population into multiple classes based on physical amounts, and then determining the required sample number (Ni) for each individual class separately using the formula Ni = (KP/ξi)² × Pi × (1-Pi). This segmented approach allows for optimized sample allocation to each class based on its specific characteristics and proportion, achieving reliable statistical data for all classes while minimizing the total number of samples required compared to uniform sampling.
Data Source
AI summary
To give reliability to statistical data on samples as discrete materials, a required sample-number determination device includes: a required sample number for each class acquisition unit configured to acquire a required sample number for each class Ni by the following Equation (1) based on a proportion P{circumflex over ( )}i, that is a ratio of the number of samples in each class to the number of the samples in the population; a temporary required sample number acquisition unit configured to acquire a temporary required sample number Nr, which may be a maximum value among the required sample numbers for each class Ni; and a required sample number determination unit configured to determine the temporary required sample number Nr as a true required sample number when the sample number reaches the temporary required sample number Nr or more,[Mathematical1]Ni=(KPξi)2P^i(1-P^i)(1)in Equation (1), ξi denotes a constant for accuracy that is set for each class, KP is a constant depending on set reliability, and i as indices denotes a class number assigned to each class.