Method, program, information processing device, and mixer for determining the degree of mixing of target particles

Abstract

When determining the degree of mixing of a particle of interest from a mixture in which the particle of interest is mixed, the present invention determines the degree of mixing of the particle of interest by calculating a size of sampling from the mixture from an expression relating the total size of the mixture and a size per particle of the particle of interest.

Description

[Technical Field]

[0001] The present invention relates to a method, a program, an information processing device, and a mixer for determining the degree of mixing of particles of interest. [Background technology]

[0002] In many industrial fields, such as the pharmaceutical, food, ceramic, and powder metallurgy fields, a mixing operation is performed in which two or more types of particles are mixed together during the manufacturing process of a product.

[0003] The mixing state of a mixture obtained by a mixing operation affects the quality of the final product that contains that mixture. Therefore, the mixing state is evaluated by the degree of mixing, which is a numerical value indicating the degree of mixing of the target particles in the mixture, to determine whether the desired mixing state has been achieved. The degree of mixing is calculated by measuring a portion (sample) taken (sampled) from the mixture into which the target particles have been mixed.

[0004] Sample measurement methods include methods for directly measuring the sample and methods for measuring the electric and magnetic properties, surface properties, physicochemical properties, mechanical properties, etc. of the sample (Non-Patent Document 1).

[0005] A conventional method is the Lacy mixing index, which expresses the degree of mixing by comparing the statistical variance of measurement data with the statistical variance of random and separated states (Non-Patent Documents 2 and 3).

[0006] In addition, for powders in which the sampling amount (number of particles) and relative error follow a logarithmic normal distribution, a method is known in which the minimum number of particles required to keep the error within a specified range at a specified confidence level is calculated by logarithmic calculation (Non-Patent Document 4). [Prior art documents] [Non-patent literature]

[0007] [Non-Patent Document 1] Yonemochi, Yoshio, Powder Mixing Process and Mixing Uniformity, Pharmaceutical Sciences Vol.64(5), 302-304(2004) [Non-patent document 2] Yoichi Nakata et al., Quantitative Evaluation of Mixing Degree of Powder and Granular Materials by Shannon Entropy, J. Soc. Powder Technol., Japan, 54, 296-304(2017) [Non-patent document 3] PMC Lacey et al., The Mixing of Solid Particles, Transactions of the Institution of Chemical Engineers, Vol.21, 53-59(1943) [Non-patent document 4] S. Sakashita, "Fundamentals of Powder Technology for Color Material Engineers," J. Jpn Soc. Colour Mater., 78(11), 520-530(2005) Summary of the Invention [Problem to be solved by the invention]

[0008] Although the degree of mixture is a statistically based quantitative index, the conditions for sampling a portion of the mixture are difficult to specify and are determined empirically. Therefore, it is desirable to determine appropriate sampling conditions based on a logical basis that can maintain the reliability of the degree of mixture.

[0009] In one aspect, the present invention aims to determine sampling conditions for measuring the degree of mixing of particles of interest in a mixture based on logical grounds, thereby eliminating the need for unnecessary sampling while maintaining the reliability of the degree of mixing, and thereby improving and optimizing the accuracy of quality control of final products that contain the mixture. [Means for solving the problem]

[0010] The method disclosed herein for determining the degree of mixing of a particle of interest determines the size of a sample to be sampled from a mixture containing the particle of interest by calculating it from a relational expression between the total size of the mixture and the size of each particle of interest. [Effects of the Invention]

[0011] In one aspect, the present invention can improve the accuracy of quality control of final products that contain a mixture by appropriately determining sampling conditions for measuring the degree of mixing of particles of interest in the mixture. [Brief explanation of the drawings]

[0012] [Figure 1] FIG. 1 is a diagram illustrating an example of mixing two types of particles in a mixer (a tumbling rotary mixer). [Figure 2] Figure 2A is a diagram illustrating the difference in the size of the sampling volume and the complete separation state, and Figure 2B is a diagram illustrating the difference in the size of the sampling volume and the complete mixing state. [Figure 3] Figure 3A shows the degree of mixing when the sampling volume is optimal, Figure 3B shows the degree of mixing when the sampling volume is small, and Figure 3C shows the degree of mixing when the sampling volume is large. [Figure 4] FIG. 4 is a diagram for explaining the definition of the completely separated state. [Figure 5] FIG. 5A is a diagram for explaining the definition of a completely mixed state, and FIG. 5B is a diagram showing an extraction model. [Figure 6] FIG. 6A is a graph when the tolerance Rv is 0.01, and FIG. 6B is a graph when the tolerance Rv is 0.2. [Figure 7] Fig. 7A is a diagram for explaining a case where the number of samplings is large, and Fig. 7B is a diagram for explaining a case where the number of samplings is large. [Figure 8]FIG. 8A shows the degree of mixing when the number of samplings is large, FIG. 8B shows the degree of mixing when the number of samplings is small, and FIG. 8C shows the degree of mixing when the number of samplings is optimal. [Figure 9] FIG. 1 is a block diagram schematically illustrating an example of a hardware configuration of an information processing apparatus according to an embodiment. [Figure 10] FIG. 2 is a block diagram schematically illustrating an example of a software functional configuration of the information processing device according to the embodiment. [Figure 11] 10 is a flowchart illustrating an example of the operation of a process for determining the degree of mixing of particles of interest according to the embodiment. [Figure 12] FIG. 2 is a block diagram schematically illustrating an example of a hardware configuration of a mixer according to an embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0013] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described below with reference to the accompanying drawings. In the drawings used in the following embodiments, parts with the same reference numerals represent the same or similar parts unless otherwise specified.

[0014] The information processing device and mixer (tumble rotary mixer) according to this embodiment that determine the mixing degree of a particle of interest from a mixture into which the particle of interest has been mixed are achieved by a method and program that causes a computer to execute the above-mentioned determination process.

[0015] As described below, the size of a particle of interest according to this embodiment represents the size of the particle of interest in the mixture. The size can be any of the volume, area, length, and number depending on the information obtained from the target mixture.

[0016] [1] Issues with sampling conditions As mentioned above, the degree of mixing is a quantitative index that represents the degree of mixing of target particles in a mixture, and is calculated by measuring a portion (sample) taken (sampled) from the mixture. The degree of mixing M can generally be expressed by Equation 1.

[0017]

number

[0018] The variables on the right side of Equation 1 are σ: standard deviation of the sample, σ0: standard deviation of the completely separated state (standard deviation when sampling the entire amount with a sample size infinitely smaller than the completely separated state). The standard deviation of the sample is calculated using Equation 2.

[0019]

number

[0020] The variables on the right side of Equation 2 are N s : Number of samplings, C i : The proportion of the particle of interest in the sampling volume, P: The proportion of the particle of interest in the total volume V of the mixture. The number of samplings is the number of times samples are taken. The sampling volume is the sampling unit per sample, and can be volume, area, length, number, etc.

[0021] From Equation 2, it can be seen that the sampling volume and the number of samplings are parameters of the sampling conditions and affect the degree of mixing, but in reality, these values ​​are determined based on empirical rules.

[0022] Therefore, in this embodiment, a method for determining the size and number of samplings, which are sampling conditions, according to the desired degree of mixing in the process of determining the degree of mixing of particles of interest will be described.

[0023] [2] Determining the sampling volume For ease of understanding, the following explanation will be given using an example where size is volume. The relationship between sampling volume and mixing level is described in item [2-1], the relationship between sampling volume and mixing level in a completely separated state is described in item [2-2], and the relationship between sampling volume and mixing level in a completely mixed state is described in item [2-3]. Furthermore, the method for determining the optimal sampling volume is described in item [2-4], and the expansion of the allowable range of sampling volume is described in item [2-5].

[0024] In the following description, for ease of understanding, a mixer using a tumbling rotary mixer for mixing two types of particles in equal numbers will be used as an example. However, the scope of application of the present invention is not limited to this form. As long as the target particle is a solid with a identifiable particle size, the other particles and medium are not limited to solids and may be liquids or gases. Furthermore, even if the target particle aggregate is pulverized in a rotary mixer, it can be used as long as the size (volume, area, length, number) of the target particle for which the degree of mixing is to be determined is known. As long as the size of the target particle is known, the shape of the particle is not important. Furthermore, any ratio of the number, amount, etc. of the target particle to other particles can be applied, not limited to that used in the description. Furthermore, the mixing method is not limited to a tumbling rotary mixer; any well-known mixing method can be applied.

[0025] [2-1] Relationship between sampling volume and degree of mixing First, we will explain the relationship between sampling volume and degree of mixing. As shown in Figure 1, we will take an example of mixing two types of particles using a tumbling rotary mixer (see Figure 1 for the conditions of the tumbling rotary mixer). The particles are two colors, black and white, with the same volume per particle, the same number of particles of each color in this example, and the particles of interest are white. During the mixing process, the particles of interest change from the completely unmixed state before mixing (completely separated state) shown in Figure 2A to the state in which the particles of interest are uniformly mixed (completely mixed state) shown in Figure 2B. The hatched black circles within the particle group represent the sampling unit per sample, with the small black circles representing small volumes and the large black circles representing large volumes.

[0026] 3A to 3C are graphs with the mixing time on the horizontal axis and the degree of mixing M on the vertical axis, and the thick solid line plots the degree of mixing M calculated based on Equation 1 and Equation 2 using samples collected at each time point. The degree of mixing is expressed as a value between 0 and 1, and the variable on the vertical axis is M. e0 : Mixing degree of completely separated state, M R : The degree of mixing in a completely mixed state. Two horizontal lines are drawn in the graph, and the dashed line is the degree of mixing M e0 The solid line indicates the degree of mixing M R Shows.

[0027] When the sampling volume v is optimal, as shown in Figure 3A, the degree of mixing M is plotted as a single curve going from the completely separated state to the completely mixed state, and the degree of mixing can be measured from 0 to 1. However, when the sampling volume v is relatively small, as shown in Figure 3B, the maximum degree of mixing that can be measured is low, and the degree of mixing may be estimated to be lower than the actual mixed state. Also, when the sampling volume v is relatively large, as shown in Figure 3C, the value of the degree of mixing at the start of mixing is greater than 0, and it is not possible to accurately measure the state at the start of mixing or immediately after the start of mixing when mixing is not progressing.

[0028] Here, the degree of mixing in the completely separated state M e0 and the degree of mixing in the complete mixed state M R Focusing on the width between e0 Error from 0 and the completely mixed state M R The sum of the errors from 1 (hereinafter referred to as "mixing degree error") D M In the completely separated state M e0 and the completely mixed state M R When expressed as the sum of

[0029]

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[0030] From Equation 3, the complete separation state M e0 Error from 0 and the completely mixed state M RWhen the sum of the error from 1 and the error from 1 is minimized, the error D M is minimized, and in this case, the sampling volume v is found to be optimal. Therefore, the degree of mixing of the completely separated state for the sampling volume v, M e0 and degree of mixing in the complete mixed state M R If the relationship between these can be expressed as a function, the optimal sampling volume v opt can be calculated.

[0031] [2-2] Relationship between sampling volume and degree of mixing in a completely separated state Mixing degree M in a completely separated state e0 is expressed by Equation 4 based on the definition of Equation 1.

[0032]

number

[0033] The variables on the right side of Equation 4 are σ e0 : Standard deviation of the sample in the completely separated state, σ0: Standard deviation of the completely separated state (standard deviation when the entire amount is sampled with a sample size infinitely smaller than the completely separated state).

[0034] First, the standard deviation σ of the completely separated samples e0 Here, the definition of a completely separated state will be explained using white particles and black particles as an example, with reference to FIG. 4. FIG. 4 is a diagram showing a completely separated state in one dimension, with all particles divided into white particles and black particles arranged in a horizontal row. The horizontal axis represents the cumulative volume, and adjacent particles are in contact with each other at a single point.

[0035] Let the sampling volume v be, for example, the volume of three particles, and collect all particles from left to right. (Even if the sampling volume v is not a factor of the total particle volume, if the total particle volume V is large enough, the remainder can be ignored.) Max N s,max The proportion of particles of interest in the particle group sampled a certain number of times, C i Standard deviation σ for population mean P e0 is expressed by Equation 5 based on the definition of Equation 2.

[0036]

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[0037] The variables on the right side of Equation 5 are Ns ,max : Maximum number of samplings, C i : The proportion of the particle of interest in the volume of the sample, P: The proportion of the particle of interest in the total volume V of the mixture.

[0038] Maximum number of samplings Ns ,max is expressed by Equation 6. The variables on the right side of Equation 6 are V: total volume, and v: sampling volume.

[0039]

number

[0040] Also, the ratio of the particle of interest to the volume of the i-th sampling, C i takes on values ​​in the range of Equation 7.

[0041]

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[0042] Maximum number of times N s,max The proportion of target particles in the sampling volume of the particle group being sampled, C i Standard deviation σ for population mean P e0 Equation 5 for calculating the degree of mixing M in a completely separated state is described above. Applying equations 6 and 7 to equation 5 results in equation 8. e0 The standard deviation σ used for e0 This is an example of the degree of mixing M e0 The standard deviation σ used in e0 is the standard deviation when the total volume of a given mixture is divided into samples and the number of samples is maximized.

[0043]

number

[0044] Next, calculate the standard deviation σ0 of the sample in the completely separated state when the sampling volume v is very small compared to the total volume V. σ0 is the standard deviation σ0| when v → 0 in the completely separated state. v→0 Then, σ0 is expressed by Equation 9.

[0045]

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[0046] Standard deviation σ calculated from Equation 8 e0 and the standard deviation σ0 calculated from Equation 9 are used to calculate the degree of mixing M e0 Substituting each of these into Equation 4 to calculate Equation 10 is obtained.

[0047]

number

[0048] As shown in Equation 10, the degree of mixing in the completely separated state, M e0 can be expressed only by the sampling volume v and the total volume V. The total volume is a measurable value, and only the sampling volume v is an unknown quantity.

[0049] [2-3] Relationship between sampling volume and degree of mixing in a completely mixed state Mixing degree M of the complete mixed state R is expressed by Equation 11 based on the definition of Equation 1.

[0050]

number

[0051] Standard deviation σ of perfectly mixed samples RHere, the definition of a completely mixed state will be explained using white particles and black particles as an example, with reference to FIG. 5A. FIG. 5A shows the completely mixed state as a homogeneous mixture, expanded to the particle scale, and expressed one-dimensionally by a random horizontal row of all particles. As in FIG. 4, adjacent particles are in contact with each other at a single point.

[0052] Let the sampling volume v be the volume of three particles, for example. Let the standard deviation when all particles are randomly sampled in the sampling volume v be σ. R In the extraction model shown in Figure 5B, the standard deviation σ R can be considered as the standard deviation of the proportion of particles of interest in a volume randomly taken out of a bag in which the particles of interest exist with a certain probability Q. When this is applied to the example of this embodiment, the standard deviation σ R is the proportion C of the particle of interest in the sampling volume v when a sampling volume v is randomly taken from the volume V of the mixture in which the particle of interest exists with a certain probability P. i It can be said that the standard deviation of σ R When n>>1 and nP>>1, nP(1-P)>>1, the binomial distribution Bin(n,P) can be approximated to the normal distribution N(nP,nP(1-P)), and is expressed as Equation 12. Note that the total number of particles is sufficiently large, so the number of random samplings is maximized.

[0053]

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[0054] The standard deviation σ of Eq. R The variable on the right side of the equation is n: the number of sampling particles, and the variable on the right side of the equation is V PT : The volume per particle of interest.

[0055] By applying the finite population correction to Equation 12, it can be transformed into the central equation of Equation 13. Equation 12 expresses the degree of mixture M R The standard deviation σ used for R This is an example of the degree of mixing MR The standard deviation σ used in R is the standard deviation when the total volume of a given mixture is divided into samples and the number of samples is maximized.

[0056]

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[0057] In the sampling model shown in Figure 5B, randomly drawn samples are not returned to the bag, and the number of particles in the bag continues to decrease. This is sampling without replacement from a finite population, and adding the finite population correction to the middle equation of Equation 13 results in the equation on the right side of Equation 13.

[0058] Standard deviation σ calculated from Equation 13 R and the standard deviation σ0 calculated from Equation 9 are used to calculate the degree of mixing M R Substituting these into Equation 11 for calculating Equation 14 is obtained.

[0059]

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[0060] As shown in Equation 14, the degree of mixing in the complete mixture state, M R are the sampling volume v, the total volume V, and the volume per particle V PT The total volume and the volume per particle are measurable values, and only the sampling volume v is unknown.

[0061] [2-4] How to determine the optimal sampling volume As mentioned above, the error in the degree of mixing D M The sampling volume is optimal when the minimum value is reached. e0 Error from 0 and the completely mixed state M R We explain how to determine the sampling volume (size) that minimizes the sum of the errors from 1.

[0062] Formula 15 is formulated to differentiate formula 3, and the degree of mixing in the completely separated state, M, calculated from formula 10, is e0 and the degree of mixing of the completely mixed state calculated from Equation 14, M R Substituting these values ​​into Equation 15, the optimal sampling volume v ОPT Equation 16 is obtained to calculate

[0063]

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[0064]

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[0065] The optimal sampling volume v is given by Equation 16. ОPT is the total volume V and the volume per particle V PT Therefore, by using Equation 16, the optimal sampling volume v ОPT Equation 16 is an example of a relational expression for the size of a sample from a mixture, the total size of the mixture, and the size of a single particle of interest. In this way, this relational expression determines the degree of mixing M in a completely separated state of the particle of interest. e0 The error from 0 and the complete mixing state M R The sum is derived based on the sum of the error from 1 of the degree of mixing in the matrix, where the sum is minimum or below a threshold.

[0066] [2-5] Sampling volume selection range In [2-4], we explained how to determine the optimal sampling volume v to measure the mixing state precisely, but depending on the product, if the degree of mixing is within a predetermined tolerance, there may be cases where the quality of the final product is not affected. In that case, the completely separated state M e0 Error from 0 and the completely mixed state M R The sum of the error from 1 does not need to be the smallest, but only needs to be below a predetermined threshold. M Threshold R v(In other words, the completely separated state M e0 Error from 0.0 and the completely mixed state M R The error D of the degree of mixing is 1 minus the sum of the error from 1.0 of M The threshold R given to v ), Equation 15 becomes Equation 17.

[0067]

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[0068] The sufficient condition for Equation 17 is Equation 18.

[0069]

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[0070] Equation 18 can be rewritten in terms of the range of sampling volume v to obtain Equation 19. As shown in Equation 19, the total size of the mixture, the size of each particle of interest, and the threshold value R of the error tolerance range are used. v Based on this, the range of sizes to sample from the mixture is expanded.

[0071]

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[0072] In Figures 6A and 6B, the horizontal axis represents the sampling volume v, and the vertical axis represents the error D of the degree of mixing. M This graph shows the allowable range of the sampling volume v calculated based on Equation 19. The value substituted for each variable in Equation 19 is the total volume V = 5.65 × 10 -2 [m 3 ], the proportion of particles of interest C i =P=0.5[-], volume per particle of interest V PT =1.77×10 -9 [m 3 ], the optimal sampling volume v ОPT =1.78×10 -4 [m 3 ], threshold R v= 0.01 (Figure 6A), 0.2 (Figure 6B).

[0073] Figure 6A shows the threshold R v = 0.01, the allowable range of the sampling volume b is 7.07 × 10 -5 ~5.64×10 -4 Figure 6B shows the threshold R v = 0.2, the allowable range of the sampling volume v is 1.77 × 10 -7 ~1.07×10 -2 is.

[0074] Mixing degree error D M Threshold R v By providing the above, a tolerance can be given to the sampling volume, and the range of selection of the sampling volume can be expanded.

[0075] [3] Determining the number of sampling times Below, the relationship between the number of samplings and the degree of mixing will be described in item [3-1], and the method for determining the number of samplings will be described in item [3-2].

[0076] [3-1] Relationship between the number of samplings and the degree of mixing First, referring to FIGS. 7A to 8C, the number of samplings N s The relationship between the volume and the degree of mixing will be explained. The conditions for the tumbling rotary mixer shown in Figures 7A and 7B are the same as those in Figure 1. As in Figures 2A and 2B, the particles are two colors, black and white, the volume per particle is the same, the number of particles is the same, and the particle of interest is a white particle. The number of small white circles in the particle group represents the number of times sampling is performed, and the volume v of each sampling is the same.

[0077] 8A to 8C are graphs with the mixing time on the horizontal axis and the degree of mixing M on the vertical axis, and the thick solid lines are plots of the degree of mixing M calculated based on Equations 1 and 2 using samples taken a predetermined number of times at each time. The degree of mixing is expressed as a value between 0 and 1. Two horizontal lines are drawn in the graphs, and the dashed line at the position of 0 on the vertical axis represents the degree of mixing M. e0The dashed line at the vertical axis position 1 indicates the degree of mixing M R Shows.

[0078] Number of samplings N s When the number of sampling times N is relatively large, the degree of mixing M is drawn as a single curve from the completely separated state to the completely mixed state, as shown in Figure 8A, and the mixed state can be measured precisely. However, the measurement time cannot be shortened because the number of steps for measurement is large. s When the number of sampling times N is relatively small, the value of the degree of mixing fluctuates significantly and is unreliable, as shown in Figure 8B. s In the optimal case, as shown in Figure 8C, the fluctuation of the mixture degree value is small and the graph follows an ideal curve. In other words, the number of sampling times N that can obtain a mixture degree with any certainty is s It can be said that it is practical.

[0079] [3-2] How to determine the number of sampling times As mentioned above, to calculate the practical range of sampling times, it is necessary to determine the range of certainty (confidence). To do this, we need to determine the number of times N for a given sampling volume v. s The proportion of particles of interest in the sampled particle group, C i The population mean P and the predetermined number of times N s The average proportion of particles of interest in the sampled particle group, C i (Small Eye Bar) Error is ±R Ns It is sufficient if it is within the range.

[0080] Mixing degree M in a completely separated state e0 and degree of mixing in the complete mixed state M R The particle ratio C of interest in each i is a normal distribution N(P,σ 2 ), the particle ratio C i The normalized z is shown in Equation 20.

[0081]

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[0082] Here, z follows the standard normal distribution N(0,1), so when the reliability is 1-α, the population mean P is within the range of Equation 21.

[0083]

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[0084] The variables in Equation 21 are z 1-α : Reliability coefficient at the reliability level (1-α), in detail, z 1-α : The value on the horizontal axis of the standard normal distribution N(0,1) corresponding to the reliability (1-α) (hereinafter referred to as the "upper value of the standard normal distribution"), in other words, the upper 100(1-α)% point of the standard normal distribution N(0,1).

[0085] A given sampling volume v is sampled a given number of times N s The proportion of particles of interest in the sampled particle group, C i The population mean P and the predetermined number of times N s The average proportion of particles of interest in the sampled particle group, C i (Small eye bar) error is ±R Ns Within the range of z in Eq. 1-α The term R as shown in Equation 22 Ns It needs to be the following:

[0086]

number

[0087] Then, the number of sampling times N s The formula for calculating the minimum value is Equation 23.

[0088]

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[0089] The proportion of target particles in the entire mixing process C i Assume that the average standard deviation σ is Eq.

[0090]

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[0091] Equation 23 can be transformed into Equation 25.

[0092]

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[0093] As shown in Equation 25, the number of times to sample from a mixture is the number of times N that can be sampled using the sampling size from an arbitrary mixture. s,max (See Equation 6), the number of samplings for the proportion of particles of interest in the completely separated state is set to the maximum (N s,max ) the standard deviation σ e0 and the number of samplings for the proportion of the target particles in a completely mixed state is set to a maximum (N s,max ) the standard deviation σ R and the tolerance R for the population mean between the proportion of the target particle in the mixture and the sample mean. Ns and the upper value z of the standard normal distribution corresponding to the confidence level 1-α 1-α The reliability coefficient z at the reliability level (1-α) is determined by Equation 25. 1-α and tolerance ±R Ns By setting an arbitrary value to , the number of sampling times N in the range that satisfies Equation 25 can be determined. s can be calculated.

[0094] [4] Variable replacement So far, the sampling size has been described as a sampling parameter in terms of volume. However, the above-described method can be applied to cases other than when a predetermined volume is sampled from a mixture having a volume. If the sampling object is a two-dimensional photograph of a flat surface, the method of the present invention can be applied by regarding the particle of interest as an area. Similarly, if the sampling object is a one-dimensional line segment, the particle of interest can be considered as the length it occupies, and if the sampling object is a particle group, the particle of interest can be considered as a number. In this case, the size of each sample can be calculated in the same way as the volume by replacing the variables in Equations 16 and 19 with the variables in Table 1.

[0095] Furthermore, the number of sampling times N s In the calculation of the above, by replacing the variables in Equation 8, Equation 13, and Equation 25 with the variables in Table 1, the number of samplings N according to each sampling size can be calculated. s can be calculated.

[0096] [Table 1]

[0097] Using Table 1, we can replace the variables in Equation 16 to find the optimal sampling area s OPT In the case of OPT In the case of Equation 27, the optimal number of optimal samplings, n OPT In this case, the formula is Equation 28. As described above, Equations 26 to 28 are examples of relational expressions between the total size of the mixture and the size of each particle of interest, for calculating the size to be sampled from the mixture.

[0098]

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[0099]

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[0100]

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[0101] Furthermore, by substituting the variables in Equation 19 using Table 1, we obtain Equation 29 for the area of ​​sampling with tolerance s, Equation 30 for the length of sampling with tolerance l, and Equation 31 for the number of samples with tolerance n. As shown in Equations 29 to 31, the total size of the mixture, the size of each particle of interest, and the threshold value R of the tolerance of error are used to calculate the error. v Based on this, the range of sizes to sample from the mixture is expanded.

[0102]

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[0103]

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[0104]

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[0105] Furthermore, by substituting the variables in Equation 8 using Table 1, the standard deviation of the sample in the completely separated state, σ e0 is derived using Equation 32 when the sampling area with a tolerance is s, is derived using Equation 33 when the sampling length with a tolerance is l, and is derived using Equation 34 when the number of samples with a tolerance is n. Equations 32 to 34 are examples of the standard deviation used for the degree of mixing in a completely separated state.

[0106]

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[0107]

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[0108]

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[0109] In addition, by substituting the variables in Equation 13 using Table 1, the standard deviation of the completely mixed sample, σ R is derived by Equation 35 when the area of ​​the sampling with tolerance is s, by Equation 36 when the length of the sampling with tolerance is l, and by Equation 37 when the number of samples with tolerance is n. Equations 35 to 37 are used to calculate the degree of mixing M R The standard deviation σ used for R This is an example.

[0110]

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[0111]

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[0112]

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[0113] The present invention is not limited to measuring volume, but can also be applied to measuring area, length, and number as described above. Therefore, even when using equipment that analyzes two-dimensional images or images obtained using a line sensor, the degree of mixing can be determined with high accuracy and with an appropriate number of images taken.

[0114] [5] Configuration of information processing device The information processing device that performs the arithmetic processing of this embodiment is realized by a general-purpose computer that can execute the computer program 18 for the determination processing described above (the process of determining the sampling size and the number of samplings of this embodiment).

[0115] [5-1] Hardware configuration of information processing device FIG. 9 is a block diagram illustrating a typical hardware configuration example of an information processing device 10 according to an embodiment. The computer (information processing device) 10 includes a CPU (processor) 11 (Central Processing Unit), a memory 12 (e.g., Read Only Memory (ROM), Random Access Memory (RAM)), an external storage device 13 (e.g., a Hard Disk Drive (HDD), a Solid State Drive (SSD), an optical drive, a flash memory, a reader / writer), an input device 14 (e.g., a keyboard, a mouse), an output device 15 (e.g., a display, a printer), a reading unit 16 (e.g., a reader), and a communication device 17 (a wireless or wired transmitting / receiving device). These are communicatively connected to one another via a bus 19 (e.g., a control bus, a data bus) provided within the computer 10. A computer program 18 is installed in the external storage device 13.

[0116] The computer program 18 may be recorded on a recording medium 20 that can be read by an optical drive, a flash memory, a reader / writer, or the like. Alternatively, the computer program 18 may be recorded on online storage on a network to which the computer 10 can connect. In either case, the computer program 18 can be executed by downloading it to the HDD, SSD, or the like of the computer 10, or by loading it into the CPU 11 or memory 12.

[0117] The CPU 11 of this embodiment loads a program installed in the external storage device 13 into the memory 12, executes it, and outputs the calculation results to the output device 15. Data required for the determination process (total size of the mixture, size of each particle of interest, threshold value of the allowable range of error, etc.) is set based on input from the input device 14 or as a given value in advance. The data required for the determination process include the total volume V of the mixture and the volume V of each particle of interest. PT and the particle volume V relative to the total volume V PTThe proportion P and the reliability coefficient z 1-α , the tolerance of the number of samplings ±R Ns This includes:

[0118] [5-2] Functional configuration of information processing device FIG. 10 is a block diagram showing a schematic example of the software configuration of an information processing device 10 according to an embodiment. The information processing device 10, which performs the above-described arithmetic processing, includes an input unit 10a, a calculation unit 10b, a control unit 10c, and an output unit 10d. These elements may be realized by electronic circuits (hardware), or the function may be subdivided into multiple parts, some of which may be implemented as hardware and the other parts as software. The following description will be given taking the case where the size is measured in terms of volume as an example.

[0119] The input unit 10a inputs the total size of the mixture and the size of each particle of interest. That is, the input unit 10a inputs data necessary for the determination process (the total volume V of the mixture and the volume V of each particle of interest). PT and the particle volume V relative to the total volume V PT The proportion P and the reliability coefficient z 1-α , the tolerance of the number of samplings ±R Ns The input unit 10a is realized by the input device 14 of the information processing device 10.

[0120] The calculation unit 10b determines the size of the sample from the total size of the mixture and the size of each particle of interest based on the method for determining the size of the sample to determine the degree of mixing M of the particles of interest described above. The calculation unit 10b determines the volume v of the sample and the number of times N of the sample based on the input from the input device 14 or by acquiring a preset value. s Based on the determination method, the sampling volume v and the number of samplings N s The calculation unit 10b of this embodiment calculates the total volume V of the mixture and the volume V per particle of interest. PT and substitute the obtained value into Equation 16 to obtain the optimal sampling volume v ОPT Determine.

[0121] The calculation unit 10b calculates the total volume V of the mixture and the volume V per particle of interest. PT In addition, if errors are allowed, the threshold R v The obtained value is substituted into Equation 19 to determine the sampling volume v within the tolerance range.

[0122] The calculation unit 10b may calculate the optimal sampling size by selecting a measure other than the volume listed in Table 1. For example, the calculation unit 10b may calculate the optimal sampling size by calculating the total area S of the mixture and the area S per particle of interest. PT and then substitute the obtained value into Equation 26 to obtain the optimal sampling area s OPT The calculation unit 10b may also determine the total length L of the mixture and the particle diameter L of each particle of interest. PT and then substitute the obtained value into Equation 27 to determine the optimal sampling length l OPT Alternatively, the calculation unit 10b may obtain the total number N of mixtures, and substitute the obtained value into Equation 28 to determine the optimal number of samples n OPT may be determined.

[0123] Similarly, when calculating the number n of samples within the allowable range, the length l of the samples, and the area s of the samples, the calculation unit 10b may replace the variables in Equation 19 with the variables in Table 1 and determine each value based on Equations 29 to 31.

[0124] Furthermore, the calculation unit 10b calculates the target particle volume V relative to the total volume V PT The proportion P and the reliability coefficient z 1-α , the tolerance of the number of samplings ±R Ns and using Equation 25, the number of samplings N in the range that satisfies Equation 25 is obtained. s Determine.

[0125] Similarly, the calculation unit 10b calculates the number of sampling times N for the number n. s , the number of sampling times N of length l s , the number of sampling times for area s is N sWhen calculating the above, the variables in Equation 8, Equation 13, and Equation 25 may be replaced with the variables in Table 1 to determine the respective values.

[0126] The calculation unit 10b calculates the optimal sampling volume v ОPT or the volume of sampling v and the number of samplings N s are stored in the external storage device 13.

[0127] Furthermore, the calculation unit 10b may determine the degree of mixture M of the particle of interest based on the determined sampling size and number of samplings. Specifically, sampling is performed using the determined sampling size and number of samplings, and the degree of mixture M of the particle of interest is calculated for the sample using the above-mentioned formula 1. The calculation unit 10b stores the determined degree of mixture M of the particle of interest in the external storage device 13. The calculation unit 10b is realized by the CPU 11 of the information processing device 10.

[0128] The control section 10c will be explained later in connection with the mixer.

[0129] The output unit 10d outputs the optimum sampling volume v calculated by the calculation unit 10b. ОPT or the volume of sampling v and the number of samplings N s and further outputs the degree of mixing M of the particle of interest. The output unit 10d is realized by the output device 15.

[0130] [6] Example of operation FIG. 11 is a flowchart showing the procedure when the computer 10 executes the computer program 18 (the method for determining the sampling volume and the number of samplings in this embodiment). As shown in FIG. 11, steps S1 and S1′ are initialization steps for steps S2 and S2′. In step S1, data required for the process of determining the sampling volume (the total volume V of the mixture and the volume V per particle of interest) are input. PT ) are prepared or input from the external storage device 13, the input device 14, etc. The above-mentioned determination unit 18b acquires the prepared or input values.

[0131] Furthermore, in step S1′, the error D of the degree of mixing is calculated as data necessary for the process of determining the sampling volume. M The threshold R given to v are prepared or input from the input unit 10a (external storage device 13, input device 14, etc.). The calculation unit 10b acquires the prepared or input values.

[0132] Step S2 is the optimal sampling volume v ОPT This step S2 is performed by the calculation unit 10b. In this step S2, the total volume V of the mixture and the volume V of each particle of interest obtained in step S1 are calculated. PT Substituting into Equation 16, the optimal sampling volume v ОPT As mentioned above, Equation 16 is used to calculate the complete separation state M e0 Error from 0 and the completely mixed state M R The sum of the error from 1 is calculated, and the sum is derived from Equation 15, which indicates that the sum is minimum.

[0133] Step S2' is a step of determining the sampling volume v within the above-mentioned allowable range, and is performed by the calculation unit 10b. In this step S2', the total volume V of the mixture obtained in step S1 and the volume V per particle of interest are calculated. PT and the error D of the degree of mixing obtained in step S1′ M The threshold R given to v and are substituted into Equation 19 to calculate the volume v of the sampling that has the tolerance range. As mentioned above, Equation 19 is used in the completely separated state M e0 Error from 0 and the completely mixed state M R The sum of the error from 1 is calculated, and the sum is the threshold R v This is derived from the sufficient condition in Equation 17, which states that

[0134] Step S3 is an initial setting step for step S4′. In this step S3, data necessary for the process of determining the number of samplings (volume V of the particle of interest relative to the total volume V) is PTProportion P, confidence coefficient z 1-α and the tolerance of the number of samplings ±R Ns ) are prepared or input from the input unit 10a (external storage device 13, input device 14, etc.). The calculation unit 10b acquires the prepared or input values.

[0135] Step S4 is the number of times N of sampling described above. s This step S4 is a step of determining the particle volume V of interest relative to the total volume V obtained in step S3. PT Proportion P, confidence coefficient z 1-α and the tolerance of the number of samplings ±R Ns Substituting into Equation 25, the practical number of sampling times N s Furthermore, the calculation unit 10b calculates the optimum sampling volume v ОPT or the volume of sampling v and the number of samplings N s The above may be stored in the external storage device 13.

[0136] In step S5, the output unit 10d outputs the optimal sampling volume v ОPT or the volume of sampling v and the number of samplings N s and then exit.

[0137] [7] Mixer configuration The information processing device 10 that performs the calculation processing of this embodiment may be incorporated inside the mixer. In other words, the computer program 18 for the determination processing described above (the process of determining the sampling size and the number of samplings of this embodiment) may be executed as part of the overall mixing processing of the mixer in the information processing device (computer) 10 inside the mixer. The information processing device 10 incorporated in the mixer controls the rotation of the drum (mixing operation) based on the calculated values. The following description will focus on the control of the mixing operation. Note that parts that are assigned the same reference numerals as those used in the description of the information processing device 10 are the same or substantially similar. The following description will be given taking the case where the size is in terms of volume as an example.

[0138] [7-1] Hardware configuration of the mixer 12 is a block diagram illustrating a hardware configuration example of a mixer 30 according to an embodiment. An example of the mixer 30 is a tumbling rotary mixer, but is not limited to this. The mixer 30 according to this embodiment includes an information processing device 10 and a drum 31.

[0139] The input device 14 of the information processing device 10 inputs data necessary for the processing of this embodiment. The input device 14 may also input data necessary for the rotation of the drum 31.

[0140] The CPU 11 of the information processing device 10 determines the sampling size (optimum sampling size or a sampling size within a selection range according to the allowable degree of mixing) and the number of samplings. Furthermore, the CPU 11 determines the degree of mixing M of the target particles based on the determined sampling size and the number of samplings. Furthermore, the CPU 11 controls the rotation of the drum 31 according to the determined degree of mixing.

[0141] Drum 31 mixes the target material (hereinafter also referred to as the target material) containing the target particles introduced therein by rolling and rotating. Drum 31 rolls and rotates in accordance with input from input device 14, a value set as a predetermined value, and the determined degree of mixing M.

[0142] [7-2] Software configuration of the mixer An example of the software configuration of the mixer 30 according to the embodiment is the same as the example configuration shown in Fig. 10. Similar to the software configuration of the information processing device 10, the mixer 30 includes an input unit 10a, a calculation unit 10b, a control unit 10c, and an output unit 10d.

[0143] The input unit 10a inputs necessary data. The calculation unit 10b determines the sampling size and the number of samplings based on the necessary data input from the input unit 10a. Furthermore, after the drum 31 mixes the objects for a predetermined time, the calculation unit 10b determines the degree of mixing M of the target particles for the mixed objects based on the determined sampling size and number of samplings and other necessary information.

[0144] The control unit 10c performs mixing according to the degree of mixing M of the particles of interest based on the sampling size determined by the calculation unit 10b. After the drum 31 has mixed the objects for a predetermined time, the control unit 10c controls the rotation (mixing operation) of the drum 31 according to the degree of mixing M of the particles of interest determined by the calculation unit 10b. The control unit 10c is realized by the CPU 11 of the information processing device 10.

[0145] The control unit 10c may determine the degree of completion of mixing of the objects based on the degree of mixing M determined by the calculation unit 10b. If the degree of mixing M of the objects is the desired degree of mixing, the control unit 10c determines that mixing is complete and ends the mixing operation. On the other hand, if the degree of mixing M of the objects has not reached the desired degree of mixing, the control unit 10c determines that mixing is incomplete and resumes the mixing operation. The control unit 10c continues the mixing operation for a predetermined time depending on the degree of completion of mixing.

[0146] The output unit 10d outputs the values ​​determined by the calculation unit 10b and the control unit 10c.

[0147] When controlling the mixing operation in the drum 31, the mixing conditions are set by using data created by general-purpose software in the computer program 18, or by inputting data from the input device 14.

[0148] Furthermore, when performing a simulation of mixing, by using the information processing device 10 that performs this calculation processing, various conditions can be set by using data created by general-purpose software in the computer program 18, or by inputting the data from the input device 14, thereby enabling an accurate simulation.

[0149] [8] Effects (1) In the above-described method for determining the degree of particle mixing, the program 18, the information processing device 10, and the mixer 30, the size of a sample to be sampled from the mixture is determined by calculating it from a relational expression between the total size of the mixture and the size of a single particle of interest. This makes it possible to easily calculate the optimal sampling size based on measurable values, namely the total size and the size of a single particle of interest.

[0150] (2) If the sampling size is volume v, then the optimal sampling volume v ОPT The volume of the mixture is V, and the volume of the particle of interest is V. PT The optimum sampling volume v ОPT The total volume V and the volume V of the particle of interest PT This can be easily calculated based on the measurable values:

[0151] Similarly, if the sampling size is area s, then the optimal sampling area s ОPT The total area of ​​the mixture is S, and the particle area of ​​the particle of interest is S. PT The optimum sampling area s is determined using Equation 28, which is derived from Equation 15, which indicates that the sum is minimized. ОPT can be easily calculated based on the total area S, which can be measured.

[0152] Similarly, if the sampling size is length l, then the optimal sampling length l ОPT The total length of the mixture is L, and the particle diameter of the particle of interest is L. PTThe optimum sampling length l is determined using Equation 27, which is derived from Equation 15, which indicates that the sum is minimized. ОPT can be easily calculated based on the total length L, which is a measurable value.

[0153] Similarly, if the sampling size is the number of samples, the optimal number of samples is n ОPT is determined using Equation 26, which is derived from Equation 15, which shows that the sum is minimized when the total number of particles contained in the mixture is N. This allows us to determine the optimal number of samples, n ОPT can be easily calculated based on the measurable value of the total number N.

[0154] (3) The equations used in the method, program 18, information processing device 10, and mixer 30 for determining the degree of mixing of particles are the degree of mixing M e0 The error from 0 and the degree of mixing M R The sum of the error from 1 and the sum is at least 0 or threshold R v This allows us to determine the optimal value for the size of the mixture portion to be sampled if the sum is at least 0, and the sum is the threshold R v The size of the mixture sample can be determined with a range of tolerances if:

[0155] (4) Mixing degree M in a completely separated state e0 is the maximum number of samplings when the total size of any mixture is divided by the sampling size (N s,max ) the standard deviation σ e0 This allows us to calculate the degree of mixing in a completely separated state M e0 The relationship can be expressed by the following equation.

[0156] (5) The degree of mixing M in the completely mixed state Ris the maximum number of samplings when the total size of any mixture is divided by the sampling size (N s,max ) the standard deviation σ R This allows us to calculate the degree of mixing M in a completely mixed state relative to the parameter for sampling a portion of the mixture (the sampling volume v). R The relationship can be expressed by the following equation.

[0157] (6) By using a threshold value for the tolerance of error between the total size of the mixture and the size of each particle of interest, the range of selection for the sampling size can be expanded. This allows for a tolerance range for the sampling size. By allowing for a tolerance range for the sampling size, it is possible to provide a degree of freedom for the sampling volume according to the desired degree of mixing while ensuring reliability.

[0158] (7) When the sampling size is volume, the volume of the sampling with an allowable range, v, is defined as the total volume of the mixture, V, and the volume of one particle of interest, V. pt and the threshold is R v When the sampling volume v is within the tolerance range R, it is selected from the range determined by Equation 19. v By providing the above, it is possible to provide a reliable degree of freedom for the sampling volume v according to the desired degree of mixing.

[0159] When the sampling size is area, the area s of the sampling with the tolerance is defined as follows: S is the total area of ​​the mixture, and S is the particle area of ​​the target particle. PT and the threshold is R s When the sampling area s is set to the tolerance range R, the area is selected from the range determined by Equation 31. v By providing the above, it is possible to provide a degree of freedom with guaranteed reliability to the sampling area s according to the desired degree of mixing.

[0160] When the sampling size is length, the sampling length l with an allowable range is defined as L, where L is the total length of the mixture, and L is the particle diameter of the target particle. PTand the threshold is R l When the sampling length l is set to the tolerance range R, the sampling length l is set to the tolerance range R. v By providing the above, it is possible to provide a degree of freedom with guaranteed reliability for the sampling length l according to the desired degree of mixing.

[0161] When the sampling size is the number of particles, the number of samples n with an acceptable range is the total number of particles contained in the mixture, N, and the threshold is R n When the number of samples n is set to the tolerance range R, the value is selected from the range determined by Equation 29. v By providing the above, the number of samples n according to the desired degree of mixing can be calculated.

[0162] (8) Number of samplings N s is the number of times that sampling can be performed for the particle of interest contained in a part of an arbitrary mixture, s,max In the completely separated state M e0 The number of samplings for the number of particles of interest in s,max ) and the standard deviation is σ ε0 In the completely mixed state M R The number of samplings for the number of particles of interest in s,max ) and the standard deviation is σ R The ratio P of the target particle in the mixture and the sample mean C i (Small Eye Bar) and the error R Ns Let z be the upper value of the standard normal distribution. 1-α (condition of Equation 21), the allowable error R is determined by Equation 25. Ns and the reliability coefficient z 1-α can be set arbitrarily, so the tolerance is ±R Ns and the reliability coefficient z at the reliability level (1-α) 1-α By setting appropriate values ​​for and , the number of samplings Ns can be determined according to the desired degree of mixing within a range that satisfies Equation 25.

[0163] (9) The mixer 30 includes an input unit 10a for inputting the total size of the mixture and the size of each particle of interest, a calculation unit 10b for determining the size and number of samples based on the input total size of the mixture and the size of each particle of interest according to the method of the present invention, and a control unit 10c for performing mixing according to the degree of mixing of the particles of interest based on the determined size and number of samples. The mixer 30 of the present invention can achieve a highly reliable degree of mixing, thereby providing a highly reliable product.

[0164] As described above, the method for determining the mixing degree of a particle of interest from a mixture containing the particle of interest, the program 18, the information processing device 10, and the mixer according to this embodiment make it possible to accurately determine the volume and number of samplings for measuring the mixing degree of a particle of interest in a mixture according to the desired mixing degree, thereby improving the accuracy of quality control of final products containing the mixture as a component.

[0165] [9] Other The disclosed technology is not limited to the above-described embodiment, and various modifications can be made without departing from the spirit of the present embodiment. The configurations and processes of the present embodiment can be selected or combined as needed.

[0166] In this embodiment, an example of mixing two types of particles has been described, but even when there are two or more types, the particles can be considered as being divided into particles of interest and other particles, and the above-mentioned method can be applied.

[0167] In this embodiment, the particles of interest are described as spherical particles, but the shape is not limited to a sphere as long as the particles are solid. When the sampling size is the particle diameter, any shape is acceptable as long as the particle diameter can be defined. In this way, the apparatus, method, and program of this embodiment are applicable to all industrial fields where solid particles of interest are mixed.

[0168]

[10] Supplementary Note The following additional notes are provided regarding the above-described embodiments.

[0169] (Appendix 1) When determining the degree of mixing of the target particle from a mixture into which the target particle is mixed, The size of the sample to be sampled from the mixture is The particle size is determined by calculation from a relational expression between the total size of the mixture and the size of each particle of interest. A computer-readable recording medium storing a program for determining the degree of mixing of target particles, the processing of which is executed by a computer.

[0170] (Appendix 2) an input unit for inputting the total size of the mixture and the size of each particle of interest; a calculation unit that determines a size to be sampled from the mixture based on the total size of the mixture and the size of each of the particles of interest, based on the method for determining the degree of mixing of particles of interest according to any one of claims 1 to 11; a control unit that performs mixing according to the degree of mixing of the target particles based on the sampling size determined by the calculation unit; Brief description of symbols

[0171] 10 Information processing equipment (computers) 10a Input section 10b Arithmetic unit 10c Control section 10d Output section 11 CPU (processor) 12 Memory 13 Storage device 14 Input Devices 15 Output Devices 16 Reading unit 17. Communications equipment 18 Programs 19 Bus 20 Recording Media 30 Mixer 31 Drums

Claims

1. When determining the degree of mixing of the target particle from a mixture into which the target particle is mixed, determining a size to be sampled from the mixture by calculation from a relational expression between the total size of the mixture and the size of each particle of interest; A method for determining the degree of mixing of particles of interest.

2. The above relation is: When the size is a sampling volume v, the following formula A is satisfied: When the size is a sampling area s, the following formula B is given: When the size is a sampling length l, it is expressed by the following formula C: When the size is the number n, the following formula D is satisfied:

2. The method of claim 1 for determining the degree of mixing of particles of interest. [Equation 1] (V: total volume of the mixture, V ＰＴ : volume per particle of interest) [Equation 2] (S: total area of ​​the mixture, S ＰＴ : particle area per particle of interest) [Equation 3] (L: total length of the mixture, L ＰＴ : particle diameter per particle of interest) [Equation 4] (N: total number of particles contained in the mixture)

3. The above relation is: is derived based on the sum of the error from 0 of the degree of mixing of the particles of interest in a completely separated state and the error from 1 of the degree of mixing of the particles of interest in a completely mixed state, the sum being a minimum or equal to or less than a threshold value.

3. A method for determining the degree of mixing of particles of interest according to claim 1 or 2.

4. The degree of mixing in the completely separated state is determined by the standard deviation obtained by maximizing the number of samplings when the total size of any of the mixtures is divided by the size.

4. The method for determining the degree of mixing of particles of interest according to claim 3.

5. The standard deviation used for the degree of mixing in the completely separated state is When the size is a sampling volume v, it is derived by the following formula E: When the size is a sampling area s, it is derived by the following formula F: When the size is a sampling length l, it is derived by the following formula G: When the size is the number n, it is derived by the following formula H:

5. The method of determining the degree of mixing of particles of interest according to claim 4. [Equation 5] (V: total volume of the mixture, P: proportion of the target particle in the total volume V of the mixture) [Equation 6] (S: total area of ​​the mixture, P: proportion of the target particle in the total area S of the mixture) [Equation 7] (L: total length of the mixture, P: proportion of the target particle in the total length L of the mixture) [Equation 8] (N: total number of particles contained in the mixture, P: proportion of the target particle in the total number N of the mixture)

6. The degree of mixing in the completely mixed state is determined by the standard deviation obtained when the total size of the mixture is divided by the size and the number of samplings is maximized. The method for determining the degree of mixing of particles of interest according to any one of claims 3 to 5.

7. The standard deviation used for the degree of mixing in the completely mixed state is When the size is a sampling volume v, it is derived by the following formula I: When the size is a sampling area s, it is derived by the following formula J: When the size is a sampling length l, it is derived by the following formula K: When the size is the number n, it is derived by the following formula L:

7. The method for determining the degree of mixing of particles of interest according to claim 6. [Equation 9] (V: total volume of the mixture, V ＰＴ : volume per particle of interest, P: proportion of particles of interest in the total volume V of the mixture) [Equation 10] (S: total area of ​​the mixture, S ＰＴ : particle area per particle of interest, P: proportion of particle of interest to total area S of the mixture) [0011] (L: total length of the mixture, L ＰＴ : particle diameter per particle of interest, P: proportion of the particle of interest to the total length L of the mixture) [0012] (N: total number of particles contained in the mixture, P: proportion of the target particle in the total size N of the mixture)

8. the total size of the mixture; and The size of each particle of interest; Based on the threshold, expanding the size selection range to sample from the mixture; 4. The method for determining the degree of mixing of particles of interest according to claim 3.

9. The size range selected for sampling from the mixture is: If the size is a sampling volume v, then the threshold is R ｖ When this is the case, it is determined by the following formula M: When the size is the sampling area s, the threshold value is R ｓ When this is the case, it is determined by the following formula N: When the size is the sampling length l, the threshold is R ｌ When this is the case, it is determined by the following formula O: When the size is the number n, the threshold value is R ｎ When this is the case, it is determined by the following formula P:

9. A method for determining the degree of mixing of particles of interest according to claim 3 or claim 8. [Equation 13] (V: total volume of the mixture, V ＰＴ : volume per particle of interest) [Equation 14] (S: total area of ​​the mixture, S ＰＴ : particle area per particle of interest) [Equation 15] (L: total length of the mixture, L ＰＴ : particle diameter per particle of interest) [Equation 16] (N: total number of particles contained in the mixture)

10. The number of times to sample the mixture is the number of times that any of the mixtures can be sampled using the sampling size; and the standard deviation of the proportion of the target particles in a completely separated state when the number of samplings is maximized; the standard deviation of the proportion of the target particles in a completely mixed state when the number of samplings is maximized; and a tolerance for the population mean between the proportion of the particles of interest in the mixture and the sample mean; The upper value of the standard normal distribution corresponding to the reliability level 1-α, Determined from A method for determining the degree of mixing of particles of interest according to any one of claims 1 to 9.

11. The number of samplings is The number of sampling times is N ｓ，ｍａｘ year, The standard deviation of the ratio of the target particles in the completely separated state when the number of samplings is maximized is σ ｅ0 year, The standard deviation of the ratio of the target particles in the completely mixed state when the number of samplings is maximized is σ Ｒ year, The error between the proportion of the target particles in the mixture and the sample average is R Ｎｓ year, The upper value of the standard normal distribution corresponding to the reliability 1-α is z １－α When Q is 1, Q is determined by the following formula:

11. The method for determining the degree of mixing of particles of interest according to claim 10. [Equation 17] where, if the size is a sampling volume v, then σ ｅ0 is derived using the following formula 18, and σ Ｒ is derived by the following equation 19. [Equation 18] [Equation 19] (V: total volume of the mixture, v: volume to be sampled, V ＰＴ : volume per particle of interest, P: proportion of particles of interest in the total volume V of the mixture) Here, when the size is the sampling area s, σ ｅ0 is derived using the following equation 20, and σ Ｒ is derived by the following equation 21. [Equation 20] [0000] (S: total area of ​​the mixture, s: area to be sampled, S ＰＴ : particle area per particle of interest, P: proportion of particle of interest to total area S of the mixture) Here, when the size is the sampling length l, σ ｅ0 is derived using the following equation 22, and σ Ｒ is derived by the following equation 23. [Equation 22] [Equation 23] (L: total length of the mixture, l: sampling length, L ＰＴ : particle diameter per particle of interest, P: proportion of the particle of interest to the total length L of the mixture) Here, when the size is the number of samples n, σ ｅ0 is derived from the following equation 24, and σ Ｒ is derived by the following equation 25. [0000] [Equation 25] (N: total number of particles in the mixture, n: number of particles to be sampled, P: proportion of particles of interest in the total number N of particles in the mixture)

12. A program that causes a computer to execute the method for determining the degree of mixing of particles of interest according to any one of claims 1 to 11.

13. An information processing device comprising a processor that executes the program according to claim 12.

14. an input unit for inputting the total size of the mixture and the size of each particle of interest; a calculation unit that determines a size to be sampled from the mixture based on the total size of the mixture and the size of each of the particles of interest, based on the method for determining the degree of mixing of particles of interest according to any one of claims 1 to 11; a control unit that performs mixing according to the degree of mixing of the target particles based on the sampling size determined by the calculation unit; A mixer equipped with:

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