Generation of random numbers and procedures applied to sampling inspection for product quality
Some standard content:
ICS 03.120.30
National Standard of the People's Republic of China
GB/T 10111-—2008
Replaces GB/T 10111-—2008
Replaces GB/T 10111-—2008, GB/T 15500—1995
Generation of random numbers and procedures applied tosampling inspection for product quality
Issued on 2008-07-28
General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China Administration of Standardization of the People's Republic of China
Implementation on 2009-01-01
GB/T 10111—2008
2 Normative References
3 Terms, Definitions and Symbols
3.1 Terms and definitions
3.2 Symbols.
4 General procedure for random sampling (see Figure 1)
4.1 Determine sample size or sampling volume
4.2 Select appropriate random sampling method
4.3 Number products in batches or batches
4.4 Generate random sample unit numbers
4.5 Take out unit products according to sample unit numbers1.6 Manage and inspect sample units|| tt||5 Methods of generating random numbers.
5.1 Random number table method
5.2 Random number table method
5.3 Pseudo-random number generator method
6 Simple random sampling
6.1 Implementation of simple random sampling
6.2 Purpose of simple random sampling
6.3 Examples of simple random sampling
7 Systematic sampling
7.1 Systematic sampling Sampling overview
7.2 Systematic sampling methods and implementation
8 Implementation of stratified random sampling
8.1: Overview of stratified sampling-
8.2 Implementation of stratified random sampling-
8.3 Examples of stratified random sampling
9 Notes on secondary or multiple sampling
Appendix A (Normative Appendix) Random number table
Appendix B (Normative Appendix)
Appendix C (Normative Appendix)
References
Poker card method for random samplingWww.bzxZ.net
Methods and procedures for generating pseudo-random numbers
GB/T10111--2008
This standard replaces GB/T10111--2008 "Methods for random sampling using random number generators" and GB/T15500-1995 "Methods for random sampling using electronic random number samplers". In order to make the technical content of this standard more systematic and convenient for operation, GB/T10111-1988 and GB/T15500-1995 are merged into one standard on the basis of retaining the main content and technical characteristics of the original standards. The main differences between this standard and GB/T10111-1988 and GB/T15500-1995 are: a) The technical framework of the standard is redesigned, and the standard text is drafted in accordance with the requirements of GB/T1.1-2000. b) In order to facilitate the understanding and implementation of the standard, relevant terms are added. 1) "General procedure for random sampling" is added. 2) "Random number table method", "pseudo-random number generator method" and "playing card method" for generating random numbers are added. 3) "Systematic random sampling" and "stratified random sampling" methods are added. f) Appendix A, Appendix B and Appendix C are added. Appendix A, Appendix B and Appendix C of this standard are all normative appendices. This standard is proposed by the China National Institute of Standardization. This standard is under the jurisdiction of the National Technical Committee for Standardization of Statistical Method Application. The drafting units of this standard are: PLA Ordnance Engineering College, China National Institute of Standardization, Institute of Mathematics and Systems Science of the Chinese Academy of Sciences, and Fuzhou Chunlun Tea Co., Ltd. The main drafters of this standard are: Zhang Yuzhu, Yu Zhenfan, Chen Min, Ding Wenxing, Feng Shiyong, and Fu Tianlong. The previous versions of the standards replaced by this standard are: GB/T101111988;
----GB/T 15500—1995,
一Scope
Generation of random numbers and their application in product quality
sampling inspection
This standard specifies the generation of random numbers and the method of random sampling using random numbers. GB/T 10111—2008
This standard is applicable to the extraction of random samples for quality sampling inspection of discrete individual products, and can also be used for the extraction of random samples in survey sampling. This standard is not applicable to the extraction of samples for quality sampling inspection of bulk products. 2 Normative references
The clauses in the following documents become clauses of this standard through reference in this standard. For any dated referenced document, all subsequent amendments (excluding errata) or revisions are not applicable to this standard. However, parties to an agreement based on this standard are encouraged to study whether the latest versions of these documents can be used. For any undated referenced document, the latest version applies to this standard. ISO3534-1:2006 Statistical vocabulary and symbols Part 1: General statistical terms and terms used in probability ISO3534-2:2006 Statistical vocabulary and symbols Part 2: Applied statistics 3 Terms, definitions and symbols
3.1 Terms and definitions
The following terms and definitions apply to this standard. 3.1.1
discreteiteml
products that are easily distinguishable from each other and that consist of a limited number of units. 3.1.2
samplingInspection
inspection carried out at a single production station from a set of products under consideration. [ISO 3534-2:2006,4.1, 6]
Note: A set of products may be a population, a batch or a submission. 3.1.3
population
the whole of the objects under consideration.
[ISO 3534-1:2006,1.1]
lot
a defined part of a population composed of essentially the same conditions for the purpose of sampling. Note: The purpose of sampling may be to determine the acceptability of a lot or to estimate the mean of a particular characteristic. [ISO 3534-2:2006,1. 2. 4
Sampling
The act of inserting or forming a sample.
[ISO 3534-2:2006,1, 3. 1]
GB/T 10111—2008
Random drawing drawanitemalrandom
A method of drawing individuals from a population consisting of N individuals in such a way that each individual has an equal probability of being drawn. 3.1.7
Sampling unit
Each part of a population into which it is divided. Note 1 to entry: A sampling unit may consist of one or more individuals. Note 2: Sampling units may consist of discrete individuals or of a certain number of bulk materials [IS0 3531-2:2006, 1, 2. 14]
sample sizesample size
The number of sampling units (or individuals) contained in the sample. [ISO 3534-2:2006, 1. 2. 26]
random sampling
Random sampling
The selection of sampling units from a population to form a sample so that each possible combination of sampling units has a certain probability of being selected.
[ISO 3534-2:2006,1, 3. 5]
sampling with replacement
replacement sampling
each sampling unit that has been selected and observed is returned to the population before the next sampling unit is selected. Note: In this sampling method, the same sampling unit may appear multiple times in the sample. [ISO 3534-2:2006,1. 3. 15
sampling without replacement sampling
each sampling unit is selected from the population only once and is not returned to the population. ISO 3534-2:2006,1. 3. 16
sample
a subset of the population consisting of one or more sampling units. Note: a sample can refer to the specific items, bulk materials, and services that constitute the sampling units., or a characteristic value of these sampling units (or unit products/individuals). When limiting the former meaning, each sampling unit (or unit product/individual) in the sample is also called a \sample\. [IS0 3534-1:2006,1. 2.17-
simple random samplingsimplerandom sampling is a sampling method in which two sampling units are selected from the population to form a sample so that all possible combinations of n sampling units have equal probability of being selected.
[ISO 3534-2:2006,1. 3. 4.
stratified samplingstratified sampling
samples are drawn from different layers of the population, and each layer has at least one sampling unit. [IS0 3534-2:2006, 1. 3. 6]
stratified simple random samplingstratified simple random sampling is a stratified sampling method in which simple random sampling is used in each layer. GB/T 10111—2008
Note: If the proportion of individuals/units of products drawn from different strata is equal to the proportion of the strata in the population, it is called proportional distribution stratified simple random sampling. [ISO3534-2.2006,1.3.7]
Systematic sampling
A sampling method in which the sampling units in the population are arranged in a certain order, one or a group of initial units are randomly selected within a specified range, and then the other sample units are determined according to a set of plans. 3.1.17
Periodic systematic sampling Arrange the N sampling units in the population in a certain order and number them from 1 to N, and select n units by equal interval sampling, that is, select n units with numbers h, h+k, h+2,, h+(n-1), where h is the integer closest to N/, and h is the number of the initial unit randomly selected from the integers from 1 to k. Synonym: periodic systematic sampling.
[IS03534-1.2006,1,3.13]
random number random number
A realization value of a specified random variable. Society, random numbers provided as a series are called random number sequences. 3.1.19
pseudo-random numberpseudo-random numberrandom number generated by a certain algorithm.
Note: In the absence of misunderstanding, pseudo-random numbers are also simply called random numbers. 3.1.20
physical random numberphysicalrandomnumberrandom numbergenerated by a certain physical device. 3.2 Symbols
K:-LN/R. ! , the integer part of N/R;
K2=[R./MI, the integer part of R./M;
an appropriate integer greater than N!
The number of random numbers determined according to the batch N; Sample size:
Total quantity of products or batch of products:
Random numbers generated by random number generation method: Pseudo-random numbers uniformly distributed on (0,1) generated by a random number generator, random numbers determined by the specified reading method, when R,>1, convert them into random numbers less than 1. General procedure for random sampling (see Figure 1)
4.1 Determine the sample size or sampling amount
According to the date of sampling inspection, the sample size or sampling amount of the sampling inspection shall be determined by appropriate standards or specifications. 4.2 Select the applicable random sampling method
According to the determined sampling inspection plan, select the applicable sampling method. This standard provides simple random sampling, systematic random sampling and stratified random sampling methods. 3
GB/T 10111-—2008
If there is a special need, cluster sampling or multi-stage sampling can also be used. Start
Determine the sample size or sampling quantity
Single random
4. 3 Number the products in the population or batch
Accumulate the sample
Number the products in the population or batch
Get the random number 1 and select the sample unit number
Take out the unit product according to the sample unit number
Manage the sample according to the regulations
Figure 1 General procedure of random sampling
According to the requirements of the selected sampling method, the product population, batch, production shift, production workshop, pallet and its unit product are numbered. The number should be unique and without duplication or omission.
Number the sampling units or unit products in sequence starting from "1" according to natural numbers. 4.4 Generate random sample unit numbers
Generate random sample unit numbers according to the sample size required by the sampling inspection plan or the sample size specified by other methods. 4.4.1 Method for obtaining random number R
This standard provides the following methods for generating random numbers or pseudo-random numbers. a) Random number Yinzi method;
b) Random number table method;
c) Pseudo-random number method;
d) Playing card method (see Appendix B).|| tt||4.4.2 Read the sample unit number K
After obtaining the random number R., the number R corresponding to the sample unit should be read correctly. 4.5 Take out the unit product according to the sample unit number Take out the corresponding unit product as the sample according to the generated random sample unit number. 4.6 Manage and inspect the sample unit
Manage and inspect the sample unit in accordance with the relevant provisions of the standard, specification or contract. 5 Method of generating random numbers
5.1 Random number table method
5.1.1 Introduction to random number table
GB/T 10111—2008
A random number table is a table consisting of numbers from 0 to 9, and each number has the same probability of appearing in each position. Appendix A provides five 50X50 random number tables (see Table A.1~Table A.5). If Table A.1 is not used, other suitable random number tables can be selected.
5.1.2 Method for obtaining random number Ro
a) Determine the random number table number and the initial point: First, randomly specify a point on the first table, and read 5 numbers to the right from it as the starting point. If the first number is less than 5, take the number plus 1 as the selected random number table number. If the first number is greater than or equal to 5, take the number minus 4. The difference is used as the selected random number table number. The 2nd to 3rd digits and the 4th to 5th digits form two two-digit numbers. If the two-digit numbers are less than 50, add 1. If the two-digit numbers are greater than or equal to 50, subtract 49. The final number represents the row and column number of the initial point.
b) The method to obtain R is: read the required m digits from the initial point downward to obtain the required random number R. During the reading process, if the last row of the page is read, go to the row and read the next column. If the last row is less than the last row, fill it up from the first column of the next two-digit table.
5.1.3 Read the sample unit number R
a) If the obtained random number Ro≤N, then the random number R Take R. ：If R>N, then set R=KiN+Ri; where K1=[N/R], when (K, + 1)N>10㎡, discard and regenerate the random number R; when (Ki + 1)N≤10㎡, measure RR (if 017
periodic systematic sampling Arrange N sampling units in a population in a certain order and number them from 1 to N. Periodic systematic sampling of n units is to select n units with numbers h, h+k, h+2, h+(n-1), where h is the integer closest to N/, and h is the number of the initial unit randomly selected from the integers from 1 to k. Synonym: periodic systematic sampling.
[IS03534-1.2006, 1, 3.13]
Random number random number
A realization value of a specified random variable. A random number provided as a series is called a random number sequence. 3.1.19
Pseudo-random number pseudo-random number A random number generated by a certain algorithm.
Note: Pseudo-random numbers are also simply called random numbers without causing misunderstanding. 3.1.20
Physical random number physicalrandomnumber A random number generated by a physical device. 3.2 Symbols
K: -LN/R. ! , the integer part of N/R;
K2=[R./MI, the integer part of R./M;
An appropriate integer greater than N!
The number of random numbers determined according to the batch N; Sample size:
The total amount of products or the batch of products:
Random numbers generated by random number generation methods: Pseudo-random numbers uniformly distributed on (0,1) generated by a random number generator, random numbers determined by the specified reading method, when R,>1, it is converted into a random number less than 1. General procedure for random sampling (see Figure 1)
4.1 Determine the sample size or sampling quantity
According to the purpose of the sampling inspection, the sample size or sampling quantity for the random sampling inspection shall be determined by appropriate standards or specifications. 4.2 Select the applicable random sampling method
According to the determined sampling inspection plan, select the applicable sampling method. This standard provides simple random sampling, systematic random sampling and stratified random sampling methods. 3
GB/T 10111-—2008
If there is a special need, cluster sampling and multi-stage sampling methods can also be used. Start
Determine the sample size or sampling size
Single random
4. 3 Number the products in the population or batch
Accumulate the dog sample
Number the products in the population or batch
Get the random number 1 and select the sample unit number
Take out the unit product according to the sample unit number
Manage the sample according to the regulations
Figure 1 General procedure of random sampling
According to the requirements of the selected sampling method, number the product population, batch, production shift, production workshop, pallet and its unit product. The number should be unique and without duplication or omission.
Number the sampling units or unit products in sequence starting from "1" according to natural numbers. 4.4 Generate random sample unit numbers
Generate random sample unit numbers according to the sample size required by the sampling inspection plan or the sample size specified by other methods. 4.4.1 Method for obtaining random number R
This standard provides the following methods for generating random numbers or pseudo-random numbers. a) Random number Yinzi method;
b) Random number table method;
c) Pseudo-random number method;
d) Playing card method (see Appendix B).|| tt||4.4.2 Read the sample unit number K
After obtaining the random number R., the number R corresponding to the sample unit should be read correctly. 4.5 Take out the unit product according to the sample unit number Take out the corresponding unit product as the sample according to the generated random sample unit number. 4.6 Manage and inspect the sample unit
Manage and inspect the sample unit in accordance with the relevant provisions of the standard, specification or contract. 5 Method of generating random numbers
5.1 Random number table method
5.1.1 Introduction to random number table
GB/T 10111—2008
A random number table is a table consisting of numbers from 0 to 9, and each number has the same probability of appearing in each position. Appendix A provides five 50X50 random number tables (see Table A.1~Table A.5). If Table A.1 is not used, other suitable random number tables can be selected.
5.1.2 Method for obtaining random number Ro
a) Determine the random number table number and the initial point: First, randomly specify a point on the first table, and read 5 numbers to the right from it as the starting point. If the first number is less than 5, take the number plus 1 as the selected random number table number. If the first number is greater than or equal to 5, take the number minus 4. The difference is used as the selected random number table number. The 2nd to 3rd digits and the 4th to 5th digits form two two-digit numbers. If the two-digit numbers are less than 50, add 1. If the two-digit numbers are greater than or equal to 50, subtract 49. The final number represents the row and column number of the initial point.
b) The method to obtain R is: read the required m digits from the initial point downward to obtain the required random number R. During the reading process, if the last row of the page is read, go to the row and read the next column. If the last row is less than the last row, fill it up from the first column of the next two-digit table.
5.1.3 Read the sample unit number R
a) If the obtained random number Ro≤N, then the random number R Take R. ：If R>N, then set R=KiN+Ri; where K1=[N/R], when (K, + 1)N>10㎡, discard and regenerate the random number R; when (Ki + 1)N≤10㎡, measure RR (if 017
periodic systematic sampling Arrange N sampling units in a population in a certain order and number them from 1 to N. Periodic systematic sampling of n units is to select n units with numbers h, h+k, h+2, h+(n-1), where h is the integer closest to N/, and h is the number of the initial unit randomly selected from the integers from 1 to k. Synonym: periodic systematic sampling.
[IS03534-1.2006, 1, 3.13]
Random number random number
A realization value of a specified random variable. A random number provided as a series is called a random number sequence. 3.1.19
Pseudo-random number pseudo-random number A random number generated by a certain algorithm.
Note: Pseudo-random numbers are also simply called random numbers without causing misunderstanding. 3.1.20
Physical random number physicalrandomnumber A random number generated by a physical device. 3.2 Symbols
K: -LN/R. ! , the integer part of N/R;
K2=[R./MI, the integer part of R./M;
An appropriate integer greater than N!
The number of random numbers determined according to the batch N; Sample size:
The total amount of products or the batch of products:
Random numbers generated by random number generation methods: Pseudo-random numbers uniformly distributed on (0,1) generated by a random number generator, random numbers determined by the specified reading method, when R,>1, it is converted into a random number less than 1. General procedure for random sampling (see Figure 1)
4.1 Determine the sample size or sampling quantity
According to the purpose of the sampling inspection, the sample size or sampling quantity for the random sampling inspection shall be determined by appropriate standards or specifications. 4.2 Select the applicable random sampling method
According to the determined sampling inspection plan, select the applicable sampling method. This standard provides simple random sampling, systematic random sampling and stratified random sampling methods. 3
GB/T 10111-—2008
If there is a special need, cluster sampling and multi-stage sampling methods can also be used. Start
Determine the sample size or sampling size
Single random
4. 3 Number the products in the population or batch
Accumulate the dog sample
Number the products in the population or batch
Get the random number 1 and select the sample unit number
Take out the unit product according to the sample unit number
Manage the sample according to the regulations
Figure 1 General procedure of random sampling
According to the requirements of the selected sampling method, number the product population, batch, production shift, production workshop, pallet and its unit product. The number should be unique and without duplication or omission.
Number the sampling units or unit products in sequence starting from "1" according to natural numbers. 4.4 Generate random sample unit numbers
Generate random sample unit numbers according to the sample size required by the sampling inspection plan or the sample size specified by other methods. 4.4.1 Method for obtaining random number R
This standard provides the following methods for generating random numbers or pseudo-random numbers. a) Random number Yinzi method;
b) Random number table method;
c) Pseudo-random number method;
d) Playing card method (see Appendix B).|| tt||4.4.2 Read the sample unit number K
After obtaining the random number R., the number R corresponding to the sample unit should be read correctly. 4.5 Take out the unit product according to the sample unit number Take out the corresponding unit product as the sample according to the generated random sample unit number. 4.6 Manage and inspect the sample unit
Manage and inspect the sample unit in accordance with the relevant provisions of the standard, specification or contract. 5 Method of generating random numbers
5.1 Random number table method
5.1.1 Introduction to random number table
GB/T 10111—2008
A random number table is a table consisting of numbers from 0 to 9, and each number has the same probability of appearing in each position. Appendix A provides five 50X50 random number tables (see Table A.1~Table A.5). If Table A.1 is not used, other suitable random number tables can be selected.
5.1.2 Method for obtaining random number Ro
a) Determine the random number table number and the initial point: First, randomly specify a point on the first table, and read 5 numbers to the right from it as the starting point. If the first number is less than 5, take the number plus 1 as the selected random number table number. If the first number is greater than or equal to 5, take the number minus 4. The difference is used as the selected random number table number. The 2nd to 3rd digits and the 4th to 5th digits form two two-digit numbers. If the two-digit numbers are less than 50, add 1. If the two-digit numbers are greater than or equal to 50, subtract 49. The final number represents the row and column number of the initial point.
b) The method to obtain R is: read the required m digits from the initial point downward to obtain the required random number R. During the reading process, if the last row of the page is read, go to the row and read the next column. If the last row is less than the last row, fill it up from the first column of the next two-digit table.
5.1.3 Read the sample unit number R
a) If the obtained random number Ro≤N, then the random number R Take R. ：If R>N, then set R=KiN+Ri; where K1=[N/R], when (K, + 1)N>10㎡, discard and regenerate the random number R; when (Ki + 1)N≤10㎡, measure RR (if 04 Generate random sample unit number
Generate random sample unit number according to the sample size required by the sampling inspection plan or the sample size specified by other methods. 4.4.1 Method for obtaining random number R
This standard provides the following methods for generating random numbers or pseudo-random numbers. a) Random number method;
b) Random number table method;
c) Pseudo-random number method;
d) Playing card method (see Appendix B).
4.4.2 Read sample unit number K
After obtaining the random number R., the number R corresponding to the sample unit should be read correctly. 4.5 Take out unit products according to the sample unit number Take out the corresponding unit products as samples according to the generated random sample unit number. 4.6 Manage and inspect sample units
Manage and inspect sample units according to the relevant provisions of standards, specifications or contracts. 5 Methods for generating random numbers
5.1 Random number table method
5.1.1 Introduction to random number table
GB/T 10111—2008
A random number table is a table consisting of numbers from 0 to 9, and each number has the same probability of appearing in each position. Appendix A provides five 50X50 random number tables (see Table A.1 to Table A.5). If Table A.1 is not used, other suitable random number tables can be selected.
5.1.2 Methods for obtaining random numbers Ro
a) Determine the random number table number and the initial point: First, randomly specify a point on the first table, and read 5 numbers to the right from it as the starting point. If the first number is less than 5, take the number plus 1 as the selected random number table number. If the first number is greater than or equal to 5, take the difference between the number minus 4 as the selected random number table number. The 2nd to 3rd digits and the 4th to 5th digits form two two-digit numbers. If the two-digit numbers are less than 50, add 1. If the two-digit numbers are greater than or equal to 50, subtract 49. The final number represents the row and column number of the initial point.
b) The method to obtain R is: read the required m digits from the initial point downwards to obtain the required random number R. During the reading process, if the last row of the page is read, go to the row and read the next column. If the last remaining column is less than the number of columns, fill it up from the first column of the next second number table.
5.1.3 Read the sample unit number R
a) If the obtained random number Ro≤N, the random number R is R. ：If R>N, then set R=KiN+Ri; where K1=[N/R], when (K, + 1)N>10㎡, discard and regenerate the random number R; when (Ki + 1)N≤10㎡, measure RR (if 04 Generate random sample unit number
Generate random sample unit number according to the sample size required by the sampling inspection plan or the sample size specified by other methods. 4.4.1 Method for obtaining random number R
This standard provides the following methods for generating random numbers or pseudo-random numbers. a) Random number method;
b) Random number table method;
c) Pseudo-random number method;
d) Playing card method (see Appendix B).
4.4.2 Read sample unit number K
After obtaining the random number R., the number R corresponding to the sample unit should be read correctly. 4.5 Take out unit products according to the sample unit number Take out the corresponding unit products as samples according to the generated random sample unit number. 4.6 Manage and inspect sample units
Manage and inspect sample units according to the relevant provisions of standards, specifications or contracts. 5 Methods for generating random numbers
5.1 Random number table method
5.1.1 Introduction to random number table
GB/T 10111—2008
A random number table is a table consisting of numbers from 0 to 9, and each number has the same probability of appearing in each position. Appendix A provides five 50X50 random number tables (see Table A.1 to Table A.5). If Table A.1 is not used, other suitable random number tables can be selected.
5.1.2 Methods for obtaining random numbers Ro
a) Determine the random number table number and the initial point: First, randomly specify a point on the first table, and read 5 numbers to the right from it as the starting point. If the first number is less than 5, take the number plus 1 as the selected random number table number. If the first number is greater than or equal to 5, take the difference between the number minus 4 as the selected random number table number. The 2nd to 3rd digits and the 4th to 5th digits form two two-digit numbers. If the two-digit numbers are less than 50, add 1. If the two-digit numbers are greater than or equal to 50, subtract 49. The final number represents the row and column number of the initial point.
b) The method to obtain R is: read the required m digits from the initial point downwards to obtain the required random number R. During the reading process, if the last row of the page is read, go to the row and read the next column. If the last remaining column is less than the number of columns, fill it up from the first column of the next second number table.
5.1.3 Read the sample unit number R
a) If the obtained random number Ro≤N, the random number R is R. ：If R>N, then set R=KiN+Ri; where K1=[N/R], when (K, + 1)N>10㎡, discard and regenerate the random number R; when (Ki + 1)N≤10㎡, measure RR (if 0
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