Sequential sampling procedures and tables for inspection by attributes
Some standard content:
National Standard of the People's Republic of China
Sequential sampling procedures and tables for inspection by attributesUDC $11,213.2
:58.562012
GB 8051—87
This standard specifies the sequential sampling plan and implementation procedures with the qualified quality level or limit quality (number of nonconforming products per 100 units or average number of defects per 100 units) as the quality indicator. This standard is mainly applicable to occasions where the inspection time or inspection cost is relatively high and the sampling quantity needs to be reduced as much as possible. It can be used for sampling inspection of continuous batches of products. Under certain conditions, it can also be used for sampling inspection of isolated batches (see 2.1). 1 Symbols
The statistical terms used in this standard can be found in GB3358-82 "Statistical Terms and Symbols". 1.1 General symbols
Nonconforming rate, or average number of defects per unit. Qualified quality, in sampling inspection, corresponds to: a certain higher acceptance probability, the quality level of a batch that is considered satisfactory, expressed in the non-conforming product rate or the average number of defects per unit. User risk quality, referred to as CRQ. The quality level of a batch that corresponds to a certain lower acceptance probability in sampling inspection. This standard specifies the quality level of a batch with an acceptance probability of 10%. Limit quality. The quality level of a batch that is considered to be not allowed to be worse, corresponding to a lower acceptance probability in sampling inspection. The value is taken as a priority number, and the corresponding user risk is about 10%. Qualified quality level. The upper limit of the process half-average of the batch submitted for inspection that is considered acceptable by sampling inspection. Producer risk, that is, the probability of rejection of a batch with quality P. User risk, that is, the probability of acceptance of a batch with quality P (or LQ). The acceptance probability of a batch, when the non-conforming product rate (or the average number of defects per unit) of the batch is P, P: (P) is the ordinate value of the sampling characteristic curve corresponding to the user value on the X axis. Sample size of a sampling plan for counting. The number of qualified judgments of a sampling plan for counting. 1.2 Symbols of sequential sampling
Serial number of the sampled unit product.
The cumulative number of nonconforming products (or defects) found in the sampled unit products. The qualified judgment number when the first unit product is sampled. The unqualified judgment number when the th unit product is sampled. The parameter of the sequential sampling plan. It is the intercept of the unqualified judgment line on the ordinate axis. The parameter of the sequential sampling plan. It is the slope of the qualified judgment line and the unqualified judgment line. The predetermined truncated sampling number, when the ntth unit product is sampled, the sequential sampling ends. The qualified judgment number at the sequential sampling end (n=nt). The average sampling number (i.e. ASN).
The average number of samples when the nonconforming product rate (or the average number of defects per unit) is P. When household=0, PPrs or P=α (average number of defects per unit), it is recorded as. ,,,n,s, or. Approved by the National Bureau of Standards on July 8, 1987
Implementation of 1988-0401
2. Determination of sampling plan
2.1 Inspection of isolated batches
GB 8051-87
When there is no direct relationship between the quality of each inspection batch, or when there is a relationship but the number of batches produced is small, the inspection batch can be treated as an isolated batch. The sequential sampling plan of this standard requires that the batch size N of the isolated batch meets the following conditions: N6nt
2.1.1 Inspection of the number of defective products per hundred units of product (1)
Tools, regulations on qualified quality and limit quality The qualified quality PA and limit quality LQ shall be determined by negotiation between the manufacturer and the user based on the quality requirements of the product standard and taking into account the maximum sample size allowed.
b. Check the sample size code
In Table IA, find the sample size code corresponding to this row by the column where the limit quality LQ (number of defective products per 100 units of product) is located and the table value closest to the required qualified quality P (number of defective products per 100 units of product). The production risk corresponding to the qualified quality P varies with different sample size codes. The larger the sample size represented by the code, the smaller the production risk α. The acceptance probabilities of each sequential sampling plan at the qualified quality and limit quality are shown in Table 1B. c. Retrieval of sampling plan
Consider the qualified quality P as the qualified quality level AQL, and find the sequential sampling plan in Table 3 according to the qualified quality record PA specified by the sample size code (the half-average sampling number of this plan is shown in Table 5). Table lookup method: Go right horizontally according to the sample size code, read the value in the truncated sampling number column, and then read the parameters and of the sequential sampling plan from the intersection of the row where the sample code is located and the column where the specified qualified quality level is located. If there is an arrow at the intersection, read the first parameter and $ pointed by the arrow along the direction of the arrow, and then go left from the row where the parameter is located and read the corresponding nt value in the truncated sampling number column.
The qualified judgment number A and the unqualified judgment number Rn of the sequential sampling plan are calculated as follows: An =-h +sn
Ra =h +en
Then calculate the truncated qualified judgment number A as follows:
(3)
2.1.2 The qualified quality inspection P of the number of defects per hundred units of products and the limit quality inspection Q are respectively expressed in terms of the average number of defects per unit of products. Their specified methods and sampling plan retrieval are the same as 2.1.1.
2.2 Inspection of continuous batches
When inspecting continuous batches, it is advisable to use the sampling plan together with the transfer rules. For the inspection procedure and random inspection characteristic curve, please refer to GB2828-81 "Batch-by-Batch Inspection Count Sampling Procedure and Sampling (Applicable to the Inspection of Continuous Batches)". The sequential sampling plan for normal and strict inspection provided in this standard has approximately the same random inspection characteristic curve as the corresponding single-bundle sampling plan in GB2828-81, and can be regarded as equivalent in practicality. For relaxed inspection, the corresponding relaxed sampling plan in GB2828-81 is used. The transfer rules between normal, strict and relaxed inspections are shown in Figure 1.
Continuous batch contains qualified, and the total number of unqualified products or defects in the sample car
is less than
or equal to the limit number: and the production is normal
and negative
, there is one batch of unqualified products:
The production is not normal with +
or||This department considers it necessary
GB 8051—87
Figure I Transfer Rules Figure
2.2.1 Inspection of the number of unqualified products per hundred units of products There are two batches in a row of batches or less than five batches that are unqualified after the initial inspection
and five batches are unqualified after the secondary inspection
and the number of unqualified products is suspended when the number of temporary batches accumulates to five
Based on the batch and the specified inspection level, the sample size code is determined by Table 2. According to the sample size code and the specified qualified quality level (number of defective products per 100 units of product), the sequential sampling plan can be found in Tables 3 and 4. Table 3 is used for normal inspection and Table 4 is used for tightened inspection (the average sampling number of these plans is shown in Table 5). For the qualified quality level value less than or equal to 10, 1 is applicable to the inspection based on the number of defective products (or defects) per unit of product. Those qualified quality levels greater than 10 are only applicable to the inspection based on the number of defects per unit of product. The table lookup method and the calculation of the qualified judgment number 4, the unqualified judgment number R and the truncated qualified judgment number At are shown in 2.1.1C. 2.2.2 Inspection of the number of defects per 100 units of product According to the batch setting and the specified inspection level, the sample size code is determined from Table 2. According to the sample size code and the specified qualified quality level (number of defects per unit of product), the sequential sampling plan can be found in Tables 3 and 4. 3 is used for normal inspection and Table 4 is used for tightened inspection.bzxZ.net
The table lookup and calculation methods are the same as 2.2.1. 3 Implementation of the sampling plan
3.1 Inspection procedure
3.1.1 Inspection of isolated batches
Number of truncation sampling
GB 805187
Table 1A Acceptable quality PA value
Limiting quality LQ
0.15 0.40
0.10 0.25 0.40
0.065 0.15 0.25
0.10 0.150,40
GB805187
1B Characteristic values of sequential scheme
[Acceptance probability P when the upper line is P, (PA), acceptance probability P when the lower line is LQ (LQ)] Truncation sampling
Number of samples n
Limiting quality
0,115
Batch range
91 ~150
151-280
281 ~ 500
501～1200
1201～3200|| tt||3201～10000
10001～3500
35 001 - 150 000
150 001 ~ 500 000
501001
GB 8051--87
Table 2 Sample size code
Special inspection
Inspection water half
Specify product quality standards;
Specify qualified quality P, and limit quality LQ, c.||tt ||Check sampling method:
d,, constitute a product batch, require batch plate NBne.
Make a record sheet or draw an inspection chart;
Sampling unit products one by one||tt| |General inspection
Inspect each unit product:
carry out inspections for times, and then make a decision on whether the batch is qualified or unqualified, or continue inspection until a conclusion is made on whether the batch is qualified or not. Inspection
specify product quality standards;
specify inspection levels,
specify qualified quality levels,
constitute product batches, confirm batches:
bend samples plan!
Make a record sheet and draw a check map
Take the unit products one by one 1
Check the unit products one by one:
Each time you check, you will make a batch of qualified and unqualified 3.2 Implementation method
GB 8061—87
Randomly select unit products from the inspection batch and The results of each inspection, that is, the number of unqualified products or defects per unit product, are accumulated with the number of unqualified products or defects found in all units of products that have been sampled before, and are calculated according to the following rules: If the cumulative number of unqualified products (or defects) D is less than or equal to the qualified judgment number A, the inspection batch is judged to be qualified. If the cumulative number of unqualified products (or defects) is greater than or equal to the unqualified judgment number R (or At+1 ), the inspection batch is judged to be unqualified.
If Dn is greater than but less than Rn (or A+1), continue to sample a unit of product for inspection and repeat the above process until a qualified or unqualified judgment can be made. When the sampling number is truncated, sampling will no longer continue, and judgment will be made according to the following rules: if the cumulative number of unqualified products (or defects) D is less than or equal to the truncated qualified judgment number 4, then it is judged as qualified; otherwise, it is judged as The specific implementation can be carried out by using the following list method or drawing method. In addition, Appendix A also recommends an equivalent method, the scoring method. 3.2.1 List method|| tt||When inspecting, first make a record sheet (see Table 6). In the first column of the table, record the serial number n of the unit product to be inspected, and in the second and fifth columns, record -4 respectively. . and R value, the former is the value calculated by formula (2) and the decimal is discarded and taken as an integer, the latter is the value calculated by formula (2) and the decimal is rounded up and taken as an integer. When the calculated Rn value is greater than 4t+1, then No more calculations are done, and Rn=A.+1 is taken as the length of the record table until n=nt. At this time, An=At, and the number A calculated according to formula (3) is taken as an integer after discarding the decimals. ) column to record the inspection results of each sampling (qualified products are recorded as "0", unqualified products are recorded as "1", and the number of defects is 0, 1, 2, ...). In column (4), record the number of (3) The cumulative value of the results in the column can be compared with Aa (or 4) R (or At+1) to make a judgment. In addition, the minimum value that allows the batch to be qualified or unqualified must be calculated. And use * to make corresponding marks in columns (2) and (5). The minimum value allowed for a batch to be qualified is an integer greater than . The minimum n value that allows a batch to be unqualified is an integer greater than - when checking the rate of unqualified products. When checking the number of defects,
#=1, but in the first unit of product under inspection The number of defects in must be greater than or equal to h+5. 3.2.2 Graphing method
: In rectangular coordinates, the horizontal axis represents the value of n, and the vertical axis represents the cumulative number of defective products (or the cumulative number of defects). )D, then formula (2) is shown in the figure as two parallel oblique lines L and R, with slopes of , and intercepts of -h and , respectively, as shown in Figure 2. At the same time, make a · The vertical line, the vertical coordinate of the intersection of this vertical line and the oblique line = 5π is the truncation qualified number At, and the broken line formed by the intersection of the waterline and the oblique line Le through the point (nt, At) is the unqualified judgment line The broken line formed by the oblique line L and the vertical line to At is the qualified judgment line. The area above the unqualified judgment line is the unqualified area, and the area below the qualified judgment line is the qualified area. The area between the two lines is the continued inspection area. The corresponding cumulative defective product value is plotted on the graph, and each point is connected by a thin line to form a broken line. If the point (n, Dn) falls within the subsequent inspection area, another sample is drawn for inspection. If point (\, D) falls in the qualified area, the batch is considered qualified. If point (\, D) falls in the unqualified area, the batch is considered unqualified. If the sequential sampling plan is correct, the three areas can be pre-made. Inspection drawings are provided for use during on-site inspections. Dn
Not in accordance with the orange zone
LetRa=h+ Bn)
GB8051—87
Continued school flag zone
-h*en)
Herong District
Number of inspection samples
Figure 2 Sequential sampling of lip cutting
8051—8
Table 3 Parameters of normal inspection lip cutting scheme||tt ||:：04
Note that the corresponding single sampling plan is used in the table, and the corresponding single sampling plan or the following sequential plan is used. 0+40
Electricity:：890
8: 29%
GB 8051—87
Continued Table 3 Parameters of the normal inspection and interception sequential scheme 4.0| |tt||8: 752e
0,4276
:：34
Tel:
GB 8051-87
Table 4 Strict inspection cut-off Number of tickets for the tail-through scheme
0: 08ia
.07.27
Note: Table* uses the corresponding "secondary sampling scheme" or the corresponding primary sampling scheme or the following sequential retention scheme rate. D, 4th
Quality level
Electricity, 559
R:：12
GB8051—87
Strictly check the parameters of the truncation scheme
te amo
0, 2a7m
2：762 Implementation method
GB 8061—87
Randomly select unit products from the inspection batch of products 4 and inspect them one by one in the order of sampling. The result of each inspection, that is, the number of unqualified products or defects of the unit products, is accumulated with the number of unqualified products or defects found in all the unit products that have been sampled before, and a judgment is made according to the following rules: If the cumulative number of unqualified products (or defects) D is less than or equal to the qualified judgment number A, the inspection batch is judged to be qualified. If the cumulative number of unqualified products (or defects) is greater than or equal to the unqualified judgment number R (or At+1), the inspection batch is judged to be unqualified.
If Dn is greater than but less than Rn (or A+1), continue to select a unit product for inspection, and repeat the above process until a qualified or unqualified judgment can be made. When the sampling number reaches the truncation sampling number, sampling will no longer continue, and judgment will be made according to the following rules: if the cumulative number of unqualified products (or defects) D, is less than or equal to the truncation qualified judgment number 4, then it is judged as qualified, otherwise it is judged as unqualified.
Specific implementation can be carried out by the following list method or drawing method. In addition, Appendix A also recommends an equivalent method-scoring method. 3.2.1 List method
During inspection, a record table (see Table 6) is first made, and the unit product number n of the sampled product is recorded in the first column of the table, and the second and fifth columns are recorded respectively. The former is the value calculated by formula (2) and the decimal is discarded and taken as an integer, and the latter is the value calculated by formula (2) and the decimal is rounded up and taken as an integer. When the calculated Rn value is greater than 4t+1, it is no longer calculated, and Rn=A.+1 is taken as the length of the record table until n=nt. At this time, An=At, and A is the integer after discarding the decimal point after calculating the number calculated by formula (3). The inspection results of each sampling are recorded in column (3) (qualified products are recorded as "0", unqualified products are recorded as "1", and the number of defects is 0, 1, 2, ...). In column (4), the cumulative value of the results in column (3) is recorded, and this value is compared with Aa (or 4)R (or At+1) to make a judgment. In addition, it is necessary to calculate the minimum value that allows the batch to be qualified and the batch to be unqualified, and use * to make corresponding marks in columns (2) and (5). The minimum value of \ allowed to make a batch qualified is an integer greater than. The minimum value of n allowed to make a batch unqualified is greater than —\- when checking the unqualified product rate. Integer, when checking the number of defects,
#=1, but the number of defects in the first unit product under inspection must be greater than or equal to h+5. 3.2.2 Drawing method
: In the rectangular coordinates, the horizontal axis represents the value of n, and the vertical axis represents the cumulative number of unqualified products (or cumulative number of defects) D. Then formula (2) is shown in the figure as two parallel oblique lines L and R, whose slopes are both, and the intercepts are respectively h and, see Figure 2. At the same time, a vertical line is drawn at the truncation sampling number. The vertical coordinate of the intersection of this vertical line and the oblique line = 5π is the truncation qualified demarcation number At. The broken line formed by the intersection of the waterline and the oblique line Le through the point (nt, At) is the unqualified judgment line, and the broken line formed by the oblique line L and the vertical line to At is the qualified judgment line. The area above the unqualified judgment line is the unqualified area, and the area below the qualified judgment line is the qualified area: the area between the two lines is the continued inspection area. During the inspection, points are drawn on the graph according to the number of products sampled and the corresponding cumulative number of unqualified products, and each point is connected by a thin line to form a broken line. If the point (n, Dn) falls within the subsequent inspection area, another sample is drawn for inspection. If the point (n, D) falls within the qualified area, the batch is judged to be qualified. If the point (\, D) falls within the unqualified area, the batch is judged to be unqualified. After the sequential sampling plan is confirmed, an inspection map divided into three areas can be prepared in advance for use during on-site inspection. Dn
Not in compliance with the requirements of the inspection area
LetRa=h+ Bn)
GB8051—87
Continued inspection area
-h*en)
Herong District
Number of inspection samples
Figure 2 Sequential sampling of cut-off lip
8051—8
Table 3 Parameters of normal inspection cut-off sequential sampling plan
:：04
Note that the corresponding single sampling plan is used in the table, and the corresponding single sampling plan or the following sequential plan is used. 0+40
Tel:：890
8: 29%
GB 8051—87
ContinuedTable 3 Parameters of the normal inspection and truncation sequential scheme4.0
8: 752e
0,4276
:：34
Tel:
GB 8051-87
Table 4 Number of signatures for the tightened inspection and truncation scheme
0: 08ia
.07.27
Note: Table * Use the corresponding "secondary sampling scheme Use the corresponding primary sampling scheme or the next sequential retention rate. D, 4th
Quality level of the grid
Electricity, 559
R:：12
GB8051—87
Strictly check the parameters of the truncation scheme
te amo
0, 2a7m
2：762 Implementation method
GB 8061—87
Randomly select unit products from the inspection batch of products 4 and inspect them one by one in the order of sampling. The result of each inspection, that is, the number of unqualified products or defects of the unit products, is accumulated with the number of unqualified products or defects found in all the unit products that have been sampled before, and a judgment is made according to the following rules: If the cumulative number of unqualified products (or defects) D is less than or equal to the qualified judgment number A, the inspection batch is judged to be qualified. If the cumulative number of unqualified products (or defects) is greater than or equal to the unqualified judgment number R (or At+1), the inspection batch is judged to be unqualified.
If Dn is greater than but less than Rn (or A+1), continue to select a unit product for inspection, and repeat the above process until a qualified or unqualified judgment can be made. When the sampling number reaches the truncation sampling number, sampling will no longer continue, and judgment will be made according to the following rules: if the cumulative number of unqualified products (or defects) D, is less than or equal to the truncation qualified judgment number 4, then it is judged as qualified, otherwise it is judged as unqualified.
Specific implementation can be carried out by the following list method or drawing method. In addition, Appendix A also recommends an equivalent method-scoring method. 3.2.1 List method
During inspection, a record table (see Table 6) is first made, and the unit product number n of the sampled product is recorded in the first column of the table, and the second and fifth columns are recorded respectively. The former is the value calculated by formula (2) and the decimal is discarded and taken as an integer, and the latter is the value calculated by formula (2) and the decimal is rounded up and taken as an integer. When the calculated Rn value is greater than 4t+1, it is no longer calculated, and Rn=A.+1 is taken as the length of the record table until n=nt. At this time, An=At, and A is the integer after discarding the decimal point after calculating the number calculated by formula (3). The inspection results of each sampling are recorded in column (3) (qualified products are recorded as "0", unqualified products are recorded as "1", and the number of defects is 0, 1, 2, ...). In column (4), the cumulative value of the results in column (3) is recorded, and this value is compared with Aa (or 4)R (or At+1) to make a judgment. In addition, it is necessary to calculate the minimum value that allows the batch to be qualified and the batch to be unqualified, and use * to make corresponding marks in columns (2) and (5). The minimum value of \ allowed to make a batch qualified is an integer greater than. The minimum value of n allowed to make a batch unqualified is greater than —\- when checking the unqualified product rate. Integer, when checking the number of defects,
#=1, but the number of defects in the first unit product under inspection must be greater than or equal to h+5. 3.2.2 Drawing method
: In the rectangular coordinates, the horizontal axis represents the value of n, and the vertical axis represents the cumulative number of unqualified products (or cumulative number of defects) D. Then formula (2) is shown in the figure as two parallel oblique lines L and R, whose slopes are both, and the intercepts are respectively h and, see Figure 2. At the same time, a vertical line is drawn at the truncation sampling number. The vertical coordinate of the intersection of this vertical line and the oblique line = 5π is the truncation qualified demarcation number At. The broken line formed by the intersection of the waterline and the oblique line Le through the point (nt, At) is the unqualified judgment line, and the broken line formed by the oblique line L and the vertical line to At is the qualified judgment line. The area above the unqualified judgment line is the unqualified area, and the area below the qualified judgment line is the qualified area: the area between the two lines is the continued inspection area. During the inspection, points are drawn on the graph according to the number of products sampled and the corresponding cumulative number of unqualified products, and each point is connected by a thin line to form a broken line. If the point (n, Dn) falls within the subsequent inspection area, another sample is drawn for inspection. If the point (n, D) falls within the qualified area, the batch is judged to be qualified. If the point (\, D) falls within the unqualified area, the batch is judged to be unqualified. After the sequential sampling plan is confirmed, an inspection map divided into three areas can be prepared in advance for use during on-site inspection. Dn
Not in compliance with the requirements of the inspection area
LetRa=h+ Bn)
GB8051—87
Continued inspection area
-h*en)
Herong District
Number of inspection samples
Figure 2 Sequential sampling of cut-off lip
8051—8
Table 3 Parameters of normal inspection cut-off sequential sampling plan
:：04
Note that the corresponding single sampling plan is used in the table, and the corresponding single sampling plan or the following sequential plan is used. 0+40
Tel:：890
8: 29%
GB 8051—87
ContinuedTable 3 Parameters of the normal inspection and truncation sequential scheme4.0
8: 752e
0,4276
:：34
Tel:
GB 8051-87
Table 4 Number of signatures for the tightened inspection and truncation scheme
0: 08ia
.07.27
Note: Table * Use the corresponding "secondary sampling scheme Use the corresponding primary sampling scheme or the next sequential retention rate. D, 4th
Quality level of the grid
Electricity, 559
R:：12
GB8051—87
Strictly check the parameters of the truncation scheme
te amo
0, 2a7m
2：7629%
GB 8051—87
ContinuedTable 3 Parameters of the normal inspection sequential plan4.0
8: 752e
0,4276
:：34
Tel:
GB 8051-87
Table 4 Number of signatures for the tightened inspection truncation plan
0: 08ia
.07.27
Note: Table * Use the corresponding "secondary sampling plan Use the corresponding primary sampling plan or the next sequential retention rate. D, 4th
Quality level of the grid
Electricity, 559
R:：12
GB8051—87
Strictly check the parameters of the truncation scheme
te amo
0, 2a7m
2：7629%
GB 8051—87
ContinuedTable 3 Parameters of the normal inspection sequential plan4.0
8: 752e
0,4276
:：34
Tel:
GB 8051-87
Table 4 Number of signatures for the tightened inspection truncation plan
0: 08ia
.07.27
Note: Table * Use the corresponding "secondary sampling plan Use the corresponding primary sampling plan or the next sequential retention rate. D, 4th
Quality level of the grid
Electricity, 559
R:：12
GB8051—87
Strictly check the parameters of the truncation scheme
te amo
0, 2a7m
2：76
Tip: This standard content only shows part of the intercepted content of the complete standard. If you need the complete standard, please go to the top to download the complete standard document for free.