Single sampling procedures and tables for inspection having desired operating characteristics by variables for mean value
Some standard content:
National Standard of the People's Republic of China
Metric standard type of mean value
Single sampling procedures and tables for Inspection having desired operating characteristics by variables for mean value1 Subject content and scope of application
GB/T8054—1995
Generated GI 8051--87
This standard specifies the procedures and implementation methods for single sampling inspection of the standard type of batch average value (average value is referred to as mean value hereafter) as the quality indicator. It is applicable to batch inspection of product quality characteristics expressed by measurement values. The quality characteristic values of the inspected products obey or approximately obey normal distribution. This standard stipulates that the risk of cattle producers is α-0.05 and the risk of users is 0.10.2 Referenced standards
The provisions contained in the following standards constitute the provisions of this standard through reference in this standard. When this standard was published, the versions shown were valid. All standards are subject to revision. Parties using this standard should explore the possibility of using the latest versions of the following standards. GB/T3358 Statistical terms
GB4091.1 General principles for control charts with gauges
GB4091.2 Mean standard deviation control charts
GB1883 Statistical processing and interpretation of data Judgment and processing of abnormal values in normal samples GB/T6583--1SO8402 Terminology for quality management and quality assurance GB/T10111 Method of random sampling using random numbers 3 Terms and symbols
3.1 Terms
3.1.1 Unit product
Basic unit for the purpose of implementing sampling inspection. 3.1.2 Inspection lot (abbreviation: lot)
A group of unit products collected for the purpose of implementing sampling inspection. 3.1.3 Test quality characteristics
Quality characteristics of the inspected unit product that can be measured using a standard. 3.1.4 Quantitative sampling inspection
A process of randomly selecting a certain number of unit products from a batch according to a specified sampling plan, obtaining their quality characteristic values by measurement, testing or other methods, comparing them with the quality requirements and judging whether the batch of products can be accepted. 3.1.5 One-time sampling inspection
A sampling inspection process of selecting only one sample from a batch and obtaining the quality characteristic values of the sample to judge whether the batch of products can be accepted. National Technical
3.1.6 Sampling characteristic curve (OC curve)
GB/T8054—1995
For a given sampling plan, a curve that represents the functional relationship between the batch quality level and its expected probability of being accepted. 3.1.7 Acceptable quality
In sampling inspection, the batch quality level that is considered satisfactory and corresponds to a certain, high probability of acceptance. 3.1.8 Limit quality
In sampling inspection, it corresponds to a certain, lower acceptance probability, and is considered that the batch quality level that is not allowed to be worse. 3.1.9 Producer's risk
On the sampling characteristic curve, it corresponds to the probability of rejection at the acceptable quality. That is, the risk rate of a batch with acceptable quality being misjudged as unacceptable.
3.1.10 User's risk
On the sampling characteristic curve, it corresponds to the probability of acceptance at the limit quality. That is, the risk rate of a batch with limit quality being misjudged as acceptable. 3.1.11 Standard sampling inspection
In order to protect the interests of both production and use forces, the producer's risk and the user's risk are simultaneously set to a certain value for a certain acceptable quality and limit quality. 3.1.12 Suppression plan
The provisions of the sample size for sampling inspection and the judgment rules for determining whether the batch can be accepted. 3.1.13 Types of sampling inspection
When determining the sampling plan, two types of sampling inspection are divided into batch standard deviation and unknown batch standard deviation according to the different distribution of batch quality basic characteristic values.
3.1.14*\ method
When the batch standard deviation is known, the method of using sample mean and batch standard deviation to determine whether the batch is acceptable. 3.1.15 "5\ method
When the batch standard deviation is unknown, the sample mean and sample standard deviation are used to determine whether the batch is acceptable. 3.1.16 Quality statistics
A function consisting of the specification limit, sample mean and batch standard deviation (or sample standard deviation): used to determine whether the batch is acceptable. There are two quality statistics: upper specification limit and lower specification limit.
3.1.17 Acceptance band number
A constant used to determine whether the batch is accepted or not. This standard gives the minimum value of the upper specification limit quality statistic and (or) lower specification limit quality statistic for an acceptable batch.
3. 1. 18 Inspection method
The inspection method is determined by the required quality specification limit. This standard has three types of specifications: upper specification limit, lower specification limit and bilateral specification limit.
3.1.19 Specification limit
The limit value of the acceptance quality or limit quality of the batch. 3.1.20 Upper specification limit
The maximum value of the acceptable quality or limit quality specified. 3.1. 21 Lower specification limit
The minimum value of the acceptable quality or limit quality characteristic specified. 3.1.22 Bilateral specification limit
The situation where both the upper specification limit and the lower specification limit are specified at the same time. 3.2 Symbols
: The average value of the batch quality characteristic value. Referred to as batch mean, 6, the statistical estimate of the batch standard deviation.
aL: Lower specification limit of acceptable quality.
: Lower specification limit of limit quality:
inu: Upper specification limit of acceptable quality.
U: Upper specification limit of limit quality,
+production risk.
; User risk,
n: Sample size.
Hole: The first: Sample size of the trial draw
CB/T 8054—1995
c: Unit product quality characteristic value in the sample. 2 represents the th unit product quality characteristic value. 1
: Standard deviation of sample quality characteristic value. Referred to as standard deviation. V(n-1)
Qu upper specification limit quality statistic.
Qu - au or Qu = N _
QL: Lower specification limit quality statistic.
Qt= Or Qr=
: Acceptance constant.
1: Acceptance probability of the inspection batch.
More (): Standard normal distribution
The density constant of the standard normal distribution is:
T-1(8.): The quantile of the non-central t distribution function with n degrees of freedom and non-central parameter. 4 Sampling inspection procedure
The implementation procedure of this standard is as follows:
Select the sampling inspection type;
Confirm the sampling inspection method:||t t||Specify the upper specification limit and (or) the lower specification limit of the acceptable quality and the limit quality; determine the sampling plan;
constitute the batch sampling;
inspect the sample and the calculation result;
determine whether the batch is acceptable;
process the inspection batch.
Implementation of sampling inspection
GB/8054—1995
When the product quality is stable and there is recent quality management data for sampling inspection that can determine the batch standard deviation in advance, the \.\ method can be used. If there is no recent data or even if there is recent data, but the quality order is unstable, the method should be used. The inspection method for whether the product quality is stable or not can be implemented in accordance with the provisions of Appendix A. When the manufacturer and the user have a long-term supply contract, whether the ".\ method or the ".\ method is used, the sample mean and sample standard deviation must be recorded in the form of a control chart. If, during the application of the "+" method, the control chart shows that the sample standard deviation is in a state of statistical control, it is allowed to convert the "+" method to the "+" method. If, during the application of the "+" method, the control chart shows that the sample standard deviation is no longer in a state of statistical control, it is necessary to immediately convert the "+" method to the "+" method. If the control chart does not show that the statistical control state has been lost, but only indicates that the batch standard deviation has become smaller or larger, the batch standard deviation value used should be updated at any time.
The use of control charts shall be carried out in accordance with GB 4091.1 and GB 4091.2. 5.2 Determine the sampling inspection method
This standard has a sampling inspection method of upper specification limit, lower specification limit and bilateral specification limit. It is provided for those who adopt this standard to select according to the different specifications required by the product standard.
When using bilateral specification limits, the condition of resistance-=m- must be met before the chart of this standard can be applied. 5.3. Specify the upper and (or) lower specification limits of acceptable quality and limit quality. The upper and lower specification limits of acceptable quality and limit quality shall be based on the quality requirements in the product standard and shall be determined by negotiation between the manufacturer and the user.
5.4 Determine the sampling plan
5.4.1 "." method
Follow the steps listed in the table below to determine the sampling plan. Working steps
Work content
Determine the quality requirements
Confirm the value
Search for sample cases
5.4.2 "\ method
Upper specification limit
Test method
Lower specification limit
Two-sided limit
E Ptr
PoL + e:1.
Provide the recent 20--25 correction 7s (or R) control chart data of the manufacturer, or the recent 20 to 25 batches of sampling inspection data. Estimate according to the method in Appendix B
Miurhar
From the calculated value in Table 1 Detect and point value
Determine the sampling plan according to the steps listed in the table below. Working steps
Work content
Present specification limit
Specify quality requirements
Inspection party
Lower specification limit
it Msu Har Ml
Calculate the rejection value in Table 2
Detection value
Bilateral specification limit
The manufacturer and the user shall agree on the acceptable value to both parties based on past experience, or directly agree on the appropriate trial sample size. Take samples from the inspection lot and use the sample standard as the estimated value of the northern standard deviation. Working steps
Work content
Search for sampling plan
5.5 Constructing lots and taking samples
GB/T 8054- 1995
Test method
Upper specification limit
Calculated value in Table 3
Detection value
Lower specification limit
Save specification limit
or
Calculated value in Table 4 If milk is detected in the batch, the unit product must be submitted in the form of a batch. The submitted batch may be the same or different from the production batch, sales batch, and transportation batch, but it should be composed of unit products of the same specification and model, the same quality grade, and the same raw material composition produced under the same process conditions. The batch size is determined by the manufacturer and the user according to the sales situation and actual production conditions. The required samples can be randomly selected from the entire batch in accordance with GB/T10111. If the trial sample estimation is adopted in the "\" method, the trial sample size n should not be less than 11. After the sample (1, 2, 3...) is determined by the "U" (or "2") value, it should be handled according to the following different situations. a. When n..n,. Then randomly select the difference number n-,...n; (=0,1,2,.) from the batch to make up for it and make a judgment: when the average is ≥20, no additional sampling is required.
b. When n:-n, no additional sample is required, that is, the sample size; The acceptance constant should be the corresponding value of the sample size n.
5.6 Inspection samples and calculation results
The sample is inspected one by one according to the test, measurement or other methods specified in the product standard or order contract and other relevant documents. The inspection results should be recorded completely and accurately, and the average and standard deviation of the sample should be calculated. If there are individual abnormal data that are obviously deviated from other inspection results of the sample, the technical or physical reasons for the abnormal data should be found first. If the cause cannot be found, it can be judged according to GB1883 with the consent of the user, and then the production party and the user can determine to eliminate them according to the nature of the normal data. After the abnormal data are eliminated, the corresponding unit products for testing should be randomly selected from the inspection batch again, and the sample size required by the sampling plan should be supplemented to determine whether the inspection batch is accepted or not. 5.7 Determine whether a batch can be accepted
5.7.1\\ Determine whether a batch can be accepted
When the upper specification limit is given, calculate
Qu Sou
If the batch is accepted, the batch is rejected.
When the lower specification limit is given, calculate
Batch acceptance and batch rejection.
When the bilateral specification limits are given, calculate
Or batch acceptance;: or batch rejection
When the upper specification limit is given, calculate
If the batch is accepted, the batch is rejected.
When the lower specification limit is given, calculate
If 2 batches are accepted, Q batch is rejected,
c.When the bilateral specification limit is given, calculate
GB/T 8054-. 1995
Qu = Pa
Qu-alr
Aromatic and batch acceptance;u or Qi<batch rejection. 5.8 Processing inspection batch
For all batches judged as accepted, the user shall accept the whole batch. For batches judged as rejected, they shall not be submitted for inspection again without processing and shall be processed in accordance with the contract provisions.
6 Example of determining the sampling plan
6.1*6\ method
6. 1. 1 Given, when the upper specification limit
Example: The iron oxide Fe:0 content in solid caustic soda is required to be low, and the batch mean is acceptable if it is below 0.0040%, and it is not accepted if it is above 0.0050%. Given: 0:0.000 6 road, try to determine the sampling plan. Determination steps:
Given = 0.0040%, -0.0050%, 0=0.0006% Calculate 0 005,0=0.004 01.667
Find the location of 1,667 from Table 1, which is within the range of numbers in the third row of the table (1.463~1.689), thus we get: c
n 4,k- -0. 822
The sampling plan is [4, -0. 822], 4 unit products are drawn from the batch, and after inspection, the sample mean is ≤ and Qu0. 004 —r
The judgment rule is:
If Qu contains -0.822, the batch is accepted, if Qt<—0.822, the batch is rejected. 6.1.2 Given the lower specification limit
Example: The tensile strength of a certain steel is better if it is larger. The batch mean is acceptable when it is above 46×10°Pa, but it is not acceptable if it is below 43×10°Pa. It is known that the batch standard deviation is 4×10'Pa. Try to determine the sampling plan. Determination steps:
Known MaL=46X10°Pa.mi-43×10°Pa.a.:4×10° Paa.
Calculate 16-43-0.750
2-46
Find the position of 0.750 from Table 14, which is within the range of the 15th row of the table (0.731~0.755), so we get: n-16,=-0.111
The sampling plan is (16,-0.411). 16 units of products are sampled from the batch, and after inspection, the sample mean is obtained. The second judgment rule is:
If Q-0.411, the batch is accepted; if Q~0.411, the batch is rejected. 6.1.3
GB/T 80541995
For example, the standard size of a certain product is 100 mm. If the batch average size is within 100±0.2mm, it is acceptable, and if it is outside 100+0.5mm, it is unacceptable. Given α=0.3mm, find the sampling plan. Determination steps:
Given m. - 99. 8 mm, ri.- 99. 5 mm, a =100. 2 mm+tiu= 1(00. 5 mm, a--0. 3 mmh=1
Calculate _= 100: =99.8=1. 33
From Table 2, first find the range of 0.580~1. 039 and the sample size n-9 for the calculated value of lan=, and then use this range to find the range of 0.867 or above for the calculated value of d.
, and thus get =-0. 548. e: The sampling plan is (9, -0.548). Select 9 units of products from the batch, and after inspection, get the sample mean and Q-to-99. 8.
100.2—x
The judgment rule is:
If Qt2 is 0.548 and QL:2 is 0.548, the batch is accepted; if Qu* is 0.548 or QL is 0.548, the batch is rejected. 6.2 “s\ method
6.2.1 When the upper specification limit is given
Example: The chemical composition S0 of a certain raw material is specified. If it is less than 1.50%, it is acceptable, and if it exceeds 2.50%, it is unacceptable. Since there is no recent quality control or sampling inspection data, the producer and the user agree on =0.85%, the sampling plan is determined by the method of unknown standard deviation.
Determination steps:
Given x: -1. 50%- Pm—2. 50%, a-- 0. 85%a.
b, calculate w=ar_2. 50-1: 501. 1760.85
From Table 3, find that the range of 1.176 is (1:160～1.259). From this, we get: c.
n-8, k=-0. 670
d, and the sampling plan is [8, one.6701. 8 unit samples are drawn from the batch, and the mean and standard deviation of the SO component of the sample are tested: and Qu=1.50-2. The judgment rule is: if Qu—0.670, the batch is accepted; if Q-0.670, the batch is accepted. 6.2.2 Given the following specification limits
Example: The Rockwell hardness mean of a batch of steel plates is required to be acceptable when it exceeds 75 and unacceptable when it is less than 70. The batch standard cannot be estimated in advance. The user and the manufacturer agree to use the trial sampling method specified in the \, \" method to estimate the standard deviation. The trial sample is set to 20. Find the sampling plan.
Chang Determine the steps:
Given μu, — 75, μ1, — 70
Randomly select 20 samples from the batch, measure the hardness, and calculate the sample standard deviation, =6, which is used as the estimated value of the batch standard deviation.
Calculate_75—70-0.833
Find the location of 0.833 in Table 3, and find the numerical function (0.8000.839) in the 12th row of the table, thus obtaining: d.
n=15,h--0.455
eDue to the trial sample size. 20,>So the above sampling plan cannot be used, and the trial sample should be used as the judgment The basis for whether the batch can be accepted is the number of acceptances, the corresponding value of the trial sample size m-20 is 0.387. The sampling plan is obtained_20,-0.3871. Calculate its mean value, and O_-75 judgment regulation GB/T8054-1995
If 2-0.387 batch is accepted: If Q0.387 batch is rejected. 6.2.3 Given the effective side specification limit
Example: Assume that the standard deviation of Example 6.1.3 is unknown, and there is no recent quality data to estimate. The manufacturer and the user agree to use the trial sample ". " method for sampling inspection, and agree on n11, find the required sampling plan. Determine the steps:
Given u:—100.2mm, u=100.5mm,.--99.8 rrmi.-99,5 mmb, test nr-11 units of products from the batch, measure the dimensions and calculate the sample standard deviation. s=0. 37, and use this as the estimated value of the batch standard deviation.
Calculate \oa
Calculate M
100.2-99.8m1.081
99.8—99.5
From Table 4, first find the range of the calculated value of 0.811 of the mountain (0.800～0.839), and the sample size n1=15. Then from this range, find the range of the calculated value of 1.081 of the mountain above 0.981, and thus get -0.455. The required sampling plan is (15,—0,455).
Since the trial sample is n=11, n>no, 4 units of products are drawn from the inspection batch to make up 15 pieces, and recalculate its mean and standard deviation s,Qt1 -
r— 99. 8
, the judgment rule is:
If Q—0.455, Q2—0.455, the batch acceptor Qu≤—0.455 or Q—0.455, the batch is rejected. 7 Sampling table
This standard gives the “. The sampling plan tables of the \ method and the "\ method are shown in Tables 1 to 4. Table
Samples and acceptance constants A or A
Calculation value range of the \ method
2. 69 and above
1.69~-2. 068
1. 463~-1. 689
1. 309--1. 462
1. 195--1. 308
1. 106~-1. 194
1.035~1.105
0. 9751.034
0. 925--0, 974
0.882--C.924
0. 845--0. 8H1
0. H11 --0. 844
0.782--0.810
—0. 496
Calculated value range
0. 731~-0. 753
0.710~0.730
0.690~0.70 9
0. 671-~0. 684
0. 654 --0. 670
0. 585.0. 653
0. 534-0. 584
0.495~-0.533
0. 463~-0. 494
#. 436~-0. 462
0.414~0.435
GB/T8054—1995
Continued Table 1
Note: (When the calculated value is less than 0. 414, the following formula can be used to calculate the sum; wing condition, -—0.562 07×《calculated value） 8. 563 82
2A-heat
—0. 278
—0.245
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[02 '0--081-0
621*0--51*0
1910-981*0
9R1'0~t\D| |tt||811*0~860*0
260 '0 ~-120 °0
020 *0--6/0'0
920'0-~5000
690~09*0
896 *0-
189 *0~12# '0
026*0695*n
92*0~107*0
902*081*0
810--291*0
1910~071*0
E1'～2I10
911\～5*D
sot\o-
+60 *0-- E20'0
220*0~050 '0
60*0~820'0
120*0~5000
629°0-~099'0
TH 9590
965 0~88# *
29 *0~898*
19*0-s2 *0
180*0-
257'0--212
11z '0--681*0
881 0--991'0
5910-611
20F*0-
6IT'0~260*0|| tt||9600200
E0 '0~150 *0
0500~620
820 '0 ~900'0
669'0--089 '00~009 °0
20~68t'0
88F*0~5860
188-0020
627*0--E61'0||tt| |121*0--Te1*0
19 yuan*0-
091'0--061'0
G210~-6010
801*0~ 680 *0
880 *0~890 *0
970'~920°0
520 *0-~900 *0
6690790
299'065+*0
82*0-09*0
6*0~20
998 *0—
[02 '0--081-0
621*0--51*0
1910-981*0
9R1'0~t\D| |tt||811*0~860*0
260 '0 ~-120 °0
020 *0--6/0'0
920'0-~5000
690~09*0
896 *0-
189 *0~12# '0
026*0695*n
92*0~107*0
902*081*0
810--291*0
1910~071*0
E1'～2I10
911\～5*D
sot\o-
+60 *0-- E20'0
220*0~050 '0
60*0~820'0
120*0~5000
629°0-~099'0
TH 9590
965 0~88# *
29 *0~898*
19*0-s2 *0
180*0-
257'0--212
11z '0--681*0
881 0--991'0
5910-611
20F*0-
6IT'0~260*0|| tt||9600200
E0 '0~150 *0
0500~620
820 '0 ~900'0
669'0--089 '0
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