Some standard content:
1 Introduction
National Standard of the People's Republic of China
Cusum charts for conted/attributes data UDC 5:2)
GB 4B87--85
1.1 This standard applies to the quality control of continuous production processes when the selected quality indicator is the number of non-conforming products or defects in the sample.
1.2 The counting cumulative sum chart uses the cumulative sum of the deviations of the number of non-conforming products or defects detected from the samples taken successively from their national standard value T (or reference value K) to determine whether the production process is abnormal by plotting the points in the coordinate system with the sample number as the horizontal axis and the cumulative sum value as the vertical axis.
1.3 When using the cumulative sum method to control the quality of the production process, there are two different types of cumulative sum charts available: a. Cumulative sum chart using a movable √-shaped template, and b. Cumulative sum chart with a certain judgment limit.
The two use different judgment rules for whether the process quality has "outliers", but the inspection results are exactly the same. 2 Symbols and their meanings
The definitions of statistical terms used in this standard can be found in GB3358-82 "Statistical Terms and Symbols". The number of defectives or defects in the first sample, +
The local average level of process quality in the section from sample number +1 to sample number (the average number of defectives or defects in the sample!
The actual defective rate of the process:
The target defective rate of process control,
Process average:
The limit quality of process control,
When the process is at a certain quality level, the average number of defects in the sample; when the process is below the target quality level, the average number of defects in the sample; when the process is at the thousand-average quality level, the average number of defects in the sample exceeds the average quality level. The average number of defects in the sample when the process is at the limit quality; 5, >0, 2 and 10m are the values when the average chain length is equal to 5, 10, 200 and 1000 respectively #m
Sample number:
Sample size;
National standard value, that is, the average number of unqualified products in the sample when the process is at the standard quality level. (Or the average number of defects An
Reference value, cumulative sum diagram parameters with fixed judgment limits, slope of V-shaped template, cumulative sum diagram parameters using V-shaped template, F=KT: judgment distance, common parameters of the cumulative sum diagram using V-shaped template and fixed judgment limits, cumulative sum value of deviation from target value T;
local cumulative sum value of deviation from reference value K
The scale coefficient of the cumulative sum diagram, which is the distance between the two adjacent sample numbers on the horizontal axis, and the distance between the two adjacent sample numbers on the vertical axis. 01- 29 Issued
1885-10-01 Implementation
The difference between the cumulative sum of the signs,
GB4B87—85
The average chain length, which is the half-average number of samples drawn from the beginning of the cumulative sum chart to the issuance of an alarm signal for a given quality characteristic level:
The average chain length of the controlled process, which indicates that when the process is at the target quality level, an alarm signal is issued after an average of L samplings:
The sub-average chain length of the out-of-control process, which indicates that when the process is at the limit quality, an alarm signal is issued after an average of 1 sample is sampled.
Cumulative sum chart using the √ shape template
3.1 Composition of the cumulative sum chart
The horizontal axis of this cumulative sum chart represents the sample number m, and the vertical axis represents the cumulative sum of the deviations of the observed value from the target value T (see Figure 1), that is,
Cmr=(, -T)
The change of the average level of process quality is shown as the change of the average slope of the graph line on the cumulative sum graph, which can clearly show the intuitive information of the trend of process quality change.
(-a) 3
3.2 Judgment rules
Judgment rules for normal or abnormal process:
Sample number
Figure 1 Cumulative sum graph
Group. Draw a point (m, Cr) on the graph 14
b. Paste a special template made of transparent material with a shaped edge (referred to as V-shaped template) onto the cumulative sum graph, and make the base point 0 of the template coincide with the point just drawn + O0 of the template, and the axis line is parallel to the horizontal axis of the cumulative sum graph (see Figure 2))
GB 4887—85
Group serial number m
《4) Process cessation
The point at which the average level rises (m-8)
Sample serial number two
(h) Sends an abnormal signal that the average level of the process is increasing Figure 2 Cumulative sum graph using a V-shaped template
c. If any of the previously drawn points exceeds or touches the lower edge AB of the V-shaped template, the process is judged to be abnormal. Otherwise, the process is considered normal. The point that touches or exceeds the lower edge of the V-shaped template may be the starting point where the average defective rate begins to rise. 3.8 Shape of the V-shaped template The shape of the V-shaped template is determined by the judgment distance H and the residual rate F of the lower edge (see Figure 3. Cumulative sum diagram with fixed judgment limit. Composition of cumulative sum diagram GB 4687-85 10 The horizontal axis of this cumulative sum diagram represents the sample number m, and the vertical axis represents the local cumulative sum value of the deviation of the observed value from the reference value K (see Figure 4), that is,
In the formula, . —The first sample number that constitutes the local cumulative sum. 8H
(y-+*)3
Decision limit
Sample number
Figure 4 Cumulative sum diagram with fixed decision limit
4,2 Decision rule
The decision on whether the process is normal depends on whether the point (m, Cms) of the local result sum falls within the decision limit, and the decision limit is determined by the decision distance H.
GB 4887-85
The construction of the local cumulative sum is discontinuous. If C0 is greater than or equal to H, it is considered that the previous process is normal, and the cumulative sum will no longer be constructed, and a new local cumulative sum will be calculated from the next observation value. - Until Cm≥H, the process is judged to be abnormal, and adjustment measures should be taken, and then the cumulative sum process should be repeated according to the above rules. The starting sample number that constitutes the "report" local cumulative sum may be the starting point where the average defective rate (or the number of groove defects) begins to rise.
4.3 List control method
When using the cumulative method with fixed judgment limits, it is also possible to use list calculations directly for control without drawing a graph, as shown in Table 1. The number of defective products in the sample No. in the table is less than the K value (C0), so it is considered to be excessive. The process is normal, and the cumulative sum is no longer constructed. Instead, a new partial cumulative sum is calculated starting from the second sample. Since the partial cumulative sum of samples No. 2 to No. 6 is equal to zero, the production process at this stage is also considered normal, and the construction of the cumulative sum starts again from the next two samples. The partial cumulative sum of samples No. 14 to No. 19 has reached H, so the production process is judged to be abnormal and an "alarm" signal is issued. Sample No. 14 may be the starting point for the average defective rate to begin to rise. Table 1 Example of the construction of partial cumulative sums (H=7, K=4) Sample number
5 Procedure for using product-sum diagram
Number of defective products
Deviation from test value
Local cumulative sum of deviation
Cax-(a, -k)
5.1 Determine the control item
The controlled item can be the non-conforming rate or unit defect number of semi-finished products or finished products, or the non-conforming rate or unit defect number of a single quality characteristic of a key process.
When the control item is the non-conforming rate (or single non-conforming rate) and the sample size n is constant, the cumulative sum chart of the number of non-conforming products can be used.
When the control item is the unit defect number of the product, the cumulative sum chart of the number of defects can be used. At this time, a certain unit (such as a certain area, a certain length, a certain number of products) specified by the event can be used as a sample for statistical defect counts. 5.2 Determine the target value
*CR≤0, the process is considered normal, and a new cumulative sum value is calculated from the next sample. **Cm=, the process is determined to be abnormal and an "alarm" signal is issued. GB 4887-85
5.2.1 Use cumulative sum charts to analyze the quality of the production process. Collect the sampling inspection data from previous production, analyze and find the causes, eliminate abnormal data, calculate the average quality level of the process (average defective rate or average number of minor defects), and use this average level (can be adjusted) as the daily standard quality level for analysis, and draw a cumulative sum chart for analysis.
If there are no previous quality records, you can specify a self-standard quality level P or according to production requirements for analysis. 5.2.2 Observe the changes of the graph on the CUSUM chart for analysis (see Figure 1). If the graph is passive near a horizontal line without an obvious downward or upward trend, it means that the average quality level of the process is relatively stable. If the average water level P or P meets the acceptance requirements of the product (such as PAQL), P or P can be used as the target quality water level P or P for the CUSUM chart for subsequent process control. Otherwise, the cause should be found out and measures should be taken to improve the process quality level until a satisfactory self-standard quality water level for the CUSUM chart for process control can be determined.
5.3 Determine the limit quality
After determining the daily standard quality level P (or P) of the CUSUM chart for control, the limit quality level (or P) that is rejected (judged as abnormal) should be determined. To ensure the highest quality of the product, P (or P) should not exceed the requirements of the inspection specification. At the same time, attention should be paid to the difference between P and P. There should be an appropriate ratio, P/P. The smaller the value of (or n,/.), the higher the sensitivity requirement for the control chart to detect abnormalities, and the larger the sample size. Generally, P1/P1 can be 1.5~5.0, and a smaller P1/P value can be taken when n is large. Otherwise, a larger value is taken. 5.4 Determine the chain length, L
-Generally, it is hoped that L has a larger value (200~1000) and L has a smaller value (2~10). However, due to the actual work, the size of the mountain group cannot be too large, so these two requirements are often not met at the same time. Usually, when the risk of false alarm signals is required to be small, L1000 and L10 can be taken. If the sensitivity of detecting abnormalities is to be improved, and the risk of false alarm signals is allowed to be appropriately increased, L200 and L16 can be used. It is also possible to determine the appropriate and L1 values according to actual needs. 5.5 Determine the parameters of the cumulative sum chart
5.5.1 The parameters of the counting cumulative circle are shown in Table 2. Table 2 Coordinate axes and parameters of the counting cumulative sum chart Cumulative sum chart using V-shaped template
Chart type
Number of defective products chart
Number of defects chart
Standard axis
5.5.2 Parameters of the cumulative sum chart of the number of defective products
Template overhang
Judgment distance
Cumulative sum chart with defined judgment limits (or list method) Coordinate axis
Judgment distance
Reference value
In 3, the cumulative sum chart parameters of the two schemes "C1 and IC2" and the schemes are listed according to the Huisong distribution. Characteristic value, applicable to the occasion of defective rate of 0.1, the ratio / 1 (or s/2m) reflects the discrimination ability of the scheme. The larger the ratio, the lower the discrimination ability. For the cumulative profit chart parameters of the number of defective products based on the binomial distribution when the defective rate P ≥ 0.1, can it be appended to Appendix A? b. When L, 1000, L, ~ 10 are required, the C1 scheme can be adopted. When L, n200, L, * 5 are required, the C2 scheme can be adopted. According to the adopted scheme, check Table 3 for the nearest 10/yuan 1000 (or 5/200) value of the ratio six P
given in China, and the corresponding sum, K value, is the required cumulative sum chart parameter value. c. The sample size is calculated according to the following formula
GB 4B87-85
n=P\P.
(take integer)
d. When using C1 and C2 schemes, the average chain length L of other quality levels (λ=p) can be found in Table 4.The H and K values corresponding to the L ratio are used as the parameters of the cumulative sum chart. For example, P = 0.03, P = 0.09, L = 500, L = 7. When calculating the cumulative sum chart parameters from Table 4, we can first calculate the ratio P / P = 0.09 / 0.03 = 3, then find the parameters corresponding to the row with the value of 1 / L closest to 3 in the columns L = 500 and L = 7, which is H = 3, K = 1.5 (L = 50m = 0.619, L = 1.83, L / L 500 = 183 / 0.619 = 2.963), which is the cumulative sum chart number that meets the requirements. The sample size is s00
=20, then the daily standard value is
T = nP. = 20 × 0. 03 = 0. 6 Because T=0.6<0.619, the L value of this scheme is slightly greater than 500 when the target value T=0.6. The parameters of the V-shaped template are H=3, F=KT=1.5-0.6=0..95.5.3 Parameters of the cumulative sum diagram of the number of defects
The parameters of the cumulative sum diagram of the number of defects should be calculated based on the Poisson distribution and meet the conditions of using Tables 3 and 4. When selecting the cumulative sum diagram parameters according to Tables 3 or 4, the steps are the same as 5.5.2, where the ratio P1/P is replaced by 1/2., and it is not necessary to calculate the sample size.
5.6 Select the type of product sum chart
: When it is required to fully display the changes in the average level of process quality, a V-shaped template cumulative sum chart can be used. When it is only required to make a judgment on abnormalities or to use a computer for monitoring, a cumulative sum chart with a certain judgment limit should be used. b. When drawing a V-shaped template cumulative sum chart, attention should be paid to the selection of the coordinate axis scale factor A. Generally, when nP. (or A.) 1. Take A=2VnP. (or A=2V.) A relatively regular value near it that is convenient for drawing. When πP. (or △,) 1, it is appropriate to take A2nP. (or A=2).
5.7 Use cumulative sum chart to control the production process
5.7.1 Draw the control cumulative sum chart according to the determined target value (T=nP, or T=2) and cumulative sum chart parameters H, K (or F). In process control, according to the judgment rules described in 3.2 or 4.2, once an "alarm" signal is issued (the process is judged to be abnormal), the cause should be found, measures should be taken, and abnormal factors should be eliminated. 5.1.2 The local average water level of process quality (such as the actual water level at the time of alarm) can be estimated according to the following formula: For the expanded template diagram:
For the fixed judgment limit diagram:
5.7. For general processes that show improved processing quality, they should also be analyzed in a timely manner and experience should be summarized to promote continuous improvement of production levels. 5.7, 4 When production conditions change (such as processing technology improvements) and the processing quality of products has been steadily improved, in order to control the process quality at the new water level, the new stable quality level should be used as the target value, and the parameters of the cumulative sum diagram should be modified accordingly. Target value 7
(ie or n)
Result product and parameter
GB4887--85
Parameters and characteristic values of cumulative and scheme
C1 scheme
Characteristic value
894 or 1827
2.10/1000
2.7 or 2.6
1.80 or 1.79
C2 scheme
Cumulative and parameter
Characteristic value
Cumulative sum number
488785
Table 4 Average chain length characteristics of purple product and scheme
Positive average missing number when the half-average chain length L is the following value ()
GB 4887—85
Appendix A
Cumulative sum diagram of binomial variables
(Supplement)
A.1 Cumulative sum diagram parameters of binomial variables with defective product rate P0.1 are shown in Table A1 and Table A2. Table A1 gives the parameters of two different schemes for selection. The L value of scheme C1 is between 1000 and 2000, and the L value of scheme C2 is between 200 and 400. The slope of the V-shaped template is calculated according to the formula F=K-nP. The corresponding cumulative sum diagram parameters H and K can be obtained by looking up Table A1 based on the set national standard quality level P. and the selected sample size n. When selecting the sample size, it should be noted that the smaller n is, the lower the sensitivity of the scheme to detect "abnormality" and the larger the L value is. Table A2 lists the L values of schemes C1 and C2 with P as a function. When P, P1, and L1 are given, the cumulative sum chart parameters H and sample size n that basically meet the requirements can be obtained by looking up Table A2. For example, P2 = 0.2, P2 = 0.35, L ~ 200, L1 4, calculate the cumulative sum chart parameters. Because L2 is 200, the C2 scheme is selected. From Table A2 (d) and P2 = 0.35, the control chart parameters that can meet L1㎡4 are: H = 7, K = 5, n = 20 (L = 239 when P = 0.2, L1 = 4,04 when P = 0.35): A.2 For any selected L value, the parameter values H and K can be obtained from Table A2 by interpolation. When interpolating, for different H values with the same P, 1 and K values, the corresponding L values can be linearly interpolated according to the logarithm of L. In other words, the L values corresponding to different F can be arranged in a geometric progression. For example, from Table A2 (e), for P = 0.3 and n = 35, we can get H = 14, K = 12, L, = 1169 for C1. From Table A2 (f), we can get H = 10, K = 12, L. = 238 for C2. To calculate the value of L when K = 12 and H are 11, 12, and 13 respectively, we can first calculate the common ratio of L·geometric sequence:
(1169 ) (1-10) = 4.9120-25 = 1.4892387
So, when H = 10, L = 238bZxz.net
When H = 11, L. =238 x1.489=354
When H = 12, La = 354 × 1.489 = 527When H = 13, L = 527 × 1.489 = 785When H = 14, L. = 785 × 1.489 = 1169Therefore, for n = 35 and P = 0.3, if L. ~ 500 is selected, the scheme with parameters H = 12 and K = 12 can be adopted. This interpolation can also be conveniently avoided using single logarithmic coordinate paper (see figure). GB4887—B5
K = 12
C1 and C2 schemes of binomial variables
K is the same, but the value of L when H is different
Define the warning factor of C2 scheme
Parameters of C1 factor
Target value
Monthly non-conforming sugar product rate
Sample population size
Group population size
H average individual rate
(a)P. =0.1 of C1
Defective rate
n = 15
GB 4887—85
Continued Table A1
Japanese standard
C1 parameter
variable cumulative sum of square capsules average chain length L
n = 25
C2 number of squares
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