Some standard content:
ICS03.120.30
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National Standard of the People's Republic of China
GB/T 17989.42020
Generation CB/Z4882006
Control charts-Part 4: Cumulative sum control charts(1S0 7870-4:2011M0D)
2020-03-06Release
State Administration for Market Regulation
National Standardization Administration
2020-10-01Implementation
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People's Republic of China
National International Standard
Control Charts
Part 4: Cumulative Sum Control Charts||t t||GE/T17$55.4
Published by Ninghui Standard Press
No. 2, Hepingli West Street, Beijing (109025) No. 6, Sanlihe North Street, Sichuan District, Beijing (0C043) Website: spc.org.cn
Service hotline: 4001580510
March 2020, first edition
Book number: 135(36:1-64097|| tt||Copyright reserved
Infringements will be prosecuted
2 Normative References
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Terms and Definitions, Abbreviations and Symbols
Terms and Definitions
Abbreviations
Overview of Product Sum Diagram
Basic Steps in Constructing Cumulative Sum Diagram
Example of Tight Product Sum Diagram
Line Chart of Observed Values
Single Value Control Drawing
Graphical display of cumulative sumWww.bzxZ.net
Construction of cumulative sum graph
Effectiveness interpretation of cumulative sum graph
Manhattan graph
Judgment based on cumulative sum
Requirement of judgment criteria
Judgment basis
Effectiveness measurement of judgment criteria
Judgment case type of Zijili graph
V-shaped template
Truncated V-shaped plate
Alternative design methods Method
Semi-parabolic V-shaped template
Flat nose V-shaped template
Full V-shaped template
Cumulative sum diagram of initial response (FIR) 8.7
8.8 Gridded cumulative sum diagram
9 Cumulative sum method for process and quality control
Type of change to be detected
Choice of target value
Cumulative sum diagram design for position monitoring
Wave Design scheme of cumulative sum diagram for dynamic monitoring
GB/T17989.4—2020
GB/T17989.4—2020
9.5 Special cases
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9.6 Cumulative sum diagram of discrete data
Appendix A (Informative Appendix) Von Neumann method Appendix B (Informative Appendix)
Gridded cumulative sum diagram Example
Appendix (Informative Appendix)
References
Change point estimation of step change
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GJ3/T17989" Control Chart" is planned to be divided into the following 9 parts: Part 1: General indicators;
- Part 2: Conventional control charts:
- Part 3: Acceptance control charts:
Part 4: Product control charts And control charts:
-Part 1: Special control charts:
-Part 6: Exponentially weighted moving average control charts; -Part 7: Multivariate control charts;
-Part 8: Short cycle and small batch control methods; -Part 9: Related process control charts,
This part is Part 2 of GB/T 17989
This part is in accordance with the specifications given in GB/T 1.1-2009 and is subject to GB/T 17989.4—2020
Guide to Quality Control and Numerical Analysis Using Cumulative and Techniques" and this part replaces GB/22887-2006 Cumulative Sum Chart GB/22887-2006 cabinet. The main technical changes are as follows: GB/24887-2006-0.1 Basis of Cumulative Sum Chart" is adjusted to Chapter 4 of this part \ Overview of Cumulative Sum Chart (especially Chapter 4 of GB/24887-2006); GB/24887-2006-9.2 * Cumulative Sum Chart Loading List Examples are adjusted to Chapter 6 of this part "Examples of Cumulative Sum Chart" and the relevant contents are enriched and improved (see 6.5~6.7. GB/24887-2005 Chapter 0); terms and definitions are added (see 3.1); abbreviations are added (! 3.2);
- Added symbols (see 3.3)
- Deleted Chapter 2 of GB/Z2887-2006, Preparation of Cumulative Sum Diagrams, and removed the representation of diagrams in Chapter 3 of GB/Z2887-2006; - Adjusted the judgment rules of diagrams in Chapter 4 of GB/Z2887-2006 to Chapters 7 and 8 of this Part. Chapter 8 is about the judgment of compact products and clarifies the basic criteria for the judgment of products and sums. Chapter 8 "Cumulative Sum Diagram Scheme Model" provides a variety of specific cumulative sum judgment methods (State Chapter 7 Chapter 11 and Chapter 8 of GB/24S87-2006 (Chapter 4 of GB/24S87-2006); - Added "Half-ground line V-shaped template" (see 8.4); - Deleted Chapter 5 of GB/Z2887-2006 \ Determination rules for retrospective analysis \ Deleted Chapter 7 of GB/24887-2006 "Application examples"; - Supplemented an example of a motor production process (see Chapter 6); - Added treatment measures based on process properties (Chapter 7.1); - Detailed description of the design scheme of the cumulative sum diagram for fluctuation monitoring (see 9.4); - Detailed description of the design scheme of the compact product and diagram of discrete data Design scheme (see 9.5); added the introduction of von Neumann's left method (Appendix VIII), the example of the gridded cumulative sum chart (Appendix [3) and the change point estimation of the cascade change (Appendix).
This part uses the redrafting method to modify and adopt 1S07870-4.2011 Control charts Part 4: Cumulative sum control charts. The technical differences between this part and TS0)7870-4:2011 and their reasons are as follows: Related normative references. This part has made technical adjustments to adapt to my country's technical conditions. The adjustment situation GB /T17989.4—2020
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In Chapter 2 "Normative References", the specific adjustments are as follows: 1. Replace ISO3534-1 with CB/T3358.1, which is equivalent to the international standard (see Chapter 3); 2. Replace ISO35342 with GB/T3358.2, which is equivalent to the international standard (see Chapter 3); → Add GB/T179S9.1 (see Chapter 3). This part also makes the following editorial amendments: Replace Chapter 6 The chapter question was changed to "Example of Cumulative Sum Graph"; Step 1 missing in the example of 9.6.1.3 was added; Step 1 missing in the example of 9.6.2.2 was added; Steps 1 and 3 missing in 9.6.2.3 were added; Step 6 of 9.6.1.3 and 9.6.2.2 was rewritten as: Based on the H and K values, the data of the il number (Poisson) in Table 24 were obtained at different H values. The performance of the product of the square root and the length of the chain under the square root is checked in the form of the active material, which is convenient for guiding the operation and use. This part is proposed and coordinated by the National Conference on Standardization Technical Application of Statistical Methods (SACTC21). The drafting units of this part are: Beijing University of Aeronautics and Astronautics, Xiamen Yiheweigui Construction Engineering Management Co., Ltd., China National Institute of Standardization, China Academy of Energy Sciences, Beijing Institute of Aeronautical Control Instruments, Haifenghang Technology Co., Ltd., and the main drafters of this part are: Yang Jun, Huang Ban, Hao Songhua, Zhang Fan, Hong Liang, Ding Shihu, Li Lei, Kong Shefeng, Wu Shengna, Yu Huan, and Chen. The previous versions of the standards replaced by this part are as follows: GB/T 48S71985, GB/2 887—2006iiiKAa~cJouaKAa
GB/T 17989.4—2020
This part introduces a simple and effective graphical data display method, showing its flexibility and practicality. This method is applicable to any meaningful series of numbers. These numbers cover a wide range, which can be macro business numbers (for example, turnover, profit or management costs) or micro operation numbers (for example, the stop and go of individual process parameters and product characteristics). Numbers can be expressed as a series of individual values. These values can be expressed using a continuous scale (for example.24, 60), 31, 21, 18, 97.). It can also be expressed in the format of "yes/no", "good/bad", "success/failure"; of course, the data can also be expressed as comprehensive indicators (for example, mean, range, number of cases). This method has a more appropriate name, "cumulative sum", abbreviated as "cumulative sum (CUSUM)", which is consistent with the data processing process. A predetermined value (for example, a standard value, a priority value, or a reference value) is subtracted from each observation to obtain a deviation, and the deviation is accumulated continuously (the cumulative deviation is added up to obtain the cumulative deviation sequence diagram, which is called a cumulative sum diagram. This simple technical process has a significant effect on the visual interpretation of the logarithmic sequence:
The world's golf ball selection has been unconsciously In the 1980s, the Cumulative Sum method was used in many fields. By scoring "such as 4 or name minus 2", the golfers used the Cumulative Sum method in a numerical sense: they subtracted "par" from their actual score and then accumulated the resulting deviations. This is the practical application of the Cumulative Sum method. However, the Cumulative Sum method is still largely unknown and rarely used in business, industry, finance and public services. This may be because the Cumulative Sum method is usually expressed in statistical terms rather than in the language of actual operations. Some people do not use the Cumulative Sum chart to help understand the Cumulative Sum chart and promote its widespread application and promotion. The Cumulative Sum control chart is a useful supplement to the conventional control chart. The Cumulative Sum chart is easy to detect and use for small deviations. In golf, when the standard changes, the cumulative sum chart is not affected, while the conventional control chart requires adjustment of the control line. In addition to the conventional control chart, the exponentially weighted moving average control chart (EWMA) can also be used. Each point in the EWMA chart summarizes the information of all the observed values, and for the more "old" process data, a smaller weight is given according to the exponential decay trend. Similar to the cumulative sum chart, the EWMA chart can also sensitively detect small deviations in the process. The EWMA chart will be discussed as another part of the series of standards.
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1Range
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Control chart||t t||Part 4: Cumulative Sum Control Chart
GB/T17989.4—2020
This part of GB/T17989 describes a general decision-making method for retrospective process monitoring, control and performance analysis using the cumulative sum (CUSUM) technique. It provides a statistical method for the cumulative sum (CUSUM) control chart for process and quality control. This part uses quantitative data and count data. 2 Normative references
The following documents are indispensable for the application of this document. For dated references, only the dated version applies to this document. For undated references, the latest version (including all amendments) applies to this document. G13/T 3358.1 Statistical vocabulary and derivative symbols Part 1: General statistical terms and terms using probability (GB/T 3358, 1: 2009, ISO 3534-1: 2006. 11)T)GB/T3358.2 Standardized vocabulary and symbols Part 2: Applied statistics (G3/T3358.2-2009.1S0) 35322:2005.IDT)
GB/T17989.1 Control charts Part 1: General guide (G3/T17989.1-2020,1S07870-1:2014.M0D) 3 Terms and definitions, abbreviations and symbols
3.1 Terms and definitions
CB/3358.1G[3/T3358.2 and G[3/17989. The following terms and definitions defined apply to this document 3.1.1
Target value targelvaluc
The average value used when locating the deviation to be detected. Note 1: The cumulative sum shown in the diagram is the accumulation of monthly tax rates. Note 2: When using the V-plan template, the monthly tax rate of the cumulative sum diagram should be based on the reference value or nominal control value. It clearly refers to the sample. Similar to the H standard, the standard value is not necessarily the most ideal or preferred value. It is just a standard value in the cumulative sum chart. 3.1.2
Benchmark value data
Standard value used to calculate the deviation in the tabulated cumulative sum chart. Note: The upper benchmark value T+5 is used for the upper shift of the monitoring average, and the lower basic value T-Fa is used for the lower shift of the monitoring average. 3.1.3
Reference shift
referenccshift
(the difference between the tabulated cumulative sum > target value (3.1.1) and benchmark value (3.1.2). Note: For standardized reference shift, F observation reference shift F=1
CB/T17989.4—2020
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refercncc shift
reference offset
(hidden V-shaped template) The slope of the oblique arm of the truncated V-shaped template. Note: Therefore, the standardized reference shift F is equal to the observed reference shift F. 3.1.5
decision interval
decisioninlerval
(tabular cumulative sum) The value of the cumulative sum of the deviation from the reference value when the tabular cumulative sum chart needs to send a signal. Note: H is used to represent the standardized decision question X, and H is used to represent the observed decision question H=h,. When the relative reference value exceeds the decision question K, a signal is sent.
decision interval decision interval
《Truncated V-shaped template）Half the height of the truncated V-shaped template at the reference value, Note: Used to represent the standardized demarcation interval, H is used to represent the observation interval H=, 3.1.7
averagecrunlength
Average chain length
The average number of samples collected before the occurrence of a signal, Note: The average chain length L is often related to a specific process level and is identified by an appropriate subscript, for example, I, which represents the average chain length at the standard level (i.e. zero shift>).
3.2 Abbreviations
The following abbreviations apply to this document.
ARL: average chain length (averagerunlength) Csl: cumulative sum scheme with a long ARl at zero shift (cusuin scherme with a long ARl at zero shift) Cs2: cumulative sum scheme with a short ARl.at zero shift (cusum srhcmc with a shortcr ARl.at zcroshift）D decision area (decision inlerval)
EWMA: exponentially weighted moving average (exponentially weighted moving average)FIR: fast initial response1cL; lower control limit (lowcr rontrol limit)RV: reference value (ttlerence valut)
UCL: upper control limit (upper control lirnit)3.3 Symbols
The following symbols apply to this document.
a: scale coefficient
(: tight identification value
, the difference in the tight product and value between the leading point and the out-of-control point: coefficient of estimating the subgroup's internal standard deviation: change to be detected
4: standardized change to be detected
(: leading distance
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(f: coefficient F of estimating the subgroup's internal standard deviation based on the subgroup's internal range: observed reference offset
to: standardized reference offset
II: observed judgment interval
t: standardized judgment interval
: Number of indices
: Process adjustment
K: Cumulative and baseline value of the data
: Number of subgroups
I: Average chain length when zero offset
l: Average chain length when offset
: Overall mean
m, mean of the number of counts
n: Number of people in the group
, "success\probability
R: Mean value of the difference
factory; Number of points drawn between the leading point and the fire control pointa: Process standard deviation
: Subgroup standard deviation
is: Estimation of subgroup standard deviation
.Standard error
s: standard deviation of subgroup observations
,, long mean of standard deviation of subgroup observations5. Standard error of the mean of a subgroup
1: daily standard value
1 reference value or daily standard value of incidence
1,: reference value or daily standard value of proportion
T: real change point
: observed change point
V: average voltage
V: estimate of average voltage
w: difference between adjacent subgroup means
3: single observation
: average value of subgroups
:: average value of subgroup means
Overview of cumulative sum chart
GB/T 17989.4—2020
The essence of the cumulative sum control chart1 is the running total deviation relative to a pre-selected reference value. The average value of any adjacent values is intuitively represented by the current slope of the mountain graph. The cumulative sum control chart has the following main features: a) It can sensitively detect changes in the average value, b) Any change in the mean value and its degree of change can be displayed by the change in the slope of the graph: 3
GB/T 17989.4—2020
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1) The horizontal line represents the monthly standard value or reference value; 2) The descending curve represents the average value less than the reference value or target value: the steeper the curve, the greater the deviation; 3) The rising curve represents the average value less than the reference value or target value: the steeper the curve, the greater the deviation, c) It can be used for prospective analysis of the purpose of investigation. And it can make short-term performance predictions based on controlled operation. From b), it can be seen that the cumulative sum control chart has the ability to clearly display process change points. These change points can be clearly displayed by the change in the slope of the cumulative sum chart. This can be a great help to process management because the CUSUM chart can quickly and accurately locate the point in time when a process has changed - and therefore the appropriate corrective action can be taken.
A very useful feature of the CUSUM system is that it can be used directly in a tabular format, rather than in a chart. This is particularly helpful if the CUSUM system is used to monitor a highly technical process (such as the manufacture of plastic film) where the number of process parameters and product characteristics is enormous. The data for the process can be acquired automatically, downloaded to the CUSUM software and automated CUSUM analysis can then be used to alert the process manager to changes in multiple characteristics at the same time. Appendix B gives an example of this method: 5 Basic Steps in CUSUM Chart Construction
For single observation data, the steps to construct a CUSUM control chart are as follows:Step 1 Select a reference, target, control, or benchmark value. An average of past results usually provides a good reference.Step 2 Tabulate the results in a meaningful order (e.g., time series). Then, subtract the reference value from each result.Step 3 Sum the values obtained in Step 2 one by one and then plot these sums on a CUSUM chart. Step 4 To achieve the best visual effect, draw a horizontal scale no wider than 2.5 mm between the plotted points (set the horizontal scale between the plotted points to no wider than 2.5 mm). Step 4 To achieve the best visual effect, draw a horizontal scale no wider than 2.5 mm between the plotted points (set the horizontal scale no wider than 2.5 mm between the plotted points). Step 4 To achieve the best visual effect, draw a horizontal scale no wider than 2.5 mm between the plotted points (set the horizontal scale no wider than 2.5 mm ...
6 Example of a CUSUM chart
6.1 Process
Suppose that a set of 40 observations are obtained for a feature of the motor production process: they are the voltage values of motors of different powers recorded in the production order at the early stage of production, but they can be in a meaningful order. Any single observation data represented by a continuous scale has the following values: 9, 16, 11, 12. 16.7. 13. 12, 13. 11, 12. 8, S, 11. 14, S, 6, 14. 4, 13. 3. 9,7, 14. 2. 6, =.12.8.8-12.6,14,13,12.14.13.10.13.13. The reference voltage or monthly standard voltage is 10V. 6.2 Line Graph of Observed Values
To better understand the underlying behavior of the process, by identifying patterns and trends: a standard approach is to simply plot the values in a natural order. As shown in Figure 1a), there is a general downward shift in the middle for a high start and a moderately high end. Apart from this, Figure 1a) does not reveal much.16, 11, 12. 16.7. 13. 12, 13. 11, 12. 8, S, 11. 14, S, 6, 14. 4, 13. 3. 9,7, 14. 2. 6, =.12.8.8-12.6,14,13,12.14.13.10.13.13. The reference voltage or monthly standard voltage is 10V. 6.2 Line graph of observed values
To better understand the underlying behavior of the process, by identifying patterns and trends: a standard approach is to simply capture points in a natural sequence of these values. As shown in Figure 1a), for the high start and moderately high end, there is a general downward excursion in the middle, except for Figure 1a) There is not much inspiration.16, 11, 12. 16.7. 13. 12, 13. 11, 12. 8, S, 11. 14, S, 6, 14. 4, 13. 3. 9,7, 14. 2. 6, =.12.8.8-12.6,14,13,12.14.13.10.13.13. The reference voltage or monthly standard voltage is 10V. 6.2 Line graph of observed values
To better understand the underlying behavior of the process, by identifying patterns and trends: a standard approach is to simply capture points in a natural sequence of these values. As shown in Figure 1a), for the high start and moderately high end, there is a general downward excursion in the middle, except for Figure 1a) There is not much inspiration.
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