Some standard content:
GE/T17989—2000
This standard is equivalent to the international standard IS07870:1993 Control charts--Genersl guideand introductian.
This standard introduces the key elements and basic principles of various control chart methods (including conventional control chart methods), and provides guidance on how to use control charts to effectively control and manage process quality. Appendix A of this standard is a prompt appendix. This standard was proposed by the China Standards Research Center. This standard was issued by the National Technical Committee for the Application of Statistical Methods. The main drafting units of this standard are; China Standards Research Center, Institute of Systems Science, Chinese Academy of Sciences. The main drafters of this standard are Liu Wen, Ma Yilin, Xiao Hui, Li Renliang and Liu Qiong. GB/T17989-2000
ISO Foreword
ISO (International Organization for Standardization) is a worldwide federation composed of national standardization bodies (ISO member groups): The work of formulating international standards is usually completed by ISO's technical committees. If a member group is interested in the work of a technical committee, it has the right to participate in the committee. International organizations (official or non-official) that maintain contact with I5O can also participate in the relevant work. In the field of electrotechnical standardization, ISO maintains a close cooperative relationship with the International Electrotechnical Commission (IEC). The draft international standards adopted by the technical committee are submitted to the member groups for voting: at least 75% of the member groups that must participate in the voting must agree to it before it can be officially published as an international standard. International standard ISO7870 was formulated by the Statistical Process Control Subcommittee of the Technical Committee on Application of Statistical Methods ISO/TC69/SC4.
Appendix A of this international standard is only a reminder appendix. ］Model
National Standard of the People's Republic of China
Control chartsGeneral guide and introduetionGR/T 17989—2000
idt IS0 7870: 1993
This standard describes the key elements and basic concepts of general control methods, and describes various control charts such as control charts related to standard control charts (specific control charts), control charts with process acceptance, or control charts with process prediction. This standard summarizes the basic principles and concepts and describes the relationship between various control chart methods to help select the most appropriate control chart standard under given conditions.
This standard does not specify statistical control methods using control charts. These methods refer to ISO 7873 and ISO7966 and related standards formulated later.
2 Referenced standards
The clauses contained in the following standards constitute the clauses of this standard by being referenced in this standard. When this standard was published: the versions shown are valid. All standards will be revised, and the parties using this standard should explore the possibility of using the latest versions of the following standards. (3/T3358.I--1993 Statistical terminology Part I General statistical terminology (neS03534-1:1993) GB/T 3358.2--1993 Statistical terminology Part II Statistical quality control terminology (ncIS03531-2:1993) 1507873:1993 Mean control chart with warning suit ISO7966:1993 Acceptance control chart
TS) 8258:1991 Conventional control chart (Shewhart control chart): my country has developed the following control chart standards! (+3/T 4091. 1~209). 9--1083 Conventional control G13/T 4886- -1085
Mean control chart with limits
GB/T 48871985
3 Definitions
Count cumulative sum
This standard adopts the relevant definitions in GB/T3358.1 and GB/T3358.2 4 General
Control chart is a basic tool for statistical quality control. It is a method to compare sample information representing the current state of the process with the selected limits established based on the inherent variation of the process. Its main use is to provide a method to evaluate whether the production operation or management process is in a "statistical control state". The control chart method was originally established for industrial production and development applications, and now the control chart method is also widely used in a wide range of service and auxiliary activities. In essence, a control chart is a management tool that helps determine when a process is stable and when it is changing. Control charts are useful for both management and field operators. Due to numerous small accidental causes, all operations have inherent variation, with the result that the observations obtained from a controlled process are not constant. Therefore, statistically valid limits are required to minimize erroneous judgments that result in over-control or under-control. If no systematic deviations enter the process, the process is considered to be in a "statistical control state." In essence, when a process is in a "controlled" state, the State Administration of Quality Supervision, Inspection and Quarantine approved m2000-11-01 implementation on March 16, 2000
GB/T 179892000
can reliably infer the behavior of the process. However, when non-accidental causes (abnormal causes) enter the system, the process will be affected, but if there is no information about their existence and influence, it is impossible to predict the results. If a process is found not to be in a "statistical control state", it is necessary to artificially predict the process into this state. For some economic or natural phenomena, there may be no known prediction methods, and control charts are used to identify whether they are out of control.
Control charts provide a simple graphical method for evaluating and monitoring whether a process has reached or maintained a "statistical control state". The judgment method obtains statistical function values or images from a series of ordered samples or subgroups and compares them with the control limits to make a judgment. According to the judgment method and the nature of the data Different types of control charts are designed based on the type of statistics used. The term "statistic" emphasizes that sample observations have inherent variability due to the inherent errors in the sample or the process itself. The main advantage of control charts is that they are easy to use and draw. It provides production or service workers, engineering and technical personnel, managers, and operators with an indicator of whether the process is in a "statistical control state." However, control charts can only be part of a complete analysis procedure. When identifiable causes enter the process, the chart can give timely indications, but a separate study is required to determine the nature of these identifiable causes and the necessary corrective measures.
5 Measurement Control Charts and Counting Control Charts
Control charts can be used for "measurement" data or "counting" data. Measurement Data is the observed value obtained by measuring and recording the numerical value of a certain characteristic of each individual in a group of objects under examination on a continuous scale. Count data is obtained by recording whether each individual in the group of objects under examination has a certain characteristic or development, calculating the number of individuals with (or without) the characteristic or development in the sample, or recording the number of times a certain characteristic or attribute appears in the individual, subgroup or a certain area or a certain amount under examination. In the case of quantitative data, network control charts are generally drawn: the first type discusses the location scale, such as the mean or median of the sample or subgroup, and the second type discusses the scale of the observations in the sample or subgroup, such as the range (R) or the sample standard deviation (s). In order to establish an effective quantitative control chart method, both types of charts are necessary.
The location chart is used to assess whether the process level has actually shifted significantly, and the sensitivity chart is used to assess whether the size of the sample or subgroup standard deviation has changed significantly. The control limit of the location chart is a function of the sample or subgroup standard deviation. It is important to verify whether the inherent variation parameter of the sample or subgroup standard deviation is kept in a state of control.
Most measurement control charts are based on the normal distribution (see ISO35341). Usually the mean of the observations in each subgroup is plotted, because except for very special cases, even if the distribution of individual observations does not follow the normal distribution, the mean also asymptotically follows the normal distribution and is ugly. Through the process of averaging, the role of random variation can be reduced, thereby enhancing the ability to find that the cause can be identified and has entered the process: the sample size is usually 1=4 or =5.When doing economic analysis, a more appropriate sample size can be taken. Detailed descriptions of these points can be found in various specific national or international standards for control charts. In the case of counting data, only one type of control chart needs to be drawn. The "\chart (the ratio of a specific category) is based on the binomial distribution, and the standard deviation (or standard error) of this ratio is recorded as: Since s = (1-)/n, s. Only depends on n and p, there is no need to draw an additional s chart. Similarly, the "\chart (the number of events of a given category) is based on the Poisson distribution, and the standard deviation (or standard error) of this number is recorded as 5. Since =, there is no need to draw an additional s, chart. 6 Control Limits || tt || Control limits are used on the control chart to decide whether to issue a signal or judgment to take action. Whether the process is in the "statistical control state". Some control charts also have "warning limits", in which case the control limits are also called "action limits". The measures that can be taken are in the following forms: a) Investigate the "source of the cause: b) Adjust the process; c) Stop the process. Various forms of judgment rules are defined in specific international standards for control charts (see ISO7873, ISO7966 and ISO8258). -2000
Determine whether the process has exceeded the action limit or warning limit. These forms include: points that fall outside the limit, chains, or graphs of observations within the limit. 7 Reasonable subgroups
Reasonable subgroups are subgroups or samples selected for technical reasons. The variation within the group can be considered to be caused only by unidentifiable accidental causes (or common causes), and the variation between the groups may be caused by identifiable causes (or outliers) that may be found and need to be identified: Technical reasons include consistency issues, sampling capabilities and economic considerations. One of the basic characteristics of control charts is to collect data in a reasonable grouping method in advance. The variability of measurements within subgroups with good consistency is used to determine control limits or verify short-term stability, while longer-term stability is evaluated by changes between subgroups. Although the influence of identifiable causes is limited over a relatively long period of time, it becomes the general basis for reasonable groups, other bases such as relatively consistent small ranges or common characteristics (such as those operated by the same specific operator) may also be applicable. The definition conditions of reasonable subgroups are also applicable For collecting data and determining control limits. For most control charts used in production, rational subgroups represent data collected over a short time interval under roughly consistent conditions of material, tool setup, environmental conditions, etc. Rational subgroups may be defined as specific periods or logical groupings of tasks for a group or team. In this case, the variability detected is due only to chance (or common causes). Over longer time periods, identifiable causes (or anomalous causes) may occur, such as changes in material sources, differences in the type of data recorded, readjusted tool setup, new work conditions, or changes in operators. Although these changes may not cause process level shifts, they may introduce variation beyond that due to chance. Therefore, the within-group standard deviation (estimated from a series of subgroups or obtained from past experience) is used as the basic measure of "random variability." If the rational number is to have a meaningful value, care must be taken to subject it to all the usual sources of random variation (or common variation). For example, a series of repeated test readings obtained from a test instrument testing a material placed in it may not include the effects of the material insertion process or the sampling process. If these effects are inherent in the usual test environment, these repeated test data will unrealistically underestimate the inherent variability of the test process. Therefore, almost any actual quantity obtained from this process will appear "out of control". However, if the subgroups are too large, the variation due to identifiable causes will increase the standard deviation within the subgroup. Many identifiable causes may occur without being detected. As mentioned above, the standard deviation of the observations obtained in each subgroup constitutes the basic measure of the inherent variability of the control chart. When the standard deviation is unknown, it is estimated by obtaining information from a relatively large series of subgroups. It is usually recommended to obtain information from at least 20 subgroups. It is important to demonstrate that the data collected during this basic period are in a state of "statistical control" and this can be achieved by plotting the ranges or standard deviations of the subgroups on the control chart (i.e., the data are in a state of statistical control with respect to within-group variation). If the data are not in this state, corrective action is required to obtain more reasonable basic data. The control limits are based on some multiplier of , with being the standard error of the plotted statistic and the within-group standard deviation. The multiplier of , the number of individual observations used to find the mean (sample range), the use of supplementary rules (such as chains), the sampling frequency, and similar issues are all considered in specific international standards for control charts (see ISO 7873 and ISC 7966). If the sample range is used as a measure of variability, the control chart is based on some multiplier of , and no estimate of the standard error is required. 5. 8 Types of Control Charts
There are three main types of control charts (including clustered and graphs): a) Gauge control charts (with several related variations, see 1S0 8258); a) Acceptance control chart (ISO7966) 5
c) Adaptive control chart.
Standard control charts are mainly used to evaluate the "statistical control state". Although they are not specifically designed for criteria involving the use of process tolerance limits, conventional control charts are often used as process acceptance tools. Acceptance control charts are designed specifically for process acceptance, and adaptive control charts manage processes by predicting trends and making adjustments in advance based on the predicted results. Chapters 1 to 11 describe some specific control charts of these basic types. 9 Conventional control charts and related control charts
9.1 General
GR/T179892000
In view of the role of control limits in providing a suitable procedure to judge the "state of control", Dr. W.A. Shewhart chose control limits based on experience when proposing control charts designed for economic quality control, but also applied some statistical knowledge. Assumptions about the collection of data, the exact form of their distribution, and other practical considerations (such as the inability to make economically justifiable judgments about minor identifiable or undiscovered causes) make it imperative to use strict theoretical probability values. Before adding control limits to a control chart, the center line must be defined: Dr. WA Shewhart constructed limits based on reasonable within-group variability, and set them at 3x (i.e., three times the standard deviation of the statistical measurement of the plotted points). Therefore, when using a mean control chart, the limits are usually set at 3x. Assuming that the initial distribution of the means of the observations follows a normal distribution, these limits will include 99.7% of the mean points as long as the process is "controlled" at the center value, which means that .3% of the (mean) plots for a "controlled\ process will exceed the limits and will incorrectly signal "out of control\". This type of error is called alpha risk (alpha = 0.003, i.e., the risk of making a type I error by concluding that the process has changed when in fact the process has not. However, in practice, if the distribution is not normal or if it is considered that a few slightly higher plots of the specified center level are not worth economic consideration, then the probability interpretation is inaccurate and is only a useful quantitative indication. When designing "\" and "\", the normal distribution is used to approximate the binomial and Poisson distribution values. It is usually sufficient to use an agreed-upon criterion (3. Limits), and from a practical point of view, the alpha risk is relatively small. On the other hand, there is also the issue of the ability to detect a specified deviation. For example, if the individual observations follow a normal distribution and the standard deviation of the individual observations in the process is <, and the process mean deviates from its standard value by 1α, what is the risk of finding that there is no such deviation (making a type I error)? If the mean of every four individual observations is plotted, the risk of making a type I error is 84.1%; if the individual observations are plotted, the risk is 97.5. One reason why conventional control charts are useful in many applications is that they are not very sensitive to small horizontal excursions that are not of practical importance. See Chapter 10 for further discussion of this topic. Sometimes, if greater sensitivity to small horizontal excursions is desired, in addition to setting control limits at ±30°, warning limits are also set, usually at ±2°, and some additional chain-based decision rules are often developed (see ISO (7873). However, this practice increases the risk of erroneously believing that the process is "out of control". Other ways to increase this sensitivity can also be achieved by using control charts drawn from the cumulative data of several subgroups. The control chart method also uses various other judgment criteria based on chain theory. A chain is a series of data points on the control chart with the same characteristics and adjacent to each other, or a group of continuous monotonically increasing values ("increasing" chains) or continuous monotonically decreasing values ("descending" chains), or a series of continuous points above (or below) the center line.
Many of the control charts listed in this section were not developed by Dr. W. A. Sliewtuart, because they are also mainly used to determine whether the process is in a "statistical control state", so they are listed together with conventional control charts, and the relationship between the control chart and the specification requirements is generally not used as a requirement for selecting its judgment criteria.
Screen gauge control charts generally have two forms. The first form of control chart has a specified standard value. The control limits used in this type of control chart are based on the data of the sample or subgroup plotted on the chart. This form Control charts are used to determine whether the within-sample variation of a series of sample observations is greater than the expected variation caused by chance alone. In essence, this type of chart, which is based entirely on estimated sample data, can be used to discover whether the cause system is lacking stability. Especially in the research and development stage, or in the initial research of early small-scale trials, government production and services, this form of control chart is useful for determining whether a new process, product or service is reproducible and whether the test method is repeatable. The control limits of the first form of control chart are based on standard values suitable for statistical mapping. This form of control chart is used to find out whether the difference between the sample observations and the adopted standard values is greater than the expected variation caused by chance alone. The standard value can be based on: a) representative prior data (e.g. data obtained from experience using control cabinets without specified standard values); b) economic values based on business needs and production costs; ) expected values or target values defined in specifications. GB/T 17989--2000
It must be noted that this form of control chart is not only used to evaluate the stability of the cause system, but also to evaluate whether the cause system is appropriate based on the standard values collected.
9.2 Conventional Control Charts and Related Control Charts (Including Cumulative Sum Charts) The control charts listed in this section fall into two categories. The first category includes control charts that use data obtained from a single subgroup, while the second category includes control charts that are obtained by accumulating data points from more than one subgroup. 9.2.1 Use of data from a single reasonable group as a control chart Control charts with values given for each point These control charts are as follows:
a) R chart (mean-range chart [median can be substituted for Xb) and moving range chart E) Moving range chart for a single value (Study 9.2.2ac) Chart (ratio circle or non-conforming rate chart)
) Chart (number of defective products chart)
e) C chart (number of defective products chart)
") Chart (number of qualified products per unit) g) Order chart (quality scan score chart, a quality penalty is the weighted number of defectives) h) D chart (defect chart), a variation of the Q chart, in which defects are used as weighting coefficients. 1 Multiple response control chart:
a control chart that uses the responses of two or more characteristics combined as a statistic of the sub-new to evaluate and monitor the process. When the variables or characteristics involved are independent (uncorrelated), the x statistic is usually plotted; when the characteristics are correlated, the 1 statistic is usually plotted (see ISO 3534).
j) Trend control charts:
The deviation of the subgroup mean from the expected value of the process level is used to assess and monitor the control level of the process. The expected value of the process level can be determined empirically or by regression techniques.bzxZ.net
9.2.2 Control charts that use the accumulated data of a reasonable subgroup as the value of each plot These control charts are as follows:
a) Moving average and moving range charts:
Control charts that assess and monitor the control level of the process using the arithmetic mean of the most recent measured values. The advantage of these control charts is that they can minimize random variability by averaging, especially when there is only one observation in a narrow group. However, they have the disadvantage that unweighted transmission effects always act on individual points. In some cases, individual observations (r = 1) are plotted on the X-ray chart, and moving ranges (usually = 2) are plotted on the range chart. These control charts do not have the advantage of minimizing random variability by averaging, and do not follow the assumption of normal distribution. The values still provide a visual aid in evaluating the data.
h) Exponentially Weighted Moving Average (FWMA) (or Exponential Smoothing Chart, or K-Weighted Chart) uses an exponential moving average to assess and monitor deviations in process level. The individual observations or subgroup means obtained from the current and previous data sets are averaged but progressively smaller weights are given to data obtained in later periods. Because of the increased transmission effect, this control chart is usually more sensitive to small shifts in level than a conventional 30. control chart. The EWMA chart provides a ready estimate of the process mean that is of particular value in determining when and how much to adjust process settings. ) Cumulative Sum Chart
A control chart that evaluates and monitors process levels using the cumulative sum of differences between individual observations or subgroup means and a standard (or reference) value. The trend of the control chart is identified by a decision template. The most popular form is the (truncated) V-shaped template. Due to the enhanced transfer effect, this control chart is usually more sensitive to small horizontal movements than the general tape gauge 35 control chart. The use of the V-shaped template and its visual graphics are often useful in determining the start of horizontal movement. 10 Acceptance Control Chart
10.1 General
WGB/T 17989-2000
The acceptance control chart is a control chart used for the following two-day evaluation process. A》Assess whether the process is in a "statistical control state" based on the variation within the sample or subgroup: b) For the measured characteristics, predict whether the process can meet the requirements of the product or service. The key point of acceptance control charts compared to conventional control charts is that processes are not usually required to be maintained under control at a standard process level, but rather can be operated at any level within a certain range of process levels established empirically, as long as the variability within the subgroups remains under control. Assuming that there are identifiable causes for process excursions, and these excursions are small relative to product or service requirements, it is uneconomical to try to control them too tightly; that is, adjusting the center of the process too finely may cost much more than the value obtained and may introduce more variability. On the other hand, some process excursions are large enough to warrant early detection, and it is important to consider the risk of not detecting these excursions. Acceptance control charts can help avoid "overcontrol," that is, avoid making unnecessary corrections to the process. Overcorrection often makes the process less stable because the process adjustments are inaccurate and lead to further corrections. For process levels within the "acceptable process area", the effect of the correction may be to create rather than reduce variability. The key feature that distinguishes acceptance control charts from gage control charts and related control charts is the consideration of product or service requirements, which is not an element of the "statistical control state". The supervisor or quality expert defines an acceptable process area bounded by an acceptable process level and a set of rejectable process levels: The sample size is then determined to meet the specified α risk (the risk of rejecting the process that should be accepted) and β risk (the risk of accepting the process that should be rejected): Based on these criteria, special control limits shown on the chart are calculated as operator judgment criteria: To verify the "statistical control state", control charts of within-group variation are required. There is considerable flexibility in control state design, including the use of asymmetric control limits when appropriate. 10.2 Modified Control Charts Control Charts with Modified Limits A special case of an acceptance control chart that relates the location of the control limits to the tolerance requirements by making the "natural process limits" equal to the tolerance limits, just as the 3 control limits are defined for individuals. To establish the modified control limits, the control limits are set at (3-3//)a within the narrow tolerance limits. This consideration is reasonable and valid, but it does not technically provide a rule for determining the risk of a specified rejectable process level or for determining the sample size. In some applications, the control limits are sometimes set at (3-2/) to provide more conservative control limits. See 150 for a more detailed description. 7966.
10.3 Acceptance Control Charts Partial List
10.3.1 Acceptance Control Charts
Acceptance control charts give acceptable process levels associated with the risk tree of rejecting a good process, and rejectable process levels associated with the risk of accepting a process deviation: these deviations can produce too many nonconforming products, or cluster more nonconforming products away from the target center than is reasonable.
There are several types of acceptance control charts;
a) R chart (mean and forging difference acceptance control chart); b) chart (nonconforming rate acceptance control chart); e) chart (nonconforming number acceptance control chart): 10.3.2 Modified Control Charts
Modified control charts relate the process level associated with the "risk" to the tolerance limit, and give control limits based on this. 11 Adaptive Control Charts
Adaptive control charts are suitable for situations where process adjustments can be made and standard levels need to be strictly adhered to. It uses prediction models of varying complexity to predict where the process will no longer continue the current state of operation and take rapid corrective measures to prevent excessive deviation from the standard level. Since the elements of the prediction model are very dependent on the specific process, the adaptive control chart is tailored to a specific application and is usually unique. Unlike the previous two types, this type of control chart uses a process level prediction estimate based on the following assumptions: the process will continue to develop along the current path: and this type of chart requires a prior change in the process to avoid any predicted deviation from the process standard. When the prediction model is good, this method is very effective in reducing variability. If the prediction model is poor, it is likely to increase variability. GB7T179892000
12 Risk effectiveness criteria associated with control chart judgments Control charts are used to send out signals of normality (such as stable process levels). There are two types of inherent errors in any statistical method used for judgment. In the application of control charts, they are: 8) Type I error (Type II error) - when the process does not actually deviate, the conclusion that a deviation has occurred is made. This type of error results in costs associated with overcontrol (unnecessary adjustments) or unnecessary investigations of nonexistent problems. h) Type II error (Type II error) - a process level shift that is not detected. In this case, waste is caused by not stopping an unsatisfactory process (one that results in a large number of unsatisfactory products or services) and missing the opportunity to identify the cause of the process shift.
For a given control configuration, including sample size and the control limits used, the characteristic curve (OC curve) represents the probability of identifying a process level deviation at a given time, which is a parameter of the process level. This (C-curve method is only useful for conventional control charts and acceptance control charts, which make decisions based on the current data point. Since the exponentially weighted moving average chart contains information about past observations, the (C-curve method is no longer applicable. Before the signal is sent, the processing average and chain length (A scale) are usually easy. Here, the chain length is defined as the number of subgroups checked from the first moment the process changes until the control chart sends a signal that the process has changed. For example, in Figure 1, the change in the process mean occurs between points 10 and 11, but the change signal is not sent until point 20. So the chain length is 10. In other cases, for a change of the same size from the desired mean, the chain length might be 5 or 20 subgroups or some other number, depending on the chance changes in the characteristic being observed. Thus, for a change of a particular size, there is a distribution of possible chain lengths. To design control charts, it is convenient to use the average chain length (ARL) of this distribution. The ARL (average chain length) can be used to indicate how long a control chart allows a process to operate out of control or out of compliance, but it should be noted that sometimes the actual chain length will be longer or shorter than the ARI.
1 Action Limit
Signal a change in the process
|Center Line
Lower Action Limit
Figure 1 Example of a chain length of 10 subgroups between a process change and a signal from a control chart. For a process at a certain level, a long ARL is desirable (to minimize the need for unnecessary investigations or corrective actions), while for a process excursion to an undesirable level, a short ARI is desirable (to require corrective action when necessary). For any control chart, the ARL curve can be used to describe the relative sensitivity of various control chart systems to detect level excursions. 13 Economic Considerations
In assessing the economic effects of alpha risk and risk, it is important to determine the sampling frequency. The rate is an important factor. Compared with determining whether the process is in a state of statistical control, this factor is more important for the purpose of process acceptance. From this economic consideration, various specific recommendations for the selection of "economic control charts" are triggered. Specific recommendations on sample size and sampling frequency can be found in the specific control chart standards. General guidance: In the initial stage of the control chart operation, judgments can be made quickly by sampling more frequently. When the process is stable and the history is clear, the frequency of sampling can be reduced. Larger sample sizes can be used to detect small changes in rate, but in order to detect larger changes more quickly, more frequent small samples may be more useful. GB/T 17989- 2000
Appendix A
(Suggested Appendix)
References
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