Some standard content:
ICS 03.120.30
National Standard of the People's Republic of China
GB/T 17989.2—2020
Replaces GB/T40912001
Control charts
Part 2: Conventional control charts
Control charts-Part 2: Shewhart control charts(IS07870-2;2013.MOD)
Release on 2020-03-06
State Administration for Market Regulation
National Administration of Standardization
Implementation on 2020-10-01
Normative references
Terms, definitions and symbols
Terms and definitions
Nature of conventional control charts
Types of control charts
Control charts when the values of process parameters are not givenControl charts when the values of process parameters are given in advance5.3
Variation control charts and numerical control charts
6Variation control charts
Mean X chart and range R chart or mean X chart and standard deviation: Figure 6.2
Single value X Chart and moving range R, chart
Median text control chart
Control procedures and interpretation of variable control charts
Collect preliminary data
Check (or R) chart
Eliminate the cause and modify the control chart
Check X chart
Continuously monitor the process
8 Fluctuation River Inspection mode for finding the cause
Process control, process capability and process improvement
Counting control chart
Preliminary preparation for setting control charts
Selection of key quality characteristics CTQ for process control Process analysis
Selection of reasonable grouping
Frequency and size of subgroups
Collection of initial data
Action plan for out-of-control conditions
GB/T 17989.2—2020
GB/T 17989.2—2020
Steps to construct a control chart
Determine the data collection strategy
Data collection and calculation
Draw X and R charts·
13 Precautions for conventional control charts
Precautions
Data correlation
3 Principles of substitution of quattrogram
Appendix A (Informative Appendix)
Appendix B (Informative Appendix)
References
Precautions for inspection mode of fluctuations that can be identified Example
GB/T17989 "Control Chart" is planned to be divided into the following 9 parts: Part 1: General Guide:
Part 2: Conventional Control Chart;
-Part 3: Acceptance Control Chart;
-Part 1: Cumulative Sum Control Chart:
Part 5: Special Control Chart:
Part 6: Exponential Weighted Moving Average Control Chart;
Part 7: Multivariate Control Chart;
-Part 8: Short Cycle and Small Batch Control Methods;-Part 9: White Correlation Process Control Chart. This part is Part 2 of GB/T17989. This part was drafted in accordance with the rules of GB/T1.12009. GB/T 17989.2-2020
This part replaces GB/T4091-2001 "Conventional Control Charts". Compared with GB/T4091-2001, the main technical changes are as follows: 4 test modes for whether the fluctuation can be explained (see Chapter 8); the construction method of measurement control charts is added (see Figure 6). The symbols and colors in the legend of conventional control charts are modified (see Figures 7 and 8. All diagrams in Appendix B). This part uses the redrafting method to modify the adoption of IS07870-2:2013 Control Charts Part 2: Conventional Control Charts.
This part has structural changes compared with IS078702:2013: the order of Appendix A and Appendix B is adjusted.
The technical differences between this part and IS07870-2:2013 and the reasons are as follows: Regarding the normative reference documents, this part has made technical adjustments to adapt to my country's technical conditions. The adjustments are concentrated in Chapter 2 "Normative Reference Documents". The specific adjustments are as follows:, replace ISO35342 with GB/T3358.2, which is equivalent to the international standard (see Chapter 3);. Add reference to G3/T 17989.1 (see 3.1); Delete IS05479 and 1S016269-4+2010, and add the term "red" (see 3.1.1). This part has been edited as follows:
- The order of references has been adjusted.
This part was proposed and submitted by the National Technical Committee for Standardization of Statistical Methods (SAC/TC21). The drafting units of this part are: Tsinghua University, Gongliya (Xiamen) Ecological Development Co., Ltd., Qingdao University, and China National Institute of Standardization. The main drafters of this part are: Sun Jing, Zhao Jing, Xu Jinfei, Li Lili, Yixing, and Wu Gang. The previous versions of the standards replaced by this part are: GB/T4091—2001.
GB/T17989.2—2020
The traditional manufacturing process is aimed at the production process of manufacturing products, and quality control is carried out by testing the final product and screening out the unqualified products. This testing strategy is usually wasteful and uneconomical because it uses post-testing, when the waste products have already been produced. On the contrary, it would be more efficient to take the most preventive measures at the beginning and effectively prevent waste from being produced. This can be achieved by collecting and analyzing process information and taking timely measures in the process. In 1924, Walter Armand Shewhart proposed the control chart method, which is a graphical tool for process control based on the principle of statistical dominance. Control chart theory is used to distinguish between two types of variation. The first is random variation caused by "accidental causes" (also called "common causes", "natural causes", "random causes", "intrinsic causes" or "uncontrolled causes"). This is because there are many causes that always exist and are not easy to distinguish, which will cause variation; and each of them is only a small part of the total variation and has no significant effect. However, the sum of the contributions of all these unidentified random causes is measurable and assumed to be inherent in the process. Eliminating or correcting common causes may require resource allocation decisions and fundamentally change the process and system. The second type of variation represents a real change in the process, which can be attributed to Due to some identifiable causes, these causes are not inherent in the production process and can be eliminated, at least in theory. These identifiable causes are called "identified causes" of variation (also called special causes, non-natural causes, systematic causes or controllable causes). They are attributed to lack of consistency in materials, broken tools, imperfect processes or procedures, abnormal performance of equipment, or environmental changes. If the process variation is only due to random causes, the process is said to be in a state of statistical control, or simply "controlled". The level of variation is determined, and any deviation from this level can be regarded as the result of identifiable causes to be identified and eliminated. Statistical process control is a method of establishing and maintaining a process at an accepted and stable level in order to ensure that the products and services of the process meet the specified requirements. Its main statistical tool is the control chart, which is a graphical method of representing and comparing information based on a series of observations that show the current state of the process compared with the control limits. The control limits are established by taking into account the inherent process variation called process capability. First of all, this control chart method helps to evaluate whether the process has reached or is still in a state of statistical control. When the process is considered stable and predictable, the ability of the process to meet customer requirements can be further analyzed. Control charts can also be used to provide a continuous record of process output quality characteristics while process activities are ongoing. Control charts help detect non-natural patterns of data variation caused by repetitive processes and provide judgment criteria for lack of statistical control. The use and detailed analysis of control charts are used to better understand the process and often identify valuable improvement methods.
1 Scope
Control charts
Part 2: Conventional control charts
GB/T 17989.2—2020
This part of GB/T17989 gives guidance on understanding and applying conventional control charts for statistical process control. This part is only applicable to situations where conventional control charts are used for statistical process control. All supplementary content involved is related to conventional control charts, such as: the use of warning lines, trend patterns and process capability analysis. Other types of control chart methods can be found in GB/T17989.1. Find a beautiful description.
2 Normative references
The following documents are indispensable for the application of this document. For dated references, the dated versions shall apply to this document. For any undated references, the latest version (including all amendments) shall apply to this document: GB/T3358.2 Statistical vocabulary and symbols Part 2: Applied statistics (GB/T3358.2-2009.IS035342:2006IDT)
GB/T17989.1 Control charts Part 1: General guidance (GB/T17989.1—2020.ISO78701:2014, MOD) ISO22514 (all parts) Statistical methods in process management Capability and performance (Statistical mcthodsinproccssmanagement
Capabilityand perlormance
3 Terms, definitions and symbols
3.1 Terms and definitions
GB/T3358.2 and GB/T17989.1 and the following terms and definitions apply to this document. 3.1.1
Subgroup
Group data taken from the same process, the obtained grouped data makes the difference within the group as small as possible and the difference between the groups as large as possible: 3.2 Symbols
The following symbols apply to this document.
n: subgroup size or subgroup sample size. That is, the number of sample observations in the subgroup.
L: lower specification limit
I: lower control limit
U: upper specification limit
Uc: "control limit
X. Quality characteristics [Each quality characteristic is expressed as (XX,,X,,), sometimes the symbol Y is used instead of Xx. Group mean
GB/T 17989.2—2020
x: Average of the estimated subgroup mean
: True value of the process mean
: True value of the process standard deviation
Given value of au0
XSubgroup median
, average of the medians
R: The difference between the most observed value and the smallest observed value R: Average of the R values of the subgroup
R.: Moving range: The absolute value of the difference between two adjacent observations: Sample standard deviation estimated from observations within the subgroup 2(X.-x)*
s: Average estimate of the sample standard deviation of the subgroup
: Estimate of the process standard deviation||tt| |p: proportion of a given category within a subgroup
p: mean of proportion
np: number of a given category within a subgroup
p: given p value
np: given np value (for a given p)
C: number of occurrences within a subgroup
co: given c value
c: average estimate of subgroup c values
u: number of occurrences per unit within a group
u: mean of subgroup u valuesbZxz.net
ua: given value of u
4 Properties of Conventional Control Charts
Conventional control charts are charts used to display statistical measures obtained from variable or count data. Control charts require that data be obtained from reasonable subgroups at relatively regular intervals. Intervals can be defined in terms of time (e.g., hourly) or number (per batch). Typically, data is obtained from the process in the form of samples or subgroups, with the same process characteristics, the same measurement units, and the same subgroup size. From each subgroup, one or more subgroup characteristics are derived. For example, the subgroup mean X and the subgroup range R, standard deviation s. Or counting characteristics such as the proportion of a given category. The points on the conventional control chart correspond to the paired data formed by the value of the subgroup characteristic and the subgroup number. Conventional control charts also have a center line (H), which is located on the center line of the plot. The reference value of the characteristic quantity is determined: when determining whether it is in a state of statistical control, the reference value is usually the mean of the statistical measurement under consideration: for process control, the reference estimate can be a long-term estimate of the characteristic described in the product specification: it can be an estimate of the characteristic quantity based on the statistical control of the process in the past. Or it can be an estimate based on the daily standard estimate of the product/service. Conventional control charts also have two control limits determined by statistical methods, located on both sides of the center line, called the control limit (c and lower control limit Lc (see Figure 1)
Control limit
Lower control limit T
Figure 1 Control chart example
GB/T17989.2—2020
Center line CL||t t||子新综合号
The control limits of conventional control charts are located at 3 sigma on both sides of the center line, where sigma is the known population standard deviation or an estimate of the population standard deviation. Shewhart chose to design control limits at a distance of 3 sigma from the center line based on economic considerations of balancing costs, especially the cost of looking for problems when the process is in a state of statistical control. And the cost of failing to find problems when the process is not in a state of statistical control. When the control limits are placed close to the center line, it will lead to finding causes for problems that may not exist: and placing the control limits too far from the center line will increase the risk of not finding the cause in time when there is a problem. Under the assumption that the drawing statistics are approximately normally distributed, the 3 sigma control limit table Explanation: As long as the process is in statistical control, approximately 99.7% of the values of the statistic will fall within the control limits. Another interpretation is that when the process is in statistical control, there is approximately a 0.3% risk that, on average, 3 plotted points in 1000 will fall outside the upper and lower control limits: the word "approximately" is used here because the probability values will be affected by deviations from basic assumptions such as the type of data distribution. In practice, the choice of 3 3 3 control limits instead of 3 ... Shewhart chose 3 to avoid the need to pay special attention to the probability of correctness. Similarly, some users use actual probability values based on non-normal distributions to construct control charts such as range control charts and nonconformance control charts. In response, given the emphasis on empirical interpretation, Shewhart also used 3 sigma control limits. When a process is in statistical control, it is a rare event that exceeds the control limit, relative to a true alarm that the process is not in statistical control. Therefore, when a point falls outside the control limit, action should be taken. Because action should be taken at this time, the 3 sigma control limits are often called "action limits". On the control chart, it is valuable to mark the 2 sigma points on both sides of the center line. Any sample value that falls outside the 2 sigma limits is a warning of an impending out-of-control condition. Therefore, the 2 sigma limits are sometimes called "warning limits". Although such a warning on the control chart does not require action, some users of the control chart still want to immediately collect a subgroup of the same size to determine whether any corrective action is needed. When using control charts to evaluate process status, two types of errors are possible. Type I error occurs when the process is actually in control but the plotted points randomly fall outside the control limits. The control chart sounds an alarm, incorrectly concluding that the process is out of control, and then some expense is incurred trying to solve a problem that does not exist. Type II error occurs when the process is not actually in control but the plotted points randomly fall within the control limits. The control chart does not sound an alarm and incorrectly concluding that the process is in statistical control. Failure to detect that the process position or variability has changed can result in the production of defective products, which can result in considerable losses. This type of error occurs because of the width of the control limits, the size of the group, and the degree to which the process is out of control. Because the magnitude of the process change is difficult to know in advance, the actual risk of this type of error is difficult to determine. Because it is usually impractical to make meaningful estimates of the risk and risk of Type II errors in any given situation, conventional control charts are designed to control Type I errors: Under the assumption of normality, the Type I error using 3-dimensional sigma control limits is 0.3%. In other words, when the process is in statistical control, this type of error will only occur 3 times in 1,000 samples. 3
GB/T 17989.2—2020
When a process is in statistical control, control charts provide a method that is similar to the null hypothesis of hypothesis testing (i.e., the process has not changed and remains in statistical control). In the presence of quantitative uncertainty, conventional control charts cannot be considered as pure hypothesis testing because the probability distribution of characteristics, randomness, and specific deviations of process characteristics from the standard value cannot be determined in advance. Shewhart emphasized the practical application of control charts to identify process deviations from the "controlled state" and weakened the probability interpretation. When the values of the plot fall outside the control limits, or the maximum values of a series of plots show an unusual pattern, as shown in Chapter 8, the statistical control state is no longer acceptable: at this time, an investigation of the identifiable cause is initiated and the process is adjusted or stopped, and the process can continue until the identifiable cause is identified and eliminated. In the rare case that no identifiable cause can be found, it is concluded that the points falling outside the control limits represent the occurrence of a small probability event caused by chance, even if the process is in control. When a process is studied for the first time, it is often necessary to use historical data previously obtained from the process in order to bring the process into a state of statistical control, or to use new data consisting of a series of samples from the process before attempting to establish a control chart. A review phase is required to establish the control chart parameters, usually referred to as Phase 1: In this phase, enough data is obtained to obtain reliable estimates of the center line and control limits of the control chart. The control limits set in Phase 1 are tentative control limits because they may be based on data from a time when the process was not in control. Due to the lack of information on the historical operating characteristics of the process, it may be difficult to identify the exact cause of the control chart alarm at this stage. However, if a common cause of fluctuation can be identified and corrective action is taken, the process data affected by the common cause should be eliminated and the control chart parameters should be re-determined. This iterative process continues until the control chart no longer alarms and the process can be considered to be in control, stable and predictable. Because some data may have to be removed during Phase 1, the user of the control chart often needs to obtain additional data from the process to ensure reliable parameter estimates and determine the state of statistical control. The centerline and control limits of the control chart obtained in Phase 1 are used as control chart parameters for continuous monitoring of the process. This is called Phase 2, which aims to maintain the process in a state of control and quickly identify common causes that may appear from time to time. However, going from Phase 1 to Phase 2 can be time-consuming and laborious. However, it is crucial. Because failure to eliminate common causes of fluctuations will lead to an overestimation of process variation, the control limits of the control chart will be set too wide, resulting in the control chart being insensitive to detecting common causes.
5 Types of Control Charts
5.1 Overview
Conventional control charts are divided into two categories: variable control charts and attribute control charts. For each control chart, there are two different situations: a) when the value of the process parameter is not predetermined; b) when the maximum value of the process parameter is predetermined. Pre-given process values can be specified conditions, either target values, or parameter estimates determined from long-term data collected when the process is under control:
5.2 Control charts when process parameter values are not given This is intended to determine whether changes in the values of a plotted characteristic (such as X, R, or other statistics) can be attributed to changes caused by chance alone: Using data collected from process samples, control charts are constructed to detect changes that are not caused by chance. The purpose is to bring the process into a state of statistical control. 5.3 Control charts when process parameter values are given This is intended to determine whether the values of X, R, etc. in the subgroups of size n are compared to the corresponding given values of X, R, etc., and whether there are fluctuations beyond those caused by chance alone. The difference between a control chart with a given parameter value and a control chart without a given parameter value lies in the additional requirements for determining the center position of the process and the process variation. The given value of the parameter can be obtained using a control chart without prior information, that is, a specified value, or an economic estimate based on considerations of service demand and production costs, or a nominal value set based on product specifications. The given value of the parameter taken by Shi Chuan is determined by investigating and analyzing the initial data that is typical of future data. The given value should be consistent with the inherent fluctuation of the process to achieve the effective operation of the control chart. The control chart based on the predetermined given value is used to control the process and maintain the consistency of products and services so that it is maintained at the expected level. 5.4 Measurement control chart and attribute control chart
The control charts involved are as follows:
a) Measurement control chart, used for continuous data: 1) Mean Y chart and range R chart or standard deviation chart; 2) Single value X chart and moving difference R chart
3) Median X chart and range R chart.
b) Attribute control chart - used for countable or categorical data: 1) Force chart: the number of days falling in a given category divided by the total number expressed as a proportion or percentage; 2) np chart: the number of days falling in a given category when the subgroup sample size is constant; 3) (chart: the number of times an event occurs when the chance of something happening is fixed; 1) chart: the number of times an event occurs per unit when the chance of an event happening is changing. Figure 2 gives a small example of how to choose an appropriate control chart for a given situation: Variable data
Subgroup size
X and R charts
6 Variable control charts
6.1 Overview
Individual value charts
Figure 2 Types of control charts
Count data
Defectives
Number of bands
Measured on a ratio
Constant
Measured on a ratio
Variable control charts for continuous data, especially graphs and scale charts, are the most commonly used, showing The following are ten reasons why variable control charts are particularly useful:5
GB/T17989.2—2020
a) Most processes and outputs have characteristics that can be measured and generate continuous data, so variable control charts are widely used because variable control charts can directly obtain specific information about the process mean and variance, so compared with attribute control charts, variable control charts provide more information than attribute control charts. h)
Control charts provide more information than attribute control charts, and variable control charts can often issue an alarm for process abnormalities before the process produces defective products.
c) Although the cost of obtaining measurement data is usually higher than the cost of obtaining pass/fail data, the subgroup sample size required for continuous data is much smaller than that required for attribute data to achieve the same control efficiency. In turn, it helps to reduce the total inspection cost and shorten the time between the occurrence of process problems and the implementation of corrective actions. d) Regardless of the specifications, these charts provide a direct visual method to evaluate process performance. Combining a variable control chart with a properly spaced histogram and observing it carefully, one will often find some ideas or suggestions for the process: All variable control charts assume that the distribution of the quality characteristic is normal (Gaussian) in their use, and deviations from this assumption will affect the performance of the control chart. The factors used to calculate the control limits are based on the assumption of normality, and since most control limits are used as empirical guides in decision making, small deviations from normality are not a cause for concern. Moreover, even if the individual observations do not follow a normal distribution, the central limit theorem will cause the mean to converge to a normal distribution. This makes the assumption of normality of the X-chart reasonable, even for subgroup sizes of 4 or 5. When dealing with individual observations to conduct capability studies, the true state of the data distribution is important. It is wise to check the continued validity of this assumption regularly, especially to ensure that the data used come from a single population. It is important to point out that the distribution of the range and standard deviation is not normal. Distribution: Although the range chart and standard deviation chart require the use of the normality assumption to determine the control limit factors, these control charts can also be used for empirical decision making if the process data do not completely obey the normality assumption. Metrology control charts describe process data based on dispersion (process fluctuation) and location (process mean). Therefore, metrology control charts always appear and are analyzed in pairs, that is, a control chart that controls the location and a control chart that controls the dispersion. The control chart that controls the dispersion is analyzed first because it provides a theoretical basis for estimating the process standard deviation. In turn, the estimated results of the process standard deviation can be used to set the control limits of the control chart that controls the location.
Each control chart uses control limits, which may be estimated based on sample data or based on given process parameters. Tables 1 and 3 use the subscript "0\" to indicate specified values. For example, , is a given process mean, and , is a given process standard deviation. The most commonly used metrology control charts are introduced below. 6.2 Mean X chart and range R chart or mean X chart and standard deviation S chart When the subgroup sample size is small (usually less than 10), you can use the Y chart and R chart: When the subgroup sample size is large (usually ≥ 10), it is preferred to use the X chart and: chart. Because as the subgroup sample size increases, the efficiency of estimating the process standard deviation using the range will decrease. When the control limit of the process can be calculated by electronic equipment, it is obviously more preferred to use the standard deviation. Tables 1 and 2 give the calculation formula and factors of the control limit of each control chart of the measurement control chart: Table 1 Calculation formula of control limit of measurement control chart Statistic
Estimated control limit
Center line
Note:: and are pre-given values
Ua and Le
XA, R or X±A
Center line
Pre-determined control limits
We and Le
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