1、Designation: E2587 12E2587 14 An American National StandardStandard Practice forUse of Control Charts in Statistical Process Control1This standard is issued under the fixed designation E2587; the number immediately following the designation indicates the year oforiginal adoption or, in the case of r
2、evision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice provides guidance for the use of control charts in statistical process control prog
3、rams, which improve processquality through reducing variation by identifying and eliminating the effect of special causes of variation.1.2 Control charts are used to continually monitor product or process characteristics to determine whether or not a process isin a state of statistical control. When
4、 this state is attained, the process characteristic will, at least approximately, vary within certainlimits at a given probability.1.3 This practice applies to variables data (characteristics measured on a continuous numerical scale) and to attributes data(characteristics measured as percentages, fr
5、actions, or counts of occurrences in a defined interval of time or space).1.4 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrationsof calculation methods. The examples are not binding on products or test methods treated.1.5
6、 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibilityof the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatorylimitations prior to use.2. Referenced Docume
7、nts2.1 ASTM Standards:2E456 Terminology Relating to Quality and StatisticsE1994 Practice for Use of Process Oriented AOQL and LTPD Sampling PlansE2234 Practice for Sampling a Stream of Product by Attributes Indexed by AQLE2281 Practice for Process and Measurement Capability IndicesE2762 Practice for
8、 Sampling a Stream of Product by Variables Indexed by AQL3. Terminology3.1 Definitions:3.1.1 See Terminology E456 for a more extensive listing of statistical terms.3.1.2 assignable cause, nfactor that contributes to variation in a process or product output that is feasible to detect and identify(see
9、 special cause).3.1.2.1 DiscussionMany factors will contribute to variation, but it may not be feasible (economically or otherwise) to identify some of them.3.1.3 attributes data, nobserved values or test results that indicate the presence or absence of specific characteristics or countsof occurrenc
10、es of events in time or space.3.1.4 average run length (ARL), nthe average number of times that a process will have been sampled and evaluated beforea shift in process level is signaled.1 This practice is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct respon
11、sibility of Subcommittee E11.30 on Statistical QualityControl.Current edition approved Dec. 1, 2012Oct. 1, 2014. Published February 2013November 2014. Originally approved in 2007. last previous edition approved in 20102012as E2587 10.E2587 12. DOI: 10.1520/E2587-12.2 For referencedASTM standards, vi
12、sit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.This document is not an ASTM standard and is intended only to provide the user of an ASTM stand
13、ard an indication of what changes have been made to the previous version. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard as published by ASTM
14、 is to be considered the official document.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.1.4.1 DiscussionA long ARL is desirable for a process located at its specified level (so as to minimize calling for unneeded investigation or
15、corrective action) and a short ARL is desirable for a process shifted to some undesirable level (so that corrective action will becalled for promptly). ARL curves are used to describe the relative quickness in detecting level shifts of various control chartsystems (see section 5.45.1.4). The average
16、 number of units that will have been produced before a shift in level is signaled mayalso be of interest from an economic standpoint.3.1.5 c chart, ncontrol chart that monitors the count of occurrences of an event in a defined increment of time or spacespace.3.1.6 center line, nline on a control cha
17、rt depicting the average level of the statistic being monitored.3.1.7 chance cause, nsource of inherent random variation in a process which is predictable within statistical limits (seecommon cause).3.1.7.1 DiscussionChance causes may be unidentifiable, or may have known origins that are not easily
18、controllable or cost effective to eliminate.3.1.8 common cause, n(see chance cause).3.1.9 control chart, nchart on which are plotted a statistical measure of a subgroup versus time of sampling along with limitsbased on the statistical distribution of that measure so as to indicate how much common, o
19、r chance, cause variation is inherent inthe process or product.3.1.10 control chart factor, na tabulated constant, depending on sample size, used to convert specified statistics or parametersinto a central line value or control limit appropriate to the control chart.3.1.11 control limits, nlimits on
20、 a control chart that are used as criteria for signaling the need for action or judging whethera set of data does or does not indicate a state of statistical control based on a prescribed degree of risk.3.1.11.1 DiscussionFor example, typical three-sigma limits carry a risk of 0.135 % of being out o
21、f control (on one side of the center line) when theprocess is actually in control and the statistic has a normal distribution.3.1.12 EWMA chart, ncontrol chart that monitors the exponentially weighted moving averages of consecutive subgroups.3.1.13 EWMV chart, ncontrol chart that monitors the expone
22、ntially weighted moving variance.3.1.14 exponentially weighted moving average (EWMA), nweighted average of time ordered data where the weights of pastobservations decrease geometrically with age.3.1.14.1 DiscussionData used for the EWMA may consist of individual observations, averages, fractions, nu
23、mbers defective, or counts.3.1.15 exponentially weighted moving variance (EWMV), nweighted average of squared deviations of observations from theircurrent estimate of the process average for time ordered observations, where the weights of past squared deviations decreasegeometrically with age.3.1.15
24、.1 DiscussionThe estimate of the process average used for the current deviation comes from a coupled EWMAchart monitoring the same processcharacteristic. This estimate is the EWMA from the previous time period, which is the forecast of the process average for thecurrent time period.3.1.16 I chart, n
25、control chart that monitors the individual subgroup observations.3.1.17 lower control limit (LCL), nminimum value of the control chart statistic that indicates statistical control.3.1.18 MR chart, ncontrol chart that monitors the moving range of consecutive individual subgroup observations.3.1.19 p
26、chart, ncontrol chart that monitors the fraction of occurrences of an event.3.1.20 R chart, ncontrol chart that monitors the range of observations within a subgroup.3.1.21 rational subgroup, nsubgroup chosen to minimize the variability within subgroups and maximize the variabilitybetween subgroups (
27、see subgroup).E2587 1423.1.21.1 DiscussionVariation within the subgroup is assumed to be due only to common, or chance, cause variation, that is, the variation is believedto be homogeneous. If using a range or standard deviation chart, this chart should be in statistical control. This implies that a
28、nyassignable, or special, cause variation will show up as differences between the subgroups on a corresponding XX chart.3.1.22 s chart, ncontrol chart that monitors the standard deviations of subgroup observations.3.1.23 special cause, n(see assignable cause).3.1.24 standardized chart, ncontrol char
29、t that monitors a standardized statistic.3.1.24.1 DiscussionA standardized statistic is equal to the statistic minus its mean and divided by its standard error.3.1.25 state of statistical control, nprocess condition when only common causes are operating on the process.3.1.25.1 DiscussionIn the stric
30、t sense, a process being in a state of statistical control implies that successive values of the characteristic have thestatistical character of a sequence of observations drawn independently from a common distribution.3.1.26 statistical process control (SPC), nset of techniques for improving the qu
31、ality of process output by reducing variabilitythrough the use of one or more control charts and a corrective action strategy used to bring the process back into a state of statisticalcontrol.3.1.27 subgroup, nset of observations on outputs sampled from a process at a particular time.3.1.28 u chart,
32、 ncontrol chart that monitors the count of occurrences of an event in variable intervals of time or space, oranother continuum.3.1.29 upper control limit (UCL), nmaximum value of the control chart statistic that indicates statistical control.3.1.30 variables data, nobservations or test results defin
33、ed on a continuous scale.3.1.31 warning limits, nlimits on a control chart that are two standard errors below and above the centerline.3.1.32 X-bar chart, ncontrol chart that monitors the average of observations within a subgroup.3.2 Definitions of Terms Specific to This Standard:3.2.1 average count
34、 c!, narithmetic average of subgroup counts.3.2.2 average moving range MR!, narithmetic average of subgroup moving ranges.3.2.3 average proportion p!, narithmetic average of subgroup proportions.3.2.4 average range R!, narithmetic average of subgroup ranges.3.2.5 average standard deviation s!, narit
35、hmetic average of subgroup sample standard deviations.3.2.6 grand average (X5), naverage of subgroup averages.3.2.7 inspection interval, na subgroup size for counts of events in a defined interval of time space or another continuum.3.2.7.1 DiscussionExamples are 10 000 metres of wire inspected for i
36、nsulation defects, 100 square feet of material surface inspected for blemishes,the number of minor injuries per month, or scratches on bearing race surfaces.3.2.8 moving range (MR), nabsolute difference between two adjacent subgroup observations in an I chart.3.2.9 observation, na single value of a
37、process output for charting purposes.3.2.9.1 DiscussionThis term has a different meaning than the term defined in Terminology E456, which refers there to a component of a test result.3.2.10 overall proportion, naverage subgroup proportion calculated by dividing the total number of events by the tota
38、l numberof objects inspected (see average proportion).3.2.10.1 DiscussionE2587 143This calculation may be used for fixed or variable sample sizes.3.2.11 process, nset of interrelated or interacting activities that convert input into outputs.3.2.12 subgroup average (XXii), naverage for the ithth subg
39、roup in an X-bar chart.3.2.13 subgroup count (ci), ncount for the ithth subgroup in a c chart.3.2.14 subgroup EWMA (Zi), nvalue of the EWMA for the ith subgroup in an EWMA chart.3.2.15 subgroup EWMV (Vi), nvalue of the EWMV for the ith subgroup in an EWMV chart.3.2.16 subgroup individual observation
40、 (XXii), nvalue of the single observation for the ithth subgroup in an I chart.3.2.17 subgroup moving range (MRi), nmoving range for the ithth subgroup in an MR chart.3.2.17.1 DiscussionIf there are k subgroups, there will be k-1 moving ranges.3.2.18 subgroup proportion ( p(pi), nproportion for the
41、ithth subgroup in a p chart.3.2.19 subgroup range (Ri), nrange of the observations for the ithth subgroup in an R chart.3.2.20 subgroup size (ni), nthe number of observations, objects inspected, or the inspection interval in the ith subgroup.3.2.20.1 DiscussionFor fixed sample sizes the symbol n is
42、used.3.2.21 subgroup standard deviation (si), nsample standard deviation of the observations for the ithth subgroup in an s chart.3.3 Symbols:A2 = Factor for converting the average range to three standard errors for the X-bar chart (Table 1)A2 = factor for converting the average range to three stand
43、ard errors for the X-bar chart (Table 1)A3 = Factor for converting the average standard deviation to three standard errors of the average for the X-bar chart (Table1)A3 = factor for converting the average standard deviation to three standard errors of the average for the X-bar chart (Table1)B3, B4 =
44、 Factors for converting the average standard deviation to three-sigma limits for the s chart (Table 1)B3, B4 = factors for converting the average standard deviation to three-sigma limits for the s chart (Table 1)ci = Counts of the observed occurrences of events in the ith subgroup (10.2.1)B5*,B6* =
45、factors for converting the initial estimate of the variance to three-sigma limits for the EWMV chart (Table 11)c = Average of the k subgroup counts (10.2.1)c4 = Factor for converting the average standard deviation to an unbiased estimate of sigma (see ) (Table 1)c4 = factor for converting the averag
46、e standard deviation to an unbiased estimate of sigma (see ) (Table 1)ci = counts of the observed occurrences of events in the ith subgroup (10.2.1)c = factor for converting the average range to an estimate of sigma (see ) (Table 1)d2 = Factor for converting the average range to an estimate of sigma
47、 (see ) (Table 1)d2 = factor for converting the average range to an estimate of sigma (see ) (Table 1)D3, D4 = Factors for converting the average range to three-sigma limits for the R chart (Table 1)D3, D4 = factors for converting the average range to three-sigma limits for the R chart (Table 1)Di2
48、= the squared deviation of the observation at time i minus its forecast average (12.1)k = Number of subgroups used in calculation of control limits (6.2.1)TABLE 1 Control Chart FactorsforX-Bar andRCharts forX-Bar andSChartsn A2 D3 D4 d2 A3 B3 B4 c42 1.880 0 3.267 1.128 2.659 0 3.267 0.79793 1.023 0
49、2.575 1.693 1.954 0 2.568 0.88624 0.729 0 2.282 2.059 1.628 0 2.266 0.92135 0.577 0 2.114 2.326 1.427 0 2.089 0.94006 0.483 0 2.004 2.534 1.287 0.030 1.970 0.95157 0.419 0.076 1.924 2.704 1.182 0.118 1.882 0.95948 0.373 0.136 1.864 2.847 1.099 0.185 1.815 0.96509 0.337 0.184 1.816 2.970 1.032 0.239 1.761 0.969310 0.308 0.223 1.777 3.078 0.975 0.284 1.716 0.9727Note: for larger numbers of n, see Ref. (1).E2587 144k = number of subgroups used in calculation of control limits (6.2.1)MRi =
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