1、Designation: E2587 16 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 revision,
2、 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 controlcharts in statistical process control programs, whi
3、ch improveprocess quality through reducing variation by identifying andeliminating the effect of special causes of variation.1.2 Control charts are used to continually monitor productor process characteristics to determine whether or not a processis in a state of statistical control. When this state
4、 is attained, theprocess characteristic will, at least approximately, vary withincertain limits at a given probability.1.3 This practice applies to variables data (characteristicsmeasured on a continuous numerical scale) and to attributesdata (characteristics measured as percentages, fractions, orco
5、unts 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 asillustrations of calculation methods. The examples are notbinding on products or test methods treated.1.5 This standard d
6、oes not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM St
7、andards:2E177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE456 Terminology Relating to Quality and StatisticsE1994 Practice for Use of Process Oriented AOQL andLTPD Sampling PlansE2234 Practice for Sampling a Stream of Product by Attri-butes Indexed by AQLE2281 Practice for P
8、rocess Capability and PerformanceMeasurementE2762 Practice for Sampling a Stream of Product by Vari-ables Indexed by AQL3. Terminology3.1 Definitions:3.1.1 See Terminology E456 for a more extensive listing ofstatistical terms.3.1.2 assignable cause, nfactor that contributes to varia-tion in a proces
9、s or product output that is feasible to detect andidentify (see special cause).3.1.2.1 DiscussionMany factors will contribute tovariation, but it may not be feasible (economically or other-wise) to identify some of them.3.1.3 accepted reference value, ARV, nvalue that serves asan agreed-upon referen
10、ce for comparison and is derived as: (1)a theoretical or established value based on scientific principles,(2) an assigned or certified value based on experimental workof some national or international organization, or (3) a consen-sus or certified value based on collaborative experimental workunder
11、the auspices of a scientific or engineering group. E1773.1.4 attributes data, nobserved values or test results thatindicate the presence or absence of specific characteristics orcounts of occurrences of events in time or space.3.1.5 average run length (ARL), nthe average number oftimes that a proces
12、s will have been sampled and evaluatedbefore a shift in process level is signaled.3.1.5.1 DiscussionA long ARL is desirable for a processlocated at its specified level (so as to minimize calling forunneeded investigation or corrective action) and a shortARL isdesirable for a process shifted to some
13、undesirable level (sothat corrective action will be called for promptly). ARL curvesare used to describe the relative quickness in detecting levelshifts of various control chart systems (see 5.1.4). The averagenumber of units that will have been produced before a shift inlevel is signaled may also b
14、e of interest from an economicstandpoint.3.1.6 c chart, ncontrol chart that monitors the count ofoccurrences of an event in a defined increment of time orspace.3.1.7 center line, nline on a control chart depicting theaverage level of the statistic being monitored.1This practice is under the jurisdic
15、tion of ASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.30 on StatisticalQuality Control.Current edition approved April 1, 2016. Published May 2016. Originallyapproved in 2007. Last previous edition approved in 2015 as E2587 15. DOI:10.1520/E2587-16.2
16、For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C7
17、00, West Conshohocken, PA 19428-2959. United States13.1.8 chance cause, nsource of inherent random variationin a process which is predictable within statistical limits (seecommon cause).3.1.8.1 DiscussionChance causes may be unidentifiable,or may have known origins that are not easily controllable o
18、rcost effective to eliminate.3.1.9 common cause, n(see chance cause).3.1.10 control chart, nchart on which are plotted a statis-tical measure of a subgroup versus time of sampling along withlimits based on the statistical distribution of that measure so asto indicate how much common, or chance, caus
19、e variation isinherent in the process or product.3.1.11 control chart factor, na tabulated constant, depend-ing on sample size, used to convert specified statistics orparameters into a central line value or control limit appropriateto the control chart.3.1.12 control limits, nlimits on a control cha
20、rt that areused as criteria for signaling the need for action or judgingwhether a set of data does or does not indicate a state ofstatistical control based on a prescribed degree of risk.3.1.12.1 DiscussionFor example, typical three-sigma lim-its carry a risk of 0.135 % of being out of control (on o
21、ne sideof the center line) when the process is actually in control andthe statistic has a normal distribution.3.1.13 EWMA chart, ncontrol chart that monitors theexponentially weighted moving averages of consecutive sub-groups.3.1.14 EWMV chart, ncontrol chart that monitors theexponentially weighted
22、moving variance.3.1.15 exponentially weighted moving average (EWMA),nweighted average of time ordered data where the weights ofpast observations decrease geometrically with age.3.1.15.1 DiscussionData used for the EWMA may consistof individual observations, averages, fractions, numbersdefective, or
23、counts.3.1.16 exponentially weighted moving variance (EWMV),nweighted average of squared deviations of observationsfrom their current estimate of the process average for timeordered observations, where the weights of past squareddeviations decrease geometrically with age.3.1.16.1 DiscussionThe estim
24、ate of the process averageused for the current deviation comes from a coupled EWMAchart monitoring the same process characteristic. This estimateis the EWMA from the previous time period, which is theforecast of the process average for the current time period.3.1.17 I chart, ncontrol chart that moni
25、tors the individualsubgroup observations.3.1.18 lower control limit (LCL), nminimum value of thecontrol chart statistic that indicates statistical control.3.1.19 MR chart, ncontrol chart that monitors the movingrange of consecutive individual subgroup observations.3.1.20 p chart, ncontrol chart that
26、 monitors the fraction ofoccurrences of an event.3.1.21 R chart, ncontrol chart that monitors the range ofobservations within a subgroup.3.1.22 rational subgroup, nsubgroup chosen to minimizethe variability within subgroups and maximize the variabilitybetween subgroups (see subgroup).3.1.22.1 Discus
27、sionVariation within the subgroup is as-sumed to be due only to common, or chance, cause variation,that is, the variation is believed to be homogeneous. If using arange or standard deviation chart, this chart should be instatistical control. This implies that any assignable, or special,cause variati
28、on will show up as differences between thesubgroups on a corresponding Xchart.3.1.23 s chart, ncontrol chart that monitors the standarddeviations of subgroup observations.3.1.24 special cause, n(see assignable cause).3.1.25 standardized chart, ncontrol chart that monitors astandardized statistic.3.1
29、.25.1 DiscussionA standardized statistic is equal to thestatistic minus its mean and divided by its standard error.3.1.26 state of statistical control, nprocess conditionwhen only common causes are operating on the process.3.1.26.1 DiscussionIn the strict sense, a process being ina state of statisti
30、cal control implies that successive values of thecharacteristic have the statistical character of a sequence ofobservations drawn independently from a common distribu-tion.3.1.27 statistical process control (SPC), nset of tech-niques for improving the quality of process output by reducingvariability
31、 through the use of one or more control charts and acorrective action strategy used to bring the process back into astate of statistical control.3.1.28 subgroup, nset of observations on outputs sampledfrom a process at a particular time.3.1.29 u chart, ncontrol chart that monitors the count ofoccurr
32、ences of an event in variable intervals of time or space,or another continuum.3.1.30 upper control limit (UCL), nmaximum value of thecontrol chart statistic that indicates statistical control.3.1.31 variables data, nobservations or test results de-fined on a continuous scale.3.1.32 warning limits, n
33、limits on a control chart that aretwo standard errors below and above the centerline.3.1.33 X-bar chart, ncontrol chart that monitors the aver-age of observations within a subgroup.3.2 Definitions of Terms Specific to This Standard:3.2.1 allowance value, K, namount of process shift to bedetected.3.2
34、.2 allowance multiplier, k, nmultiplier of standarddeviation that defines the allowance value, K.3.2.3 average count c!,narithmetic average of subgroupcounts.3.2.4 average moving range MR!,narithmetic average ofsubgroup moving ranges.3.2.5 average proportion p!,narithmetic average of sub-group propo
35、rtions.E2587 1623.2.6 average range R!,narithmetic average of subgroupranges.3.2.7 average standard deviation s!,narithmetic averageof subgroup sample standard deviations.3.2.8 cumulative sum, CUSUM, ncumulative sum of de-viations from the target value for time-ordered data.3.2.8.1 DiscussionData us
36、ed for the CUSUM may consistof individual observations, subgroup averages, fractionsdefective, numbers defective, or counts.3.2.9 CUSUM chart, ncontrol chart that monitors thecumulative sum of consecutive subgroups.3.2.10 decision interval, H, nthe distance between thecenter line and the control lim
37、its.3.2.11 decision interval multiplier, h, nmultiplier of stan-dard deviation that defines the decision interval, H.3.2.12 grand average (X5), naverage of subgroup averages.3.2.13 inspection interval, na subgroup size for counts ofevents in a defined interval of time space or another continuum.3.2.
38、13.1 DiscussionExamples are 10 000 metres of wireinspected for insulation defects, 100 square feet of materialsurface inspected for blemishes, the number of minor injuriesper month, or scratches on bearing race surfaces.3.2.14 moving range (MR), nabsolute difference betweentwo adjacent subgroup obse
39、rvations in an I chart.3.2.15 observation, na single value of a process output forcharting purposes.3.2.15.1 DiscussionThis term has a different meaningthan the term defined in Terminology E456, which refers thereto a component of a test result.3.2.16 overall proportion, naverage subgroup proportion
40、calculated by dividing the total number of events by the totalnumber of objects inspected (see average proportion).3.2.16.1 DiscussionThis calculation may be used for fixedor variable sample sizes.3.2.17 process, nset of interrelated or interacting activitiesthat convert input into outputs.3.2.18 pr
41、ocess target value, T, ntarget value for theobserved process mean.3.2.19 relative size of process shift, ,nsize of processshift to detect in standard deviation units.3.2.20 subgroup average (Xi), naverage for the ith sub-group in an X-bar chart.3.2.21 subgroup count (ci), ncount for the ith subgroup
42、 ina c chart.3.2.22 subgroup EWMA (Zi), nvalue of the EWMAfor theith subgroup in an EWMA chart.3.2.23 subgroup EWMV (Vi), nvalue of the EWMV for theith subgroup in an EWMV chart.3.2.24 subgroup individual observation (Xi), nvalue of thesingle observation for the ith subgroup in an I chart.3.2.25 sub
43、group moving range (MRi), nmoving range forthe ith subgroup in an MR chart.3.2.25.1 DiscussionIf there are k subgroups, there will bek-1 moving ranges.3.2.26 subgroup proportion (pi), nproportion for the ithsubgroup in a p chart.3.2.27 subgroup range (Ri), nrange of the observations forthe ith subgr
44、oup in an R chart.3.2.28 subgroup size (ni), nthe number of observations,objects inspected, or the inspection interval in the ith subgroup.3.2.28.1 DiscussionFor fixed sample sizes the symbol n isused.3.2.29 subgroup standard deviation (si), nsample standarddeviation of the observations for the ith
45、subgroup in an s chart.3.3 Symbols:A2= factor for converting the average range to threestandard errors for the X-bar chart (Table 1)A3= factor for converting the average standard devia-tion to three standard errors of the average for theX-bar chart (Table 1)B3,B4= factors for converting the average
46、standard devia-tion to three-sigma limits for the s chart (Table 1)B5*,B6*= factors for converting the initial estimate of thevariance to three-sigma limits for the EWMV chart(Table 11)C0= cumulative sum (CUSUM) at time zero (12.2.2)c4= factor for converting the average standard devia-tion to an unb
47、iased estimate of sigma (see )(Table 1)TABLE 1 Control Chart Factorsfor X-Bar and RCharts for X-Bar and S ChartsnA2D3D4d2A3B3B4c42 1.880 0 3.267 1.128 2.659 0 3.267 0.79793 1.023 0 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
48、.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).AAThe boldfa
49、ce numbers in parentheses refer to a list of references at the end of this standard.E2587 163ci= counts of the observed occurrences of events in theith subgroup (10.2.1)Ci= cumulative sum (CUSUM) at time, i (12.1)c = average of the k subgroup counts (10.2.1)d2= factor for converting the average range to anestimate of sigma (see )(Table 1)D3,D4= factors for converting the average range to three-sigma limits for the R chart (Table 1)Di2= the squared deviation of the observation at time imin
