1、Designation: E2587 10Standard 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, the year of last revision. A
2、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, which improveprocess quality thro
3、ugh 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 is attained, theprocess chara
4、cteristic 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, orcounts of occurrences in a defin
5、ed 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 does not purport to address all
6、 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 Standards:2E456 Terminology Rela
7、ting to Quality and StatisticsE1994 Practice for Use of Process Oriented AOQL andLTPD Sampling PlansE2234 Practice for Sampling a Stream of Product byAttributes Indexed by AQLE2281 Practice for Process and Measurement CapabilityIndices3. Terminology3.1 DefinitionsSee Terminology E456 for a more exte
8、n-sive listing of statistical terms.3.1.1 assignable cause, nfactor that contributes to varia-tion in a process or product output that is feasible to detect andidentify (see special cause).3.1.1.1 DiscussionMany factors will contribute to varia-tion, but it may not be feasible (economically or other
9、wise) toidentify some of them.3.1.2 attributes data, nobserved values or test results thatindicate the presence or absence of specific characteristics orcounts of occurrences of events in time or space.3.1.3 average run length (ARL), nthe average number oftimes that a process will have been sampled
10、and evaluatedbefore a shift in process level is signaled.3.1.3.1 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 undesirable level (sothat
11、 corrective action will be called for promptly). ARL curvesare used to describe the relative quickness in detecting levelshifts of various control chart systems (see section 5.4). Theaverage number of units that will have been produced before ashift in level is signaled may also be of interest from
12、aneconomic standpoint.3.1.4 c chart, ncontrol chart that monitors the count ofoccurrences of an event in a defined increment of time or space3.1.5 center line, nline on a control chart depicting theaverage level of the statistic being monitored.3.1.6 chance cause, nsource of inherent random variatio
13、nin a process which is predictable within statistical limits (seecommon cause).3.1.6.1 DiscussionChance causes may be unidentifiable,or may have known origins that are not easily controllable orcost effective to eliminate.3.1.7 common cause, n(see chance cause).3.1.8 control chart, nchart on which a
14、re 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, cause variation isinherent in the process or product.1This practice is under the jurisdiction of ASTM Committee
15、E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.30 on StatisticalQuality Control.Current edition approved Oct. 1, 2010. Published November 2010. Originallyapproved in 2007. last previous edition approved in 2007 as E2587071. DOI:10.1520/E2587-10.2For referenced ASTM
16、 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.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohoc
17、ken, PA 19428-2959, United States.3.1.9 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.3.1.10 control limits, nlimits on a control chart that areused
18、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.3.1.10.1 DiscussionFor example, typical three-sigma lim-its carry a risk of 0.135 % of being out of control (on one sideof the ce
19、nter line) when the process is actually in control andthe statistic has a normal distribution.3.1.11 EWMA chart, ncontrol chart that monitors theexponentially weighted moving averages of consecutive sub-groups.3.1.12 exponentially weighted moving average (EWMA),nweighted average of time ordered data
20、 where the weights ofpast observations decrease geometrically with age.3.1.12.1 DiscussionData used for the EWMAmay consistof individual observations, averages, fractions, numbers defec-tive, or counts.3.1.13 I chart, ncontrol chart that monitors the individualsubgroup observations.3.1.14 lower cont
21、rol limit (LCL), nminimum value of thecontrol chart statistic that indicates statistical control.3.1.15 MR chart, ncontrol chart that monitors the movingrange of consecutive individual subgroup observations.3.1.16 p chart, ncontrol chart that monitors the fraction ofoccurrences of an event.3.1.17 R
22、chart, ncontrol chart that monitors the range ofobservations within a subgroup.3.1.18 rational subgroup, nsubgroup chosen to minimizethe variability within subgroups and maximize the variabilitybetween subgroups (see subgroup).3.1.18.1 DiscussionVariation within the subgroup is as-sumed to be due on
23、ly 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 variation will show up as differences between thesubgroups on a c
24、orresponding X chart.3.1.19 s chart, ncontrol chart that monitors the standarddeviations of subgroup observations.3.1.20 special cause, n(see assignable cause).3.1.21 state of statistical control, nprocess conditionwhen only common causes are operating on the process.3.1.21.1 DiscussionIn the strict
25、 sense, a process being ina state of statistical control implies that successive values of thecharacteristic have the statistical character of a sequence ofobservations drawn independently from a common distribu-tion.3.1.22 statistical process control (SPC), nset of tech-niques for improving the qua
26、lity of process output by reducingvariability through the use of one or more control charts and acorrective action strategy used to bring the process back into astate of statistical control.3.1.23 subgroup, nset of observations on outputs sampledfrom a process at a particular time.3.1.24 upper contr
27、ol limit (UCL), nmaximum value of thecontrol chart statistic that indicates statistical control.3.1.25 variables data, nobservations or test results de-fined on a continuous scale.3.1.26 warning limits, nlimits on a control chart that aretwo standard errors below and above the centerline.3.1.27 X-ba
28、r chart, ncontrol chart that monitors theaverage of observations within a subgroup.3.2 Definitions of Terms Specific to This Standard:3.2.1 average count ( c ), narithmetic average of sub-group counts.3.2.2 average moving range ( MR ), narithmetic averageof subgroup moving ranges.3.2.3 average propo
29、rtion ( p ), narithmetic average ofsubgroup proportions.3.2.4 average range ( R ), narithmetic average of sub-group ranges.3.2.5 average standard deviation ( s ), narithmetic aver-age of subgroup sample standard deviations.3.2.6 grand average (X5), naverage of subgroup averages.3.2.7 moving range (M
30、R), nabsolute difference betweentwo adjacent subgroup observations in an I chart.3.2.8 observation, na single value of a process output forcharting purposes.3.2.8.1 DiscussionThis term has a different meaning thanthe term defined in Terminology E456, which refers there to acomponent of a test result
31、.3.2.9 process, nset of interrelated or interacting activitiesthat convert input into outputs.3.2.10 subgroup average (Xi), naverage for the ithsub-group in an X-bar chart.3.2.11 subgroup count (ci), ncount for the ithsubgroup ina c chart.3.2.12 subgroup individual observation (Xi), nvalue ofthe sin
32、gle observation for the ithsubgroup in an I chart.3.2.13 subgroup moving range (MRi), nmoving range forthe ithsubgroup in an MR chart.3.2.13.1 DiscussionIf there are k subgroups, there will bek-1 moving ranges.3.2.14 subgroup proportion ( pi), nproportion for the ithsubgroup in a p chart.3.2.15 subg
33、roup range (Ri), nrange of the observationsfor the ithsubgroup in an R chart.3.2.16 subgroup standard deviation (si), nsample stan-dard deviation of the observations for the ithsubgroup in an schart.E2587 1023.3 Symbols:A2= Factor for converting the average range to threestandard errors for the X-ba
34、r 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 standard de-viation to three-sigma limits for the s chart (Table1)ci= Counts of the observed occurrences of events
35、inthe ithsubgroup (10.2.1)c = Average of the k subgroup counts (10.2.1)c4= Factor for converting the average standard devia-tion to an unbiased estimate of sigma (see s)(Table 1)d2= Factor for converting the average range to anestimate of sigma (see s)(Table 1)D3,D4= Factors for converting the avera
36、ge range tothree-sigma limits for the R chart (Table 1)k = Number of subgroups used in calculation ofcontrol limits (6.2.1)MRi= Absolute value of the difference of the observa-tions in the (i-1)thand the ithsubgroups in a MRchart (8.2.1)MR = Average of the subgroup moving ranges (8.2.2.1)n = Subgrou
37、p size, number of observations in asubgroup (5.1.3)pi= Proportion of the observed occurrences of eventsin the ithsubgroup (9.2.1)p = Average of the k subgroup proportions (9.2.1)Ri= Range of the observations in the ithsubgroup forthe R chart (6.2.1.2)R = Average of the k subgroup ranges (6.2.2)si= S
38、ample standard deviation of the observations inthe ithsubgroup for the s chart (7.2.1)sz= Standard error of the EWMA statistic (11.2.1.2)s = Average of the k subgroup standard deviations(7.2.2)Xi= Single observation in the ithsubgroup for the Ichart (8.2.1)Xij= The jthobservation in the ithsubgroup
39、for theX-bar chart (6.2.1)Xi= Average of the ithsubgroup observations for theX-bar chart (6.2.1)X = Average of the individual observations over ksubgroups for the I chart (8.2.2)X5= Average of the k subgroup averages for the X-barchart (6.2.2)Yi= Value of the statistic being monitored by anEWMA char
40、t at time i (11.2.1)Zi= Exponentially-weighted average (EWMA) statis-tic at time i (11.2.1)l = Factor (0 l 1) which determines the weighingof data in the EWMA statistic (11.2.1)s= Estimated common cause standard deviation ofthe process (6.2.4)sc= Standard error of c, the number of observedcounts (10
41、.2.1.2)sp= Standard error of p, the proportion of observedoccurrences (9.2.2.4)4. Significance and Use4.1 This practice describes the use of control charts as a toolfor use in statistical process control (SPC). Control charts weredeveloped by Shewhart (1) in the 1920s and are still in wideuse today.
42、 SPC is a branch of statistical quality control (2, 3),which also encompasses process capability analysis and accep-tance sampling inspection. Process capability analysis, asdescribed in Practice E2281, requires the use of SPC in someof its procedures.Acceptance sampling inspection, described inPrac
43、tices E1994 and E2234, requires the use of SPC so as tominimize rejection.4.2 Principles of SPCAprocess may be defined as a set ofinterrelated activities that convert inputs into outputs. SPC usesvarious statistical methodologies to improve the quality of aprocess by reducing the variability of one
44、or more of itsoutputs, for example, a quality characteristic of a product orservice.4.2.1 Acertain amount of variability will exist in all processoutputs regardless of how well the process is designed ormaintained. A process operating with only this inherent vari-ability is said to be in a state of
45、statistical control, with itsoutput variability subject only to chance, or common, causes.TABLE 1 Control Chart Factorsfor X-Bar and R Charts 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
46、 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
47、: for larger numbers of n, see Ref. (11).E2587 1034.2.2 Process upsets, said to be due to assignable, or specialcauses, are manifested by changes in the output level, such asa spike, shift, trend, or by changes in the variability of anoutput. The control chart is the basic analytical tool in SPC and
48、is used to detect the occurrence of special causes operating onthe process.4.2.3 When the control chart signals the presence of aspecial cause, other SPC tools, such as flow charts, brainstorm-ing, cause-and-effect diagrams, or Pareto analysis, described invarious references (3-7), are used to ident
49、ify the special cause.Special causes, when identified, are either eliminated orcontrolled. When special cause variation is eliminated, processvariability is reduced to its inherent variability, and controlcharts then function as a process monitor. Further reduction invariation would require modification of the process itself.4.3 The use of control charts to adjust one or more processinputs is not recommended, although a control chart may signalthe need to do so. Process adjustment schemes are outside thescope of this practi
