1、Designation: E2281 15 An American National StandardStandard Practice forProcess Capability and Performance Measurement1This standard is issued under the fixed designation E2281; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the y
2、ear 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 determining processcapability and performance under several common scenario
3、s ofuse including: (a) normal distribution based capability andperformance indices such as Cp, Cpk, Pp, and Ppk;(b) processcapability using attribute data for non-conforming units andnon-conformities per unit type variables, and (c) additionalmethods in working with process capability or performance
4、.2. Referenced Documents2.1 ASTM Standards:2E456 Terminology Relating to Quality and StatisticsE2334 Practice for Setting an Upper Confidence Bound Fora Fraction or Number of Non-Conforming items, or a Rateof Occurrence for Non-conformities, Using AttributeData, When There is a Zero Response in the
5、Sample2.2 Other Document:MNL 7 Manual on Presentation of Data and Control ChartAnalysis33. Terminology3.1 DefinitionsUnless otherwise noted, all statisticalterms are defined in Terminology E456.3.1.1 long term standard deviation, LT,nsample standarddeviation of all individual (observed) values taken
6、 over a longperiod of time.3.1.1.1 DiscussionA long period of time may be definedas shifts, weeks, or months, etc.3.1.2 process capability, PC, nstatistical estimate of theoutcome of a characteristic from a process that has beendemonstrated to be in a state of statistical control.3.1.3 process capab
7、ility index, Cp,nan index describingprocess capability in relation to specified tolerance.3.1.4 process performance, PP, nstatistical measure of theoutcome of a characteristic from a process that may not havebeen demonstrated to be in a state of statistical control.3.1.5 process performance index, P
8、p,nindex describingprocess performance in relation to specified tolerance.3.1.6 short term standard deviation, ST,nthe inherentvariation present when a process is operating in a state ofstatistical control, expressed in terms of standard deviation.3.1.6.1 DiscussionThis may also be stated as the inh
9、erentprocess variation.3.1.7 stable process, nprocess in a state of statisticalcontrol; process condition when all special causes of variationhave been removed.3.1.7.1 DiscussionObserved variation can then be attrib-uted to random (common) causes. Such a process will gener-ally behave as though the
10、results are simple random samplesfrom the same population.3.1.7.2 DiscussionThis state does not imply that therandom variation is large or small, within or outside ofspecification, but rather that the variation is predictable usingstatistical techniques.3.1.7.3 DiscussionThe process capability of a
11、stable pro-cess is usually improved by fundamental changes that reduceor remove some of the random causes present or adjusting themean towards the preferred value, or both.3.1.7.4 DiscussionContinual adjustment of a stable pro-cess will increase variation.3.2 Definitions of Terms Specific to This St
12、andard:3.2.1 lower process capability index, Cpkl,nindex describ-ing process capability in relation to the lower specificationlimit.3.2.2 lower process performance index, Ppkl,nindex de-scribing process performance in relation to the lower specifi-cation limit.3.2.3 minimum process capability index,
13、 Cpk,nsmaller ofthe upper process capability index and the lower processcapability index.3.2.4 minimum process performance index, Ppk,nsmallerof the upper process performance index and the lower processperformance index.1This practice is under the jurisdiction ofASTM Committee E11 on Quality andStat
14、istics and is the direct responsibility of Subcommittee E11.30 on StatisticalQuality Control.Current edition approved Oct. 1, 2015. Published October 2015. Originallyapproved in 2003. Last previous edition approved in 2012 as E2281 08a (2012)1.DOI: 10.1520/E2281-15.2For referenced ASTM standards, vi
15、sit 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.3Available from ASTM Headquarters, 100 Barr Harbor Drive, W.Conshohocken, PA 19428.Copyright AS
16、TM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.2.5 special cause, nvariation in a process coming fromsource(s) outside that which may be expected due to chancecauses (or random causes).3.2.5.1 DiscussionSometimes “special cause” is taken tobe
17、synonymous with “assignable cause.” However, a distinc-tion should be recognized. A special cause is assignable onlywhen it is specifically identified.Also, a common cause may beassignable.3.2.5.2 DiscussionA special cause arises because of spe-cific circumstances which are not always present.As suc
18、h, in aprocess subject to special causes, the magnitude of the varia-tion from time to time is unpredictable.3.2.6 upper process capability index, Cpku,nindex de-scribing process capability in relation to the upper specificationlimit.3.2.7 upper process performance index, Ppku,nindexdescribing proce
19、ss performance in relation to the upper speci-fication limit.4. Significance and Use4.1 Process CapabilityProcess capability can be definedas the natural or inherent behavior of a stable process that is ina state of statistical control (1).4A “state of statistical control”is achieved when the proces
20、s exhibits no detectable patterns ortrends, such that the variation seen in the data is believed to berandom and inherent to the process. Process capability is linkedto the use of control charts and the state of statistical control.Aprocess must be studied to evaluate its state of control beforeeval
21、uating process capability.4.2 Process ControlThere are many ways to implementcontrol charts, but the most popular choice is to achieve a stateof statistical control for the process under study. Special causesare identified by a set of rules based on probability theory. Theprocess is investigated whe
22、never the chart signals the occur-rence of special causes. Taking appropriate actions to eliminateidentified special causes and preventing their reappearance willultimately obtain a state of statistical control. In this state, aminimum level of variation may be reached, which is referredto as common
23、 cause or inherent variation. For the purpose ofthis standard, this variation is a measure of the uniformity ofprocess output, typically a product characteristic.4.3 Process Capability IndicesThe behavior of a process(as related to inherent variability) in the state of statisticalcontrol is used to
24、describe its capability. To compare a processwith customer requirements (or specifications), it is commonpractice to think of capability in terms of the proportion of theprocess output that is within product specifications or toler-ances. The metric of this proportion is the percentage of theprocess
25、 spread used up by the specification. This comparisonbecomes the essence of all process capability measures. Themanner in which these measures are calculated defines thedifferent types of capability indices and their use. Two processcapability indices are defined in 5.2 and 5.3. In practice, thesein
26、dices are used to drive process improvement through con-tinuous improvement efforts. These indices may be used toidentify the need for management actions required to reducecommon cause variation, compare products from differentsources, and to compare processes.4.4 Process Performance IndicesWhen a p
27、rocess is not ina state of statistical control, the process is subject to specialcause variation, which can manifest itself in various ways onthe process variability. Special causes can give rise to changesin the short-term variability of the process or can causelong-term shifts or drifts of the pro
28、cess mean. Special causescan also create transient shifts or spikes in the process mean.Even in such cases, there may be a need to assess the long-termvariability of the process against customer specifications usingprocess performance indices, which are defined in 6.2 and 6.3.These indices are simil
29、ar to those for capability indices anddiffer only in the estimate of variability used in the calculation.This estimated variability includes additional components ofvariation due to special causes. Since process performanceindices have additional components of variation, process per-formance usually
30、 has a wider spread than the process capabilityspread. These measures are useful in determining the role ofmeasurement and sampling variability when compared toproduct uniformity.4.5 Attribute capability applications occur where attributedata are being used to assess a process and may involve the us
31、eof non-conforming units or non-conformities per unit.4.6 Additional measures and methodology to process as-sessments include the index Cpm, which incorporates a targetparameter for variable data, and the calculation of RolledThroughput Yield (RTY), that measures how good a series ofprocess steps ar
32、e.5. Process Capability Analysis5.1 It is common practice to define process behavior interms of its variability. Process capability, PC, is calculated as:PC 5 6ST(1)where STis the inherent variability of a controlled process(2, 3). Since control charts can be used to achieve and verifycontrol for ma
33、ny different types of processes, the assumptionof a normal distribution is not necessary to affect control, butcomplete control is required to establish the capability of aprocess (2). Thus, what is required is a process in control withrespect to its measures of location and spread. Once this isachi
34、eved, the inherent variability of the process can be esti-mated from the control charts. The estimate obtained is anestimate of variability over a short time interval (minutes,hours, or a few batches). From control charts, STmay beestimated from the short-term variation within subgroupsdepending on
35、the type of control chart deployed, for example,average-range (X R) or individual-moving range (X MR).The estimate is:ST5Rd2orMRd2(2)where, Ris the average range, MRis the average movingrange, d2is a factor dependent on the subgroup size, n,ofthe4The boldface numbers in parentheses refer to the list
36、 of references at the end ofthis standard.E2281 152control chart (see ASTM MNL 7, Part 3). If an average-standard deviation (X s) chart is used, the estimate becomes:ST5sc4(3)where s is the arithmetic average of the sample standarddeviations, and c4is a factor dependent on the subgroup size,n, of th
37、e control chart (see ASTM MNL 7, Part 3).5.1.1 Therefore, PC is estimated by:6 ST56Rd2or6sc4(4)5.2 Process Capability Index, CP:5.2.1 The process capability index relates the process capa-bility to the customers specification tolerance. The processcapability index, Cp, is:Cp5Specification ToleranceP
38、rocess Capability5USL 2 LSL6ST(5)where USL = upper specification limit and LSL = lowerspecification limit. For a process that is centered with anunderlying normal distribution, Fig. 1, Fig. 2, and Fig. 3denotes three cases where PC, the process capability, is widerthan (Fig. 1), equal to (Fig. 2), a
39、nd narrower than (Fig. 3) thespecification tolerance.5.2.2 Since the tail area of the distribution beyond specifi-cation limits measures the proportion of product defectives, alarger value of Cpis better. The relationship between Cpandthe percent defective product produced by a centered process(with
40、 a normal distribution) is:CpPercentDefectiveParts perMillionCpPercentDefectiveParts perMillion0.6 7.19 71900 1.1 0.0967 9670.7 3.57 35700 1.2 0.0320 3180.8 1.64 16400 1.3 0.0096 960.9 0.69 6900 1.33 0.00636 641.0 0.27 2700 1.67 0.00006 0.575.2.3 From these examples, one can see that any processwith
41、 a Cp1. Some industriesconsider Cp= 1.33 (an 8STspecification tolerance) a mini-mum with a Cp= 1.66 preferred (4). Improvement of Cpshoulddepend on a companys quality focus, marketing plan, and theircompetitors achievements, etc.5.3 Process Capability Indices Adjusted For Process Shift,Cpk:5.3.1 The
42、 above examples depict process capability for aprocess centered within its specification tolerance. Processcentering is not a requirement since process capability isindependent of any specifications that may be applied to it. Theamount of shift present in a process depends on how far theprocess aver
43、age is from the center of the specification spread.In the last part of the above example (Cp 1), suppose that theprocess is actually centered above the USL. The Cphas a value1, but clearly this process is not producing as much conform-ing product as it would have if it were centered on target.5.3.2
44、For those cases where the process is not centered,deliberately run off-center for economic reasons, or only asingle specification limit is involved, Cpis not the appropriateprocess capability index. For these situations, the Cpkindex isused. Cpkis a process capability index that considers theprocess
45、 average against a single or double-sided specificationlimit. It measures whether the process is capable of meeting thecustomers requirements by considering:5.3.2.1 The specification limit(s),5.3.2.2 The current process average, and5.3.2.3 The current ST.5.3.3 Under the assumption of normality,5Cpki
46、s calculatedas:Cpk5 minCpku, Cpkl# (6)and is estimated by:Cpk5 min Cpku, Cpkl# (7)where the estimated upper process capability index isdefined as:Cpku5USL 2 X3 ST(8)and the estimated lower process capability index is definedas:5Testing for the normality of a set of data may range from simply plottin
47、g thedata on a normal probability plot (2) to more formal tests, for example, Anderson-Darling test (which can be found in many statistical software programs, for example,Minitab).FIG. 1 Process Capability Wider Than Specifications, Cp1, the process is capable andperforming within the specifications
48、,5.3.5.5 If both Cpand Cpkare 1 and Cpkis 200 or a minimumof 100) are required to estimate Cpkwith a high level ofconfidence (at least 95 %).FIG. 2 Process Capability Equal to Specification Tolerance, Cp=1FIG. 3 Process Capability Narrower Than Specifications, Cp1FIG. 4 Noncentered Process, Cp 1 and
49、 Cpku) = 100(1 )%.Letz1-be a point on a standard normal distribution such P(Z z1-)=100 %. For the statistic, Pp, an exact result for the lowerconfidence bound may be given (Ref (8). The lower 100(1-)% confidence bound for process capability index Ppis:Pp$ Ppun 2 1(17)The approximate standard error for the statistic Ppis:se Pp! 5Pp=2n 2 1!(18)For the process capability index Ppk, the approximate100(1-) % lower confidence bound is:Ppk$ Ppk2 z1219 n1Ppk22n 2 2(19)The approximate standard error fo
