ASTM E2281-08a
(Practice)Standard Practice for Process and Measurement Capability Indices
Standard Practice for Process and Measurement Capability Indices
SIGNIFICANCE AND USE
Process Capability—Process capability can be defined as the natural or inherent behavior of a stable process that is in a state of statistical control (1). A “state of statistical control” is achieved when the process exhibits no detectable patterns or trends, such that the variation seen in the data is believed to be random and inherent to the process. Process capability is linked to the use of control charts and the state of statistical control. A process must be studied to evaluate its state of control before evaluating process capability.
Process Control—There are many ways to implement control charts, but the most popular choice is to achieve a state of statistical control for the process under study. Special causes are identified by a set of rules based on probability theory. The process is investigated whenever the chart signals the occurrence of special causes. Taking appropriate actions to eliminate identified special causes and preventing their reappearance will ultimately obtain a state of statistical control. In this state, a minimum level of variation may be reached, which is referred to as common cause or inherent variation. For the purpose of this standard, this variation is a measure of the uniformity of process output, typically a product characteristic.
Process Capability Indices—The behavior of a process (as related to inherent variability) in the state of statistical control is used to describe its capability. To compare a process with customer requirements (or specifications), it is common practice to think of capability in terms of the proportion of the process output that is within product specifications or tolerances. The metric of this proportion is the percentage of the process spread used up by the specification. This comparison becomes the essence of all process capability measures. The manner in which these measures are calculated defines the different types of capability indices and their use. Two process capability indices are defi...
SCOPE
1.1 This practice provides guidance for the use of capability indices for evaluating process capability and performance. Process capability indices compare the variability of a process quality measure against product specifications or tolerances and assume the process is in a state of statistical control. Process performance indices are useful in situations when the process is not in a state of statistical control.
General Information
Relations
Buy Standard
Standards Content (Sample)
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E2281 − 08a AnAmerican National Standard
Standard Practice for
1
Process and Measurement Capability Indices
This standard is issued under the fixed designation E2281; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 3.2.2.1 Discussion—A long period of time may be defined
as shifts, weeks, or months, etc.
1.1 Thispracticeprovidesguidancefortheuseofcapability
indices for evaluating process capability and performance. 3.2.3 lower process capability index, C ,n—indexdescrib-
pkl
Process capability indices compare the variability of a process
ing process capability in relation to the lower specification
quality measure against product specifications or tolerances limit.
and assume the process is in a state of statistical control.
3.2.4 lower process performance index, P ,n—index de-
pkl
Process performance indices are useful in situations when the
scribing process performance in relation to the lower specifi-
process is not in a state of statistical control.
cation limit.
3.2.5 minimum process capability index, C ,n—smaller of
2. Referenced Documents pk
the upper process capability index and the lower process
2
2.1 ASTM Standards:
capability index.
E456Terminology Relating to Quality and Statistics
3.2.6 minimum process performance index, P ,n—smaller
E2586Practice for Calculating and Using Basic Statistics pk
of the upper process performance index and the lower process
2.2 ISO Standard:
performance index.
ISO 3534-2Statistics—Vocabulary and Symbols-Statistical
3
3.2.7 process capability, PC, n—statistical estimate of the
Quality Control
outcome of a characteristic from a process that has been
2.3 Other Document:
demonstrated to be in a state of statistical control.
MNL 7Manual on Presentation of Data and Control Chart
4
Analysis 3.2.8 process capability index, C,n—an index describing
p
process capability in relation to specified tolerance.
3. Terminology
3.2.9 process performance, PP, n—statisticalmeasureofthe
3.1 Definitions—Unlessotherwisenoted,allstatisticalterms
outcome of a characteristic from a process that may not have
are defined in Terminology E456.
been demonstrated to be in a state of statistical control.
3.2 Definitions of Terms Specific to This Standard:
3.2.10 process performance index, P,n—index describing
p
3.2.1 average standard deviation, s¯, n—arithmetic average
process performance in relation to specified tolerance.
of sample standard deviations.
3.2.11 range, R, n—maximum value minus the minimum
3.2.2 long term standard deviation,σ ,n—samplestandard
LT value in a sample. E2586
deviation of all individual (observed) values taken over a long
3.2.12 short term standard deviation, σ ,n—the inherent
ST
period of time.
variation present when a process is operating in a state of
statistical control, expressed in terms of standard deviation.
3.2.12.1 Discussion—This may also be stated as the inher-
1
ThispracticeisunderthejurisdictionofASTMCommitteeE11onQualityand
ent process variation.
Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical
Quality Control.
3.2.13 special cause, n—sourceofintermittentvariationina
Current edition approved Oct. 1, 2008. Published October 2008. Originally
process. ISO 3534-2
approved in 2003. Last previous edition approved in 2008 as E2281–08. DOI:
10.1520/E2281-08A.
3.2.13.1 Discussion—Sometimes“specialcause”istakento
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
besynonymouswith“assignablecause.”Howeveradistinction
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
should be recognized.Aspecial cause is assignable only when
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. it is specifically identified. Also a common cause may be
3
Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
assignable.
4th Floor, New York, NY 10036, http://www.ansi.org.
4
3.2.13.2 Discussion—A special cause arises because of
Available from ASTM Headquarters, 100 Barr Harbor Drive, W.
Conshohocken, PA 19428. specific circumstances which are not always present.As such,
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1
---------------------- Page: 1 ----------------------
E2281 − 08a
in a process subject to special causes, the magnitude of the ances. The metric of this proportion is the percentage of the
variation from time to time is unpredictable. process spread used up by the specification. This comparison
becomes the essence of all process capability measures
...
This document is not anASTM standard and is intended only to provide the user of anASTM standard an indication of what changes have been made to the previous version. Because
it 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 version
of the standard as published by ASTM is to be considered the official document.
Designation:E2281–08 Designation: E 2281 – 08a
Standard Practice for
1
Process and Measurement Capability Indices
This standard is issued under the fixed designation E2281; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 Thispracticeprovidesguidancefortheuseofcapabilityindicesforevaluatingprocesscapabilityandperformance.Process
capabilityindicescomparethevariabilityofaprocessqualitymeasureagainstproductspecificationsortolerancesandassumethe
process is in a state of statistical control. Process performance indices are useful in situations when the process is not in a state
of statistical control.
2. Referenced Documents
2
2.1 ASTM Standards:
E456 Terminology Relating to Quality and Statistics Terminology Relating to Quality and Statistics
E2586 Practice for Calculating and Using Basic Statistics
2.2 ISO Standard:
3
ISO 3534-2 Statistics—Vocabulary and Symbols-Statistical Quality Control
2.3 Other Document:
4
MNL 7 Manual on Presentation of Data and Control Chart Analysis
3. Terminology
3.1 Definitions—Unless otherwise noted, all statistical terms are defined in Terminology E456.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 average standard deviation, s¯, n—arithmetic average of sample standard deviations.
3.2.2 long term standard deviation, s , n—sample standard deviation of all individual (observed) values taken over a long
LT
period of time.
3.2.2.1 Discussion—A long period of time may be defined as shifts, weeks, or months, etc.
3.2.3 lower process capability index, C , n—index describing process capability in relation to the lower specification limit.
pkl
3.2.4 lower process performance index, P , n—index describing process performance in relation to the lower specification
pkl
limit.
3.2.5 minimum process capability index, C , n—smalleroftheupperprocesscapabilityindexandthelowerprocesscapability
pk
index.
3.2.6 minimum process performance index, P , n—smaller of the upper process performance index and the lower process
pk
performance index.
3.2.7 process capability, PC, n—statisticalestimateoftheoutcomeofacharacteristicfromaprocessthathasbeendemonstrated
to be in a state of statistical control.
3.2.8 process capability index, C , n—an index describing process capability in relation to specified tolerance.
p
3.2.9 process performance, PP, n—statisticalmeasureoftheoutcomeofacharacteristicfromaprocessthatmaynothavebeen
demonstrated to be in a state of statistical control.
3.2.10 process performance index, P , n—index describing process performance in relation to specified tolerance.
p
3.2.11 range, R, n—thelargestobservationminusthesmallestobservationinasetofvaluesorobservations.—maximumvalue
minus the minimum value in a sample. E 2586
1
This practice is under the jurisdiction ofASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical Quality
Control.
Current edition approved AprilOct. 1, 2008. Published JuneOctober 2008. Originally approved in 2003. Last previous edition approved in 20032008 as
e1
E2281–03 .E2281–08.
2
ForreferencedASTMstandards,visittheASTMwebsite,www.astm.org,orcontactASTMCustomerServiceatservice@astm.org.For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
3
Available from American National Standards Institute, 11 W. 42nd St., 13th Floor, New York, NY 10036.
3
Available from American National Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036, http://www.ansi.org.
4
Available from ASTM Headquarters, 100 Barr Harbor Drive, W. Conshohocken, PA 19428.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
1
---------------------- Page: 1 ----------------------
E 2281 – 08a
3.2.12 short term standard deviation, s , n—the inherent variation present when a process is operating in a state of statistical
ST
control, expressed in terms of standard deviation.
3.2.12.1 Discussion—This may also be stated as the inherent process variation.
3.2.13 special cause, n—source of intermittent variation in a process. ISO 3534-2
3.2.13.1 Discussion—Sometimes “special cause” is taken to be synonymous with “assignable cause.” However a distinction
shouldberecognized.Aspecialcauseisassignableonlywhenitissp
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.