ASTM E2281-15

Standard Practice for Process Capability and Performance Measurement

ABSTRACT
This practice provides guidance for determining process capability and performance under several common scenarios of use including: normal distribution-based capability and performance indices such as Cp, Cpk, Pp, and Ppk; process capability using attribute data for non-conforming units and non-conformities per unit type variables; and additional methods in working with process capability or performance.
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. The behavior of a process in the state of statistical control is used to describe its capability.
SIGNIFICANCE AND USE
4.1 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).4 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.  
4.2 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.  
4.3 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 i...
SCOPE
1.1 This practice provides guidance for determining process capability and performance under several common scenarios of use including: (a) normal distribution based capability and performance indices such as Cp, Cpk, Pp, and Ppk; (b) process capability using attribute data for non-conforming units and non-conformities per unit type variables, and (c) additional methods in working with process capability or performance.

General Information

• Status: Historical
• Publication Date: 30-Sep-2015
• ICS: 25.040.40 - Industrial process measurement and control
• Technical Committee: E11 - Quality and Statistics
• Drafting Committee: E11.30 - Statistical Quality Control

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 − 15 An American National Standard
Standard Practice for
1
Process Capability and Performance Measurement
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 3.1.3 process capability index, C,n—an index describing
p
process capability in relation to specified tolerance.
1.1 Thispracticeprovidesguidancefordeterminingprocess
3.1.4 process performance, PP, n—statisticalmeasureofthe
capabilityandperformanceunderseveralcommonscenariosof
use including: (a) normal distribution based capability and outcome of a characteristic from a process that may not have
been demonstrated to be in a state of statistical control.
performance indices such as C , C , P , and P ;(b) process
p pk p pk
capability using attribute data for non-conforming units and
3.1.5 process performance index, P,n—index describing
p
non-conformities per unit type variables, and (c) additional
process performance in relation to specified tolerance.
methods in working with process capability or performance.
3.1.6 short term standard deviation, σ ,n—the inherent
ST
variation present when a process is operating in a state of
2. Referenced Documents
statistical control, expressed in terms of standard deviation.
2
2.1 ASTM Standards:
3.1.6.1 Discussion—This may also be stated as the inherent
E456Terminology Relating to Quality and Statistics
process variation.
E2334Practice for Setting an Upper Confidence Bound For
3.1.7 stable process, n—process in a state of statistical
aFractionorNumberofNon-Conformingitems,oraRate
control; process condition when all special causes of variation
of Occurrence for Non-conformities, Using Attribute
have been removed.
Data, When There is a Zero Response in the Sample
3.1.7.1 Discussion—Observed variation can then be attrib-
2.2 Other Document:
uted to random (common) causes. Such a process will gener-
MNL 7Manual on Presentation of Data and Control Chart
ally behave as though the results are simple random samples
3
Analysis
from the same population.
3.1.7.2 Discussion—This state does not imply that the
3. Terminology
random variation is large or small, within or outside of
specification, but rather that the variation is predictable using
3.1 Definitions—Unless otherwise noted, all statistical
statistical techniques.
terms are defined in Terminology E456.
3.1.7.3 Discussion—The process capability of a stable pro-
3.1.1 long term standard deviation,σ ,n—samplestandard
LT
cess is usually improved by fundamental changes that reduce
deviation of all individual (observed) values taken over a long
or remove some of the random causes present or adjusting the
period of time.
mean towards the preferred value, or both.
3.1.1.1 Discussion—A long period of time may be defined
3.1.7.4 Discussion—Continual adjustment of a stable pro-
as shifts, weeks, or months, etc.
cess will increase variation.
3.1.2 process capability, PC, n—statistical estimate of the
outcome of a characteristic from a process that has been 3.2 Definitions of Terms Specific to This Standard:
demonstrated to be in a state of statistical control. 3.2.1 lower process capability index, C ,n—indexdescrib-
pkl
ing process capability in relation to the lower specification
limit.
1
ThispracticeisunderthejurisdictionofASTMCommitteeE11onQualityand
3.2.2 lower process performance index, P ,n—index de-
pkl
Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical
scribing process performance in relation to the lower specifi-
Quality Control.
cation limit.
Current edition approved Oct. 1, 2015. Published October 2015. Originally
ɛ1
approved in 2003. Last previous edition approved in 2012 as E2281–08a (2012) .
3.2.3 minimum process capability index, C ,n—smaller of
pk
DOI: 10.1520/E2281-15.
the upper process capability index and the lower process
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
capability index.
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on
3.2.4 minimum process performance index, P ,n—smaller
pk
the ASTM website.
3
of the upper process performance index and the lower process
Available from ASTM Headquarters, 100 Barr Harbor Drive, W.
Conshohocken, PA 19428. performance index.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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E2281 − 15
3.2.5 special cause, n—variation in a process coming from tinuous improvem
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM 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.
´1
Designation: E2281 − 08a (Reapproved 2012) E2281 − 15 An American National Standard
Standard Practice for
Process and Measurement Capability IndicesCapability and
1
Performance Measurement
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. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1
ε NOTE—Editorial corrections were made to Equation 20 in October 2012.
1. Scope
1.1 This practice provides guidance for the use of capability indices for evaluating determining process capability and
performance. Process capability indices compare the variability of a process qualityperformance under several common scenarios
of use including: (a measure against product specifications or tolerances and assume the process is in a state of statistical control.
Process performance indices are useful) normal distribution based capability and performance indices such as inC , situationsC ,
p pk
whenP the, and P ; (bprocess is not ) process capability using attribute data for non-conforming units and non-conformities per
p pk
unit type variables, and (cin a state of statistical control.) additional methods in working with process capability or performance.
2. Referenced Documents
2
2.1 ASTM Standards:
E456 Terminology Relating to Quality and Statistics
E2586E2334 Practice for Calculating and Using Basic StatisticsSetting an Upper Confidence Bound For a Fraction or Number
of Non-Conforming items, or a Rate of Occurrence for Non-conformities, Using Attribute Data, When There is a Zero
Response in the Sample
2.2 ISO Standard:
3
ISO 3534-2 Statistics—Vocabulary and Symbols-Statistical Quality Control
2.2 Other Document:
3
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.
3.1 Definitions of Terms Specific to This Standard:
3.2.1 average standard deviation, s¯, n—arithmetic average of sample standard deviations.—Unless otherwise noted, all
statistical terms are defined in Terminology E456.
3.1.1 long term standard deviation, σ , n—sample standard deviation of all individual (observed) values taken over a long
LT
period of time.
1
This practice is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical Quality
Control.
Current edition approved Oct. 1, 2012Oct. 1, 2015. Published October 2012October 2015. Originally approved in 2003. Last previous edition approved in 20082012 as
ɛ1
E2281 – 08a.E2281 – 08a (2012) . DOI: 10.1520/E2281-08AR12E01.10.1520/E2281-15.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. 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 (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036, http://www.ansi.org.
3
Available from ASTM Headquarters, 100 Barr Harbor Drive, W. Conshohocken, PA 19428.
3.1.1.1 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.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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E2281 − 15
3.2.5 minimum process capability index, C ,n—smaller of the upper process capability index and the lower process capability
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.
3.1.2 process capability, PC, n—statistical estimate of the outcome of a characteristic from a process that has been demonstrated
to be in a state of statistical control.
3.1.3 process capability index, C , n—an index describing process capability in relation to specified tolerance.
p
3.1.4 process performance, PP, n—statistical measure of the outcome of a characteristic from a process that may not have been
demonstrated to be in a state of stati
...