ISO 22514-3:2008
(Main)Statistical methods in process management — Capability and performance — Part 3: Machine performance studies for measured data on discrete parts
Statistical methods in process management — Capability and performance — Part 3: Machine performance studies for measured data on discrete parts
ISO 22514-3:2008 prescribes the steps to be taken in conducting short-term performance studies that are typically performed on machines where parts produced consecutively under repeatability conditions are considered. The number of observations to be analysed will vary according to the patterns the data produce, or if the runs (the rate at which items are produced) on the machine are low in quantity. The methods are not recommended where the sample size produced is less than 30 observations. Methods to be used for handling the data and carrying out the calculations are described. In addition, machine performance indices and the actions required at the conclusion of a machine performance study are described. ISO 22514-3:2008 is not applicable when tool wear patterns are expected to be present during the duration of the study, nor if autocorrelation between observations is present. The situation where a machine has captured the data, sometimes thousands of data points collected in a minute, is not considered suitable for the application of ISO 22514-3:2008.
Méthodes statistiques dans la gestion de processus — Aptitude et performance — Partie 3: Études de performance de machines pour des données mesurées sur des parties discrètes
Statistične metode za obvladovanje procesov - Sposobnost in delovanje - 3. del: Študije strojnega delovanja za izmerjene podatke na diskretnih delih
Ta del ISO 22514 predpisuje korake, ki jih je potrebno podvzeti pri izvajanju kratkoročnih študij delovanja, ki so običajno izvedene na strojih, kjer so upoštevani deli, proizvedeni zaporedno, pod pogoji ponovljivosti. Število ugotovitev, ki jih je potrebno analizirati, se razlikuje glede na vzorce, ki jih proizvedejo podatki, če je tempo stroja(stopnja, po kateri so predmeti proizvedeni) počasen. Te metode niso priporočljive pri vzorcih, kjer je proizvedena velikost vzorca manjša od 30 ugotovitev. Opisane so metode, ki se uporabljajo za ravnanje s podatki in opravljanje izračunov. Poleg tega so opisani kazalniki strojnega delovanja in dejanja, ki so potrebna pri zaključku študije strojnega delovanja. Ta dokument ne velja, kadar se med trajanjem študije pričakuje prisotnost vzorcev izrabe orodja, in niti, če je prisotna avtokorelacija med ugotovitvami. Situacija, kjer je stroj zajel podatke, včasih na tisoče podatkovnih točk, zajetih v minuti, se ne šteje za primerno za uporabo tega dela ISO 22514.
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SLOVENSKI STANDARD
SIST ISO 22514-3:2010
01-julij-2010
6WDWLVWLþQHPHWRGH]DREYODGRYDQMHSURFHVRY6SRVREQRVWLQGHORYDQMHGHO
âWXGLMHVWURMQHJDGHORYDQMD]DL]PHUMHQHSRGDWNHQDGLVNUHWQLKGHOLK
Statistical methods in process management - Capability and performance - Part 3:
Machine performance studies for measured data on discrete parts
Méthodes statistiques dans la gestion de processus - Aptitude et performance - Partie 3:
Études de performance de machines pour des données mesurées sur des parties
discrètes
Ta slovenski standard je istoveten z: ISO 22514-3:2008
ICS:
03.120.30 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical
methods
SIST ISO 22514-3:2010 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST ISO 22514-3:2010
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SIST ISO 22514-3:2010
INTERNATIONAL ISO
STANDARD 22514-3
First edition
2008-02-15
Statistical methods in process
management — Capability and
performance —
Part 3:
Machine performance studies for
measured data on discrete parts
Méthodes statistiques dans la gestion de processus — Aptitude et
performance —
Partie 3: Études de performance de machines pour des données
mesurées sur des parties discrètes
Reference number
ISO 22514-3:2008(E)
©
ISO 2008
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SIST ISO 22514-3:2010
ISO 22514-3:2008(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
COPYRIGHT PROTECTED DOCUMENT
© ISO 2008
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2008 – All rights reserved
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SIST ISO 22514-3:2010
ISO 22514-3:2008(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Symbols and abbreviations . 1
3 Pre-conditions for application. 2
4 Data collection . 3
5 Analysis . 4
6 Reporting . 14
7 Actions following a machine performance study. 16
Annex A (informative) Tables and worksheets . 17
Annex B (informative) Computer analysis of data . 20
Bibliography . 23
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ISO 22514-3:2008(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 22514-3 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 4, Applications of statistical methods in process management.
ISO 22514 consists of the following parts, under the general title Statistical methods in process
management — Capability and performance:
⎯ Part 1: General principles and concepts
⎯ Part 3: Machine performance studies for measured data on discrete parts
⎯ Part 4: Process capability estimates and performance measures [Technical Report]
In the future, it is planned to revise ISO 21747:2006 (Statistical methods — Process performance and
capability statistics for measured quality characteristics) as Part 2.
NOTE ISO 22514-3 was initially prepared as ISO/DIS 13700. It was renumbered before publication to include it in the
ISO 22514 series.
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Introduction
This part of ISO 22514 has been prepared to provide guidance in circumstances where a study is necessary
to determine if the output from a machine, for example, is acceptable according to some criteria. Such
circumstances are common in engineering when the purpose for the study is part of an acceptance trial.
These studies may also be used when diagnosis is required concerning a machine’s current level of
performance or as part of a problem solving effort. The method is very versatile and has been applied to many
situations.
Machine performance studies of this type provide information about the behaviour of a machine under very
restricted conditions such as limiting, as far as possible, external sources of variation that are commonplace
within a process, e.g. multi-factor and multi-level situations. The data gathered in a study might come from
items made consecutively, although this may be altered according to the study requirements. The data are
assumed to have been, generally, gathered manually.
The study procedure and reporting will be of interest to engineers, supervisors and management wishing to
establish whether a machine should be purchased or put in for maintenance, to assist in problem solving or to
understand the level of variation due to the machine itself.
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SIST ISO 22514-3:2010
INTERNATIONAL STANDARD ISO 22514-3:2008(E)
Statistical methods in process management — Capability and
performance —
Part 3:
Machine performance studies for measured data on discrete
parts
1 Scope
This part of ISO 22514 prescribes the steps to be taken in conducting short-term performance studies that are
typically performed on machines where parts produced consecutively under repeatability conditions are
considered. The number of observations to be analysed will vary according to the patterns the data produce,
or if the runs (the rate at which items are produced) on the machine are low in quantity. The methods are not
recommended where the sample size produced is less than 30 observations. Methods to be used for handling
the data and carrying out the calculations are described. In addition, machine performance indices and the
actions required at the conclusion of a machine performance study are described.
The document is not applicable when tool wear patterns are expected to be present during the duration of the
study, nor if autocorrelation between observations is present. The situation where a machine has captured the
data, sometimes thousands of data points collected in a minute, is not considered suitable for the application
of this part of ISO 22514.
2 Symbols and abbreviations
P machine performance index
m
P minimum machine performance index
mk
P lower machine performance index
mkL
P upper machine performance index
mkU
f frequency
Σf cumulative frequency
i subscript used to identify values of a variable
L lower specification limit
N total sample size
X α % distribution fractile
α %
X ith value in a sample
i
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σ standard deviation, population
N
2
XX−
()
∑ i
i=1
S standard deviation, sample statistic, S =
N −1
U upper specification limit
z fractile of the standardized normal distribution from −∞ to α
α
µ population mean value in relation to the machine location
N
X
∑ i
i=1
X arithmetic mean value, sample, X =
N
GRR gauge repeatability and reproducibility
2
χ fractile of the Chi-square distribution
α
3 Pre-conditions for application
3.1 General
The pre-conditions given below are the minimum and may be exceeded when needed. In this type of study, it
is important to maintain constant all factors, other than the machine, which will influence the results, if the
study is to properly represent the machine itself, e.g. the same operator, same batch of material, etc.
3.2 Number of parts to be used in the study
The number specified will usually be 100. However, if the pattern of variation is expected to form a non-normal
distribution, the number of parts should be at least 100. The methods given within this part of ISO 22514 may
also be used when conducting audits of a process, in which case the number of measurements taken might
be less than the above number, e.g. 50.
NOTE 1 This is to ensure that a reasonably narrow confidence interval can be calculated for the machine performance
indices when a normal distribution has been used. The interval will be approximately ± 12 % of the estimated index with a
confidence of 90 % for samples of 100.
Some machines have very slow cycle times and a “run” cannot produce 100 parts. In such circumstances, it
will be necessary to proceed with available data. The minimum number that this part of ISO 22514
recommends with the methods described herein is 30.
NOTE 2 Special techniques beyond the scope of this part of ISO 22514 exist for circumstances when there are fewer
samples.
By contrast, a machine that produces parts at a very high rate, e.g. a rivet-making machine, the sampling
strategy may require alteration since 100 parts will be produced in a few seconds. In circumstances such as
these, several studies may be required each allowing a different sampling approach to examine the machine’s
behaviour.
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3.3 Materials to be used
Ensure all input materials to be used in the study have been checked, conform to specifications and belong to
the same batches. It is not advised that a study be conducted with materials that are outside specification
since this could lead to unrepresentative results.
Care should be exercised not to introduce any other sources of variation other than those to be studied. A
typical example is where a machine run has to change to another batch of a particular material within a single
process batch, and batch material variation is not included in the study. In this instance, only data taken while
the first batch of that particular material was in use should be used in the analysis.
3.4 Measurement system
Ensure the measurement system to be used during the study has adequate properties, is calibrated and the
measurement system variation has been quantified and minimized. Special studies on the measurement
system should be undertaken to establish the amount of variation present due to measuring. The
measurement system should ideally have a combined gauge repeatability and reproducibility (GRR) of less
than 10 % of the process spread of the characteristic that the machine study is to investigate as determined
through a properly conducted measurement system analysis. This analysis should address issues of bias,
stability, linearity and discrimination, as well as GRR.
It may be appropriate to express the GRR as a percentage of a given specification tolerance. If the
measurement system has between 10 % and 30 % GRR, it may still be regarded as acceptable dependant
upon application. If it exceeds 30 %, the measurement system should be regarded as inappropriate. In
addition, the measurement system should have a measurement uncertainty appreciably less than the
tolerance or of the expected total variation of the characteristic, if known, as indicated above. Should a study
be performed using a measurement system with a performance worse than these requirements, some
erroneous conclusions to the study might be reached.
3.5 Running the study
Ensure an uninterrupted run takes place, under normal operating conditions. This will include any warm-up
time for the machine necessary to bring it up to its usual operating condition and with the machine set at
nominal for the characteristic to be studied. If the machine is stopped during the study for whatever reason,
either re-run the study again or analyse the data collected, as long as sufficient data has been collected and
as long as the repeatability conditions have not been violated. Under no circumstance should less than 30
results be used.
3.6 Special circumstances
In a multiple fixture set-up, multiple-cavity or multi-stream situation, each station, fixture, cavity or stream
should be treated as a separate machine for machine performance purposes since those streams may violate
the repeatability conditions.
In the case of a multiple-cavity tool, some extra studies may be performed to examine the between-cavity and
within-cavity variation. Consecutive observations from all cavities may be used in the study so as to examine
the total machine performance. Other statistical techniques may be employed, e.g. analysis of variance
(ANOVA), to assist with the analysis of such circumstances.
4 Data collection
4.1 Traceability of data
It is important for all data to be traceable so that unexpected values can be investigated. The collection
sequence should be preserved so that a time series can be plotted of the data that might indicate unexpected
variations. Such occurrences should be explained and a decision taken about the admissibility of such data. A
“log-book” would be suitable for recording all machine settings including any prior work on the machine, e.g.
maintenance, and for recording all events during the study, such as adjustments.
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4.2 Retention of specimens
Unless the tests performed are destructive in their nature, all specimens should be retained so that all
necessary examinations can be made. They should only be disposed of once the study is complete and all
conclusions determined.
4.3 Data recording
Data should be clearly recorded either electronically or on the appropriate analysis sheet in numerical form to
the appropriate number of significant digits. This should be determined prior to the measuring process and will
be dependent on the resolution of the measuring instrument.
5 Analysis
5.1 General
The analysis of the data generated in the study may be done manually, an example of which is given within
this clause, or by means of computer programs an example of which is in given in Annex B.
5.2 Run chart
5.2.1 Purpose
When conducting a machine study, it is important to understand whether the data collected form a single and
stable pattern or not. There will be occasions when the conditions within the machine under study will lead to
a drift in its settings that will influence the pattern of data produced. There might be occasions when an
unauthorized adjustment has been made to the machine or data have been mixed in some way. Such an
event should stop the study and a new study should be begun. A run chart will be helpful to identify such
circumstances. The pattern on the run chart in Figure 1 might have been caused by such an adjustment or
something might have gone wrong with the machine itself or it is being used wrongly.
If a change such as that indicated in Figure 1 occurs, it will be necessary to take special measures according
to the circumstances. These might range between repeating the whole study to analysing the data in its
separate parts or eliminating certain results.
A manual graphical approach or a suitable software tool may be used to construct the run chart.
ISO 7873 contains guidance about the application of control charts and their associated statistical tests that
should be applied to plots such as that shown in Figure 1 to assist with the interpretation of the plots.
5.2.2 Review the plot
Inspect the plot for evidence of instability. This may be apparent as in Figure 1 where there has been a step
change in the data. Other patterns might appear such as a drift. It is possible to use control limits and control
chart rules to assess, easily, for any other assignable causes in the data. The data might be put into an
individuals and moving range chart to check for potential outliers in the data. (See ISO 8258 for further
information about such limits and rules.)
There exist a number of software products that can replace the above manual methods. These have become
popular because they produce the graphs mentioned above quickly and easily.
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1)
Figure 1 — Example of a run chart
5.3 Analyze the pattern of the data
5.3.1 Manual approach
A simple manner to begin analyzing the pattern the data form is to construct a tally chart.
The data are arranged into “classes”. The convention of counting the data into groups of five is often used and
an example of this can be seen in Figure 2. In this example, the data have been recorded to the nearest 5 mm
that is appropriate for the process from which the data are coming from.
1) This run chart was generated using a software programme called MINITAB™. MINITAB™ is the trade name of a
product supplied by Minitab Inc. This information is given for the convenience of users of this document and does not
constitute an endorsement by ISO of the product named. Equivalent products may be used if they can be shown to lead to
the same results.
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Figure 2 — Example of a worksheet for normally distributed data
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5.3.2 Software approach
As an alternative to a manual approach, the data should be entered into a software tool and a histogram
produced of the data. There exist a number of suitable software products that will carry out such analysis.
5.3.3 Check the pattern of the data
Study the pattern of the data to see if it conforms to a known distribution. Investigate the cause if the data
appear to form a quite different pattern. If the data do not form a normal distribution, it may become necessary
to employ a different worksheet such as that shown in Figure 3. An analysis carried out on non-normal data
using the worksheet designed for the normal distribution may produce inaccurate results. Non-normality can
occur from circumstances where the data are limited in some way, such as the results of measurements of
stress or of concentricity. There might be some anticipation of non-normal data if geometric tolerances have
been specified for a dimension or characteristic, for example. Consult the Bibliography for assistance in
determining if the data conform to a normal distribution (e.g. ISO 5479) as well as using other statistical
procedures beyond the scope of this part of ISO 22514.
Special cases, such as skewed distributions and bimodal data, are discussed in 5.6.
If similar studies have been conducted prior to the current one, there will be a certain expectation of what the
distribution might be. Scientific knowledge might also suggest what the pattern ought to be and this will be an
important reference should the pattern appear unusual. It will be likely that something has happened to induce
a non-random pattern and an investigation should be conducted.
Misleading results can occur if a computer program is used, that does not check for normality, as an
alternative to the manual method.
5.3.4 Summarize the data
Calculate the sample mean X and the sample standard deviation (S ) using the formulae shown in Clause 2.
()
If the distribution is non-normal, calculate the sample statistics corresponding to the relevant parameters for
the assumed distribution.
5.4 Construct a probability plot
5.4.1 General
A probability plot should be produced of the data. This may be achieved by using either a manual method or
by using a software tool described in 5.3.2 to 5.3.3. An example of the output of one software package can be
seen in Annex B.
5.4.2 Plot the cumulative frequency percentages
Using the bottom percentage scale on the probability paper, plot the cumulative frequency percentage for
each value in the tally chart at the intersection of its upper class limit and its cumulative frequency percentage.
NOTE 1 It will not be possible to plot the last cumulative frequency percentage (which will be 100 %) onto the
probability paper because the scale terminates at 99,997 %. Do not plot this percentage value at 99,997 % as it may
mislead and cause false conclusions. Loss of data can be avoided by plotting the average of the last two cumulative
frequency percentages at the mid-point of the last value rather than at its upper class limit.
NOTE 2 Some software products do not use grouped frequencies to generate the probability plot. Instead, the
individual values are used.
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ISO 22514-3:2008(E)
Figure 3 — Example of a worksheet for extreme value distributed data
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SIST ISO 22514-3:2010
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5.4.3 Draw a fitted line through the plotted points
Examine the plotted points to see if they can be approximately described by a straight line. If so, draw a best-
judged line through them. As a help to the judgment of where to draw the fitted line, the user should:
a) plot the sample mean, X ;
b) plot XS± 3 ;
c) draw the line between these plotted points.
Extend the line so that it meets the vertical lines at the extremes of the percentage scales (i.e. the ± 4σ lines).
If the drawn line does not fit the plotted data points very well, it indicates the data have not come from the
normal distribution. Special cases such as this are discussed in 5.6.
The worksheet shown in Figure 2 is based on normal probability paper. It is constructed so that when the
cumulative percentages are plotted onto it they will be represented by a straight-line plot if the data have come
from a normal distribution. Otherwise, the plot will not be a straight line and will indicate to the analyst that
other methods or other such papers should be used, such as the example in Figure 3. It is recommended that
at least six cumulative percentages be available for plotting, to improve the position of the drawn line.
5.4.4 Superimpose specification limit lines
Draw the specification limit lines onto the tally chart and extend them across the full scale of the probability
paper.
5.5 Interpretation of the worksheet
5.5.1 Assess conformance to specification
5.5.1.1 General
In the case of a two-sided specification, if the fitted line does not cross either of the specification limit lines, the
machine is deemed to be performing with at least 99,994 % of its output within specification. The percentage
performing deemed acceptable will vary according to the industry sector, the characteristic used in the study,
its significance and the opinion of the customer. The minimum acceptable percentage should always be stated.
It might be, for example, that a performance of 99,999 94 %, i.e. ± 5σ, is required before a machine can be
regarded as acceptable in certain circumstances. Machine performance indices (P and P ) can be reported
m mk
using the method of calculation shown in 5.7. Because these studies are carried out with minimal data over a
very short interval of time the user is advised to also compute the confidence intervals for the indices. The
calculations are shown in 6.2.
If the fitted line crosses one or both of the specification limit lines, the machine performance may be
considered not acceptable, i.e. it crosses at a point that corresponds to less than ± 4σ. If it is required that, as
indicated above, at least 99,999 9 % of output to be within specification, then the point will correspond to less
than ± 5σ. This may be the result of one or both of the conditions described in 5.5.1.2 and 5.5.1.3.
5.5.1.2 The spread of the data is too large
This condition may be caused by a problem with the machine itself, e.g. excessive wear on internal parts such
as bearings or slides. In order to satisfy the specification, it will be necessary to reduce the variation by
identifying the sources of the excessive variation and removing them. If a reduction in the variation is achieved,
a further study will show the drawn line X ± 4σ to have a smaller gradient, and if small enough, this line will
()
lie between the specification limit lines indicating an acceptable machine. See Figure 4.
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Figure 4 — Variation too large — Machine after improvement
5.5.1.3 Location (setting) is too high or too low
If the mean of the distribution could be shifted, e.g. by adjusting the machine setting, the fitted line might then
lie within the specification limit lines and the machine performance might be considered acceptable.
A prediction about any adjustment and if it would achieve the required result can be made by shifting the line
on the probability paper keeping it parallel to its original position. If the fitted line then lies within the
specification limit lines, a machine adjustment could correct the condition. See Figure 5.
Figure 5 — Mean incorrect — Reset machine
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5.5.2 Estimate the percentage out of specification
If the fitted line cuts through a specification limit line, an estimate can be made of the proportion out of
specification that would be found if the machine were to continue running. At the intersection of the fitted line
with the specification limit line, read off the nearest percentage scale the estimated percentage. For example,
in Figure 2, to estimate the percentage occurring beyond the upper specification limit (U ), read off the
percentage scale on the top of the worksheet probability plot. To estimate the percentage below the lower
specification limit (L), use the percentage scale on the bottom of the worksheet. The total estimated out of
specification is the sum of
...
INTERNATIONAL ISO
STANDARD 22514-3
First edition
2008-02-15
Statistical methods in process
management — Capability and
performance —
Part 3:
Machine performance studies for
measured data on discrete parts
Méthodes statistiques dans la gestion de processus — Aptitude et
performance —
Partie 3: Études de performance de machines pour des données
mesurées sur des parties discrètes
Reference number
ISO 22514-3:2008(E)
©
ISO 2008
---------------------- Page: 1 ----------------------
ISO 22514-3:2008(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
COPYRIGHT PROTECTED DOCUMENT
© ISO 2008
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2008 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 22514-3:2008(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Symbols and abbreviations . 1
3 Pre-conditions for application. 2
4 Data collection . 3
5 Analysis . 4
6 Reporting . 14
7 Actions following a machine performance study. 16
Annex A (informative) Tables and worksheets . 17
Annex B (informative) Computer analysis of data . 20
Bibliography . 23
© ISO 2008 – All rights reserved iii
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ISO 22514-3:2008(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
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International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
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International Standard requires approval by at least 75 % of the member bodies casting a vote.
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rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 22514-3 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 4, Applications of statistical methods in process management.
ISO 22514 consists of the following parts, under the general title Statistical methods in process
management — Capability and performance:
⎯ Part 1: General principles and concepts
⎯ Part 3: Machine performance studies for measured data on discrete parts
⎯ Part 4: Process capability estimates and performance measures [Technical Report]
In the future, it is planned to revise ISO 21747:2006 (Statistical methods — Process performance and
capability statistics for measured quality characteristics) as Part 2.
NOTE ISO 22514-3 was initially prepared as ISO/DIS 13700. It was renumbered before publication to include it in the
ISO 22514 series.
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ISO 22514-3:2008(E)
Introduction
This part of ISO 22514 has been prepared to provide guidance in circumstances where a study is necessary
to determine if the output from a machine, for example, is acceptable according to some criteria. Such
circumstances are common in engineering when the purpose for the study is part of an acceptance trial.
These studies may also be used when diagnosis is required concerning a machine’s current level of
performance or as part of a problem solving effort. The method is very versatile and has been applied to many
situations.
Machine performance studies of this type provide information about the behaviour of a machine under very
restricted conditions such as limiting, as far as possible, external sources of variation that are commonplace
within a process, e.g. multi-factor and multi-level situations. The data gathered in a study might come from
items made consecutively, although this may be altered according to the study requirements. The data are
assumed to have been, generally, gathered manually.
The study procedure and reporting will be of interest to engineers, supervisors and management wishing to
establish whether a machine should be purchased or put in for maintenance, to assist in problem solving or to
understand the level of variation due to the machine itself.
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INTERNATIONAL STANDARD ISO 22514-3:2008(E)
Statistical methods in process management — Capability and
performance —
Part 3:
Machine performance studies for measured data on discrete
parts
1 Scope
This part of ISO 22514 prescribes the steps to be taken in conducting short-term performance studies that are
typically performed on machines where parts produced consecutively under repeatability conditions are
considered. The number of observations to be analysed will vary according to the patterns the data produce,
or if the runs (the rate at which items are produced) on the machine are low in quantity. The methods are not
recommended where the sample size produced is less than 30 observations. Methods to be used for handling
the data and carrying out the calculations are described. In addition, machine performance indices and the
actions required at the conclusion of a machine performance study are described.
The document is not applicable when tool wear patterns are expected to be present during the duration of the
study, nor if autocorrelation between observations is present. The situation where a machine has captured the
data, sometimes thousands of data points collected in a minute, is not considered suitable for the application
of this part of ISO 22514.
2 Symbols and abbreviations
P machine performance index
m
P minimum machine performance index
mk
P lower machine performance index
mkL
P upper machine performance index
mkU
f frequency
Σf cumulative frequency
i subscript used to identify values of a variable
L lower specification limit
N total sample size
X α % distribution fractile
α %
X ith value in a sample
i
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σ standard deviation, population
N
2
XX−
()
∑ i
i=1
S standard deviation, sample statistic, S =
N −1
U upper specification limit
z fractile of the standardized normal distribution from −∞ to α
α
µ population mean value in relation to the machine location
N
X
∑ i
i=1
X arithmetic mean value, sample, X =
N
GRR gauge repeatability and reproducibility
2
χ fractile of the Chi-square distribution
α
3 Pre-conditions for application
3.1 General
The pre-conditions given below are the minimum and may be exceeded when needed. In this type of study, it
is important to maintain constant all factors, other than the machine, which will influence the results, if the
study is to properly represent the machine itself, e.g. the same operator, same batch of material, etc.
3.2 Number of parts to be used in the study
The number specified will usually be 100. However, if the pattern of variation is expected to form a non-normal
distribution, the number of parts should be at least 100. The methods given within this part of ISO 22514 may
also be used when conducting audits of a process, in which case the number of measurements taken might
be less than the above number, e.g. 50.
NOTE 1 This is to ensure that a reasonably narrow confidence interval can be calculated for the machine performance
indices when a normal distribution has been used. The interval will be approximately ± 12 % of the estimated index with a
confidence of 90 % for samples of 100.
Some machines have very slow cycle times and a “run” cannot produce 100 parts. In such circumstances, it
will be necessary to proceed with available data. The minimum number that this part of ISO 22514
recommends with the methods described herein is 30.
NOTE 2 Special techniques beyond the scope of this part of ISO 22514 exist for circumstances when there are fewer
samples.
By contrast, a machine that produces parts at a very high rate, e.g. a rivet-making machine, the sampling
strategy may require alteration since 100 parts will be produced in a few seconds. In circumstances such as
these, several studies may be required each allowing a different sampling approach to examine the machine’s
behaviour.
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3.3 Materials to be used
Ensure all input materials to be used in the study have been checked, conform to specifications and belong to
the same batches. It is not advised that a study be conducted with materials that are outside specification
since this could lead to unrepresentative results.
Care should be exercised not to introduce any other sources of variation other than those to be studied. A
typical example is where a machine run has to change to another batch of a particular material within a single
process batch, and batch material variation is not included in the study. In this instance, only data taken while
the first batch of that particular material was in use should be used in the analysis.
3.4 Measurement system
Ensure the measurement system to be used during the study has adequate properties, is calibrated and the
measurement system variation has been quantified and minimized. Special studies on the measurement
system should be undertaken to establish the amount of variation present due to measuring. The
measurement system should ideally have a combined gauge repeatability and reproducibility (GRR) of less
than 10 % of the process spread of the characteristic that the machine study is to investigate as determined
through a properly conducted measurement system analysis. This analysis should address issues of bias,
stability, linearity and discrimination, as well as GRR.
It may be appropriate to express the GRR as a percentage of a given specification tolerance. If the
measurement system has between 10 % and 30 % GRR, it may still be regarded as acceptable dependant
upon application. If it exceeds 30 %, the measurement system should be regarded as inappropriate. In
addition, the measurement system should have a measurement uncertainty appreciably less than the
tolerance or of the expected total variation of the characteristic, if known, as indicated above. Should a study
be performed using a measurement system with a performance worse than these requirements, some
erroneous conclusions to the study might be reached.
3.5 Running the study
Ensure an uninterrupted run takes place, under normal operating conditions. This will include any warm-up
time for the machine necessary to bring it up to its usual operating condition and with the machine set at
nominal for the characteristic to be studied. If the machine is stopped during the study for whatever reason,
either re-run the study again or analyse the data collected, as long as sufficient data has been collected and
as long as the repeatability conditions have not been violated. Under no circumstance should less than 30
results be used.
3.6 Special circumstances
In a multiple fixture set-up, multiple-cavity or multi-stream situation, each station, fixture, cavity or stream
should be treated as a separate machine for machine performance purposes since those streams may violate
the repeatability conditions.
In the case of a multiple-cavity tool, some extra studies may be performed to examine the between-cavity and
within-cavity variation. Consecutive observations from all cavities may be used in the study so as to examine
the total machine performance. Other statistical techniques may be employed, e.g. analysis of variance
(ANOVA), to assist with the analysis of such circumstances.
4 Data collection
4.1 Traceability of data
It is important for all data to be traceable so that unexpected values can be investigated. The collection
sequence should be preserved so that a time series can be plotted of the data that might indicate unexpected
variations. Such occurrences should be explained and a decision taken about the admissibility of such data. A
“log-book” would be suitable for recording all machine settings including any prior work on the machine, e.g.
maintenance, and for recording all events during the study, such as adjustments.
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4.2 Retention of specimens
Unless the tests performed are destructive in their nature, all specimens should be retained so that all
necessary examinations can be made. They should only be disposed of once the study is complete and all
conclusions determined.
4.3 Data recording
Data should be clearly recorded either electronically or on the appropriate analysis sheet in numerical form to
the appropriate number of significant digits. This should be determined prior to the measuring process and will
be dependent on the resolution of the measuring instrument.
5 Analysis
5.1 General
The analysis of the data generated in the study may be done manually, an example of which is given within
this clause, or by means of computer programs an example of which is in given in Annex B.
5.2 Run chart
5.2.1 Purpose
When conducting a machine study, it is important to understand whether the data collected form a single and
stable pattern or not. There will be occasions when the conditions within the machine under study will lead to
a drift in its settings that will influence the pattern of data produced. There might be occasions when an
unauthorized adjustment has been made to the machine or data have been mixed in some way. Such an
event should stop the study and a new study should be begun. A run chart will be helpful to identify such
circumstances. The pattern on the run chart in Figure 1 might have been caused by such an adjustment or
something might have gone wrong with the machine itself or it is being used wrongly.
If a change such as that indicated in Figure 1 occurs, it will be necessary to take special measures according
to the circumstances. These might range between repeating the whole study to analysing the data in its
separate parts or eliminating certain results.
A manual graphical approach or a suitable software tool may be used to construct the run chart.
ISO 7873 contains guidance about the application of control charts and their associated statistical tests that
should be applied to plots such as that shown in Figure 1 to assist with the interpretation of the plots.
5.2.2 Review the plot
Inspect the plot for evidence of instability. This may be apparent as in Figure 1 where there has been a step
change in the data. Other patterns might appear such as a drift. It is possible to use control limits and control
chart rules to assess, easily, for any other assignable causes in the data. The data might be put into an
individuals and moving range chart to check for potential outliers in the data. (See ISO 8258 for further
information about such limits and rules.)
There exist a number of software products that can replace the above manual methods. These have become
popular because they produce the graphs mentioned above quickly and easily.
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1)
Figure 1 — Example of a run chart
5.3 Analyze the pattern of the data
5.3.1 Manual approach
A simple manner to begin analyzing the pattern the data form is to construct a tally chart.
The data are arranged into “classes”. The convention of counting the data into groups of five is often used and
an example of this can be seen in Figure 2. In this example, the data have been recorded to the nearest 5 mm
that is appropriate for the process from which the data are coming from.
1) This run chart was generated using a software programme called MINITAB™. MINITAB™ is the trade name of a
product supplied by Minitab Inc. This information is given for the convenience of users of this document and does not
constitute an endorsement by ISO of the product named. Equivalent products may be used if they can be shown to lead to
the same results.
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ISO 22514-3:2008(E)
Figure 2 — Example of a worksheet for normally distributed data
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5.3.2 Software approach
As an alternative to a manual approach, the data should be entered into a software tool and a histogram
produced of the data. There exist a number of suitable software products that will carry out such analysis.
5.3.3 Check the pattern of the data
Study the pattern of the data to see if it conforms to a known distribution. Investigate the cause if the data
appear to form a quite different pattern. If the data do not form a normal distribution, it may become necessary
to employ a different worksheet such as that shown in Figure 3. An analysis carried out on non-normal data
using the worksheet designed for the normal distribution may produce inaccurate results. Non-normality can
occur from circumstances where the data are limited in some way, such as the results of measurements of
stress or of concentricity. There might be some anticipation of non-normal data if geometric tolerances have
been specified for a dimension or characteristic, for example. Consult the Bibliography for assistance in
determining if the data conform to a normal distribution (e.g. ISO 5479) as well as using other statistical
procedures beyond the scope of this part of ISO 22514.
Special cases, such as skewed distributions and bimodal data, are discussed in 5.6.
If similar studies have been conducted prior to the current one, there will be a certain expectation of what the
distribution might be. Scientific knowledge might also suggest what the pattern ought to be and this will be an
important reference should the pattern appear unusual. It will be likely that something has happened to induce
a non-random pattern and an investigation should be conducted.
Misleading results can occur if a computer program is used, that does not check for normality, as an
alternative to the manual method.
5.3.4 Summarize the data
Calculate the sample mean X and the sample standard deviation (S ) using the formulae shown in Clause 2.
()
If the distribution is non-normal, calculate the sample statistics corresponding to the relevant parameters for
the assumed distribution.
5.4 Construct a probability plot
5.4.1 General
A probability plot should be produced of the data. This may be achieved by using either a manual method or
by using a software tool described in 5.3.2 to 5.3.3. An example of the output of one software package can be
seen in Annex B.
5.4.2 Plot the cumulative frequency percentages
Using the bottom percentage scale on the probability paper, plot the cumulative frequency percentage for
each value in the tally chart at the intersection of its upper class limit and its cumulative frequency percentage.
NOTE 1 It will not be possible to plot the last cumulative frequency percentage (which will be 100 %) onto the
probability paper because the scale terminates at 99,997 %. Do not plot this percentage value at 99,997 % as it may
mislead and cause false conclusions. Loss of data can be avoided by plotting the average of the last two cumulative
frequency percentages at the mid-point of the last value rather than at its upper class limit.
NOTE 2 Some software products do not use grouped frequencies to generate the probability plot. Instead, the
individual values are used.
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Figure 3 — Example of a worksheet for extreme value distributed data
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5.4.3 Draw a fitted line through the plotted points
Examine the plotted points to see if they can be approximately described by a straight line. If so, draw a best-
judged line through them. As a help to the judgment of where to draw the fitted line, the user should:
a) plot the sample mean, X ;
b) plot XS± 3 ;
c) draw the line between these plotted points.
Extend the line so that it meets the vertical lines at the extremes of the percentage scales (i.e. the ± 4σ lines).
If the drawn line does not fit the plotted data points very well, it indicates the data have not come from the
normal distribution. Special cases such as this are discussed in 5.6.
The worksheet shown in Figure 2 is based on normal probability paper. It is constructed so that when the
cumulative percentages are plotted onto it they will be represented by a straight-line plot if the data have come
from a normal distribution. Otherwise, the plot will not be a straight line and will indicate to the analyst that
other methods or other such papers should be used, such as the example in Figure 3. It is recommended that
at least six cumulative percentages be available for plotting, to improve the position of the drawn line.
5.4.4 Superimpose specification limit lines
Draw the specification limit lines onto the tally chart and extend them across the full scale of the probability
paper.
5.5 Interpretation of the worksheet
5.5.1 Assess conformance to specification
5.5.1.1 General
In the case of a two-sided specification, if the fitted line does not cross either of the specification limit lines, the
machine is deemed to be performing with at least 99,994 % of its output within specification. The percentage
performing deemed acceptable will vary according to the industry sector, the characteristic used in the study,
its significance and the opinion of the customer. The minimum acceptable percentage should always be stated.
It might be, for example, that a performance of 99,999 94 %, i.e. ± 5σ, is required before a machine can be
regarded as acceptable in certain circumstances. Machine performance indices (P and P ) can be reported
m mk
using the method of calculation shown in 5.7. Because these studies are carried out with minimal data over a
very short interval of time the user is advised to also compute the confidence intervals for the indices. The
calculations are shown in 6.2.
If the fitted line crosses one or both of the specification limit lines, the machine performance may be
considered not acceptable, i.e. it crosses at a point that corresponds to less than ± 4σ. If it is required that, as
indicated above, at least 99,999 9 % of output to be within specification, then the point will correspond to less
than ± 5σ. This may be the result of one or both of the conditions described in 5.5.1.2 and 5.5.1.3.
5.5.1.2 The spread of the data is too large
This condition may be caused by a problem with the machine itself, e.g. excessive wear on internal parts such
as bearings or slides. In order to satisfy the specification, it will be necessary to reduce the variation by
identifying the sources of the excessive variation and removing them. If a reduction in the variation is achieved,
a further study will show the drawn line X ± 4σ to have a smaller gradient, and if small enough, this line will
()
lie between the specification limit lines indicating an acceptable machine. See Figure 4.
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ISO 22514-3:2008(E)
Figure 4 — Variation too large — Machine after improvement
5.5.1.3 Location (setting) is too high or too low
If the mean of the distribution could be shifted, e.g. by adjusting the machine setting, the fitted line might then
lie within the specification limit lines and the machine performance might be considered acceptable.
A prediction about any adjustment and if it would achieve the required result can be made by shifting the line
on the probability paper keeping it parallel to its original position. If the fitted line then lies within the
specification limit lines, a machine adjustment could correct the condition. See Figure 5.
Figure 5 — Mean incorrect — Reset machine
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5.5.2 Estimate the percentage out of specification
If the fitted line cuts through a specification limit line, an estimate can be made of the proportion out of
specification that would be found if the machine were to continue running. At the intersection of the fitted line
with the specification limit line, read off the nearest percentage scale the estimated percentage. For example,
in Figure 2, to estimate the percentage occurring beyond the upper specification limit (U ), read off the
percentage scale on the top of the worksheet probability plot. To estimate the percentage below the lower
specification limit (L), use the percentage scale on the bottom of the worksheet. The total estimated out of
specification is the sum of these two percentages.
When a software tool is used for this work, the proportion of out of specification estimation is usually a
standard output. This is shown in the example in Annex B.
5.6 Special cases
5.6.1 Data indicate a skewed distribution
There are occasions when machine studies produce data that indicate a skewed distribution. These often
arise when a natural limit exists beyond which data cannot occur. An example of this is the measurement of
concentricity where it is impossible to obtain readings less than zero.
If skewed data are plotted onto normal probability paper, the progression of the points on the probability paper
will deviate away from a straight line and indicate some curvature. To analyse the skewed distribution, it is
necessary to select a different probability paper that is based on the same skew distribution as that from which
the data has come. This should result in a straight-line plot. An example of the method is given in Figure 3 for
the extreme value distribution. Other papers that are generally available include the log-normal, exponential
and Weibull distributions.
The average value can be read from the plot. Estimate the value on the value axis where the drawn line
passes through the line at µ on the cumulative percentage axis. Alternatively, the mean value can be
calculated using a calculator.
5.6.2 Bimodal data
If the machine
...
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