ISO 22514-8:2014

INTERNATIONAL ISO
STANDARD 22514-8
First edition
2014-06-01
Statistical methods in process
management — Capability and
performance —
Part 8:
Machine performance of a multi-state
production process
Méthodes statistiques dans la gestion de processus — Aptitude et
performance —
Partie 8: Aptitude machine d’un procédé de production multimodal
Reference number
©
ISO 2014
© ISO 2014
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ii © ISO 2014 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 2
3 Terms and definitions . 2
4 Symbols and abbreviations . 5
5 Preliminary technical analysis of the process . 6
5.1 General . 6
5.2 Identification of intrinsic factors . 6
5.3 Determination of process-specific states . 7
6 Preliminary verifications before calculating the machine performance indices .7
6.1 Measurement system. 7
6.2 Definition of the sampling plan for estimating global intrinsic dispersion . 8
7 Estimation of global intrinsic dispersion and calculation of machine performance indices 8
7.1 General . 8
7.2 Verification on the absence of outliers in the set of made measurement results. 9
7.3 Determination of the widths of local intrinsic dispersions .10
7.4 Determination of the locations of local intrinsic dispersions .11
7.5 Global intrinsic dispersion: type and estimation .12
7.6 Calculation of capability indices P and P .
m mk 14
7.7 Acceptance thresholds for the machine performance indices .15
Annex A (informative) States qualifying a processing process .16
Annex B (normative) Statistical tests .32
Bibliography .37
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
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electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
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patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
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For an explanation on the meaning of ISO specific terms and expressions related to conformity
assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers
to Trade (TBT) see the following URL: Foreword - Supplementary information
The committee responsible for this document is 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 2: Process capability and performance of time-dependent process models
— Part 3: Machine performance studies for measured data on discrete parts
— Part 4: Process capability estimates and performance measures [Technical Report]
— Part 6: Process capability statistics for characteristics following a multivariate normal distribution
— Part 7: Capability of measurement processes
— Part 8: Machine performance of a multi-state production process
iv © ISO 2014 – All rights reserved

Introduction
The methodology introduced through this part of ISO 22514 provides the platform for producing the items
required for building a long-term process capability and its leading, for a given product characteristic.
This can, for example, make it possible to
— define the in-process or mid-process sampling procedure,
— predict, for batch furnaces, a process capability variation range covering all the parts in the batch
load, once a recorded partial load variation has been characterized beforehand, and
— follow, for multi-cavity casting, the changes of extreme variation field based on different positions
in the mould, each variation of the mould cavities have been characterized beforehand.
INTERNATIONAL STANDARD ISO 22514-8:2014(E)
Statistical methods in process management — Capability
and performance —
Part 8:
Machine performance of a multi-state production process
1 Scope
This part of ISO 22514 aims to define the evaluation method to quantify the short-term capability
of a production process (capacity of the production tool, widely termed capability), i.e. the machine
performance index, to ensure compliance to a toleranced measurable product characteristic, when said
process does not feature any kind of sorting system.
If the production process integrates a sorting system, then this one (clearing away nonconforming parts)
should be analysed independently.
This part of ISO 22514 does not aim to define evaluation methods of the capability of a production process
that is gauged through long-term observation (capability process or performance process indices).
This part of ISO 22514 defines
— the principles guiding the development of indicators for quantifying capability, and
— the statistical methods to be employed.
The characteristics used to evaluate production process capability have statistical distributions, and it
is presumed, a priori, that at least one of these distributions is multi-modal. A distribution is presumed
to be multimodal if it results from the marked effect of at least one cause inducing a significant difference
between the produced items.
This part of ISO 22514 applies, for example, to characteristics generated by processes such as the
following:
— multi-cavity casting: simultaneously producing several identical parts from a mould featuring
several cavities.
Since each cavity has its own geometry and its own position in the mould architecture, it can create
a systemic difference on the output result;
— multi-fixture machining: a part produced at the same time, but the produced parts are positioned in
relation to the production tool by different fixture systems.
Since each fixture has its own geometry, mount clamps, etc., it can create a systematic difference on
the output result;
— batch load treatments: heat treatment applied at the same time on a set of identical parts (the batch
load), distributed within a pre-defined space of furnace. The position of an item of the batch relative
to the furnace can influence the output result.
Each cavity, fixture, or position in the batch load corresponds to a different state. The multi-state
process can be understood as the result of the combination of different states within the same process
(e.g. cavity, fixture, position in the batch load).
NOTE It needs to be ensured that such systematic differences, if any, constitute only a very small proportion
of permissible error so that their impact is harmless and do not affect the capabilities of the process.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 3534 (all parts), Statistics — Vocabulary and symbols
ISO 5725 (all parts), Accuracy (trueness and precision) of measurement methods and results
ISO 22514-3, Statistical methods in process management — Capability and performance — Part 3: Machine
performance studies for measured data on discrete parts
ISO/IEC Guide 98-3:2008, Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in
measurement (GUM:1995)
ISO/IEC Guide 99:2007, International vocabulary of metrology — Basic and general concepts and associated
terms (VIM)
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
production tool
machine or production machinery performing all the operations necessary for production, from
delivered supplies through product deliverable
3.2
process
set of interrelated or interacting activities which transforms inputs into outputs
Note 1 to entry: Inputs to a process are generally outputs of other processes.
Note 2 to entry: Processes in an organization are generally planned and carried out under controlled conditions
to add value.
Note 3 to entry: A process where the conformity of the resulting product cannot be readily or economically
verified is frequently referred to as a “special process”.
Note 4 to entry: This set includes all the factor resources necessary: production tools, labour, operating procedures,
maintenance, etc.
[SOURCE: ISO 9000:2005, 3.4.1]
3.3
equipment (or tools)
interchangeable component of a production tool for producing different products, and which cannot be
considered a wear-out component
EXAMPLE Mould of an injection-moulding machine — Counter-example: in machining, a cutting tool cannot
be considered as a piece of equipment.
3.4
process operation
step in the production process leading to a final or intermediate product status
3.5
toleranced characteristic of the product
quantitative characteristic of the product, and for which the upper specification limits (ISO 3534-2)
and/or lower specification limits (ISO 3534-2) are prescribed
2 © ISO 2014 – All rights reserved

3.6
dispersion interval (or dispersion of a characteristic)
interval within which all items are produced
Note 1 to entry: Where the dispersion interval is estimated based on statistical methods, it is estimated based on
its reference interval (ISO 3534-2).
Note 2 to entry: Any one process carries as many dispersion intervals as it does characteristics produced. For
example, a product presenting four different characteristics, i.e. length, width, height, and weight, is produced
including systematic (controllable) and random (uncontrollable) sources of variation by a single production tool
in a single operation. This operation is thus associated with four different dispersion intervals.
3.7
intrinsic dispersion interval (or instantaneous dispersion)
observable dispersion interval for a characteristic observed on produced items over a period during
which the process implementation parameters have not varied: same operator, same method, same
equipment, same batch of homogeneous raw materials, same temperature, etc.
Note 1 to entry: The underlying statistical distribution is called intrinsic (or instantaneous) distribution.
Note 2 to entry: In the event of drift in a process setting (such as drift caused by tool wear-out), it is common
practice to include this drift in the production dispersion instead of integrating it into the estimate of intrinsic
dispersion.
Note 3 to entry: This intrinsic dispersion interval is also called instantaneous dispersion because it affects
production at a given point in time.
Note 4 to entry: Any one process operation carries as many intrinsic dispersion intervals as it does characteristics
produced. A product presenting four different characteristics, i.e. length, width, height, and weight, is produced in
a single operation. This operation is thus associated with four different intrinsic dispersion intervals.
Note 5 to entry: The intrinsic dispersion interval is same as natural or inherent spread.
Note 6 to entry: In some industries, the intrinsic dispersion interval is called “production tool dispersion”; the
production tool featuring machine and its equipment.
3.8
intrinsic factor
internal condition to the production process and involved in the intrinsic dispersion interval, and which
has different aspects, each produced item comes across only one of these aspects
EXAMPLE 1 The cavities of a mould; each cavity defines one aspect of the “cavity” factor; machining fixtures
assumed to be identical; each fixture defines one aspect of the “fixture” factor.
EXAMPLE 2 If two different speeds are applied during the same production process to manufacture the
product (a first run at low speed followed by a second run at high speed), then the speed is not an intrinsic factor.
3.9
process state
specific configuration of the full set of intrinsic factors, where each intrinsic factor takes one of its states
EXAMPLE See Figure 1.
This setup involves six states:
— State C1 F1;
— State C2 F1;
— State C3 F1;
— State C1 F2;
— State C2 F2;
— State C3 F2.
Figure 1 — Process with two intrinsic factors (cavity identifier, fixture udentifier)
Note 1 to entry: One process state generates one statistical distribution. The statistical distributions tied to the
different states of the process can be similar or different.
Note 2 to entry: For a simple process that only produces one part at a time using single equipment and a single
quality of inputs, there will, a priori, be only one state. From the moment that several parts are produced
simultaneously under different conditions (different equipment, different positions in the batch load, etc.), there
will, a priori, be different states.
Note 3 to entry: If the production process simultaneously handles a set of p parts, then there can be p different
states.
3.10
multi-state (production) process
process through which different states generate statistical distributions that have different dispersion
widths and/or dispersion locations (see Figure 2)
Figure 2 — Example illustrating the distribution of a multi-state process and its breakdown
into states that each follow Gaussian distribution
3.11
local intrinsic dispersion (interval)
observable intrinsic dispersion interval associated with one of the process states
EXAMPLES
— local intrinsic dispersion interval connected to mould No. 2 on cavity No. 5;
4 © ISO 2014 – All rights reserved

— local intrinsic dispersion interval at coordinates X = 500, Y = 500, Z = 500 inside the batch furnace;
— local intrinsic dispersion interval on the left-hand side of the conveyer over a given time slot in a
continuous furnace.
3.12
global intrinsic dispersion (interval)
observable intrinsic dispersion interval when pooling the results of the combination of different process
states
3.13
production dispersion (interval)
observable dispersion interval for a characteristic, observed on produced items over a typical
representative period during which the different process implementation parameters may have varied
Note 1 to entry: The parameter that has varied in the production dispersion interval, can be, for example,
— change of operators,
— settings, or
— change in raw material batch, etc.
Note 2 to entry: The underlying statistical distribution is called production distribution.
Note 3 to entry: The production timeframe observed is not standardized. Depending on how the capability indices
are used, this time frame is set either internally by the product manufacturer or contractually by agreement
between supplier and customer.
3.14
measurement uncertainty
parameter, associated with the result of a measurement, that characterizes the dispersion of the values
that could reasonably be attributed to the measurand (quantity-of-interest)
Note 1 to entry: The parameter defining an interval bounding the result of a measurement and that can be
expected to encompass a large fraction of the distribution of values that could reasonably be attributed to the
measurand, is called enlarged uncertainty.
[SOURCE: adapted to the VIM]
Note 2 to entry: This part of ISO 22514 works on the basis that enlarged uncertainty is evaluated at a 95,44 %
confidence level, as is common practice.
4 Symbols and abbreviations
For the purposes of this document, the following symbols and abbreviations apply.
L lower specification limit
U upper specification limit
T specified tolerance (= U – L)
Di generic term used to denote the width of intrinsic dispersion
Dig width of the global intrinsic dispersion
k number of investigated states
n sampling size (number of measured parts per state), which is considered the same for all states
N total sample size (total number of parts sampled: N = n · k)
Di width of the local intrinsic dispersion in state j
j
Dil width of the local intrinsic dispersion when widths are not state-dependent
Di half-width of the bottom-slope side of the local intrinsic dispersion interval in state j (see Figure 3)
l,j
Di half-width of the top-slope side of the local intrinsic dispersion interval in state j (see Figure 3)
u,j
Di half-width of the bottom-slope side of the local intrinsic dispersion interval of the state with the
l,el
smallest dispersion bound
Di half-width of the top-slope side of the local intrinsic dispersion of the state with the highest disper-
u,er
sion bound
Di half-width of the bottom-slope side of the local intrinsic dispersion when widths are not state-
i
dependent
Di half-width of the top-slope side of the local intrinsic dispersion when widths are not state-dependent
u
X quantile at α % of the distribution without taking into account the different states
α %
X quantile at α % of the distribution of state j
α %,j
x mean of state j
j
 median of state j
x
j
mean of the values of samples, once outliers have been eliminated
X
Δm range of extreme locations of local intrinsic dispersion intervals when this difference is significantly
different from zero
Δm* maximal value of the observable Δm when the relative locations of the different local intrinsic disper-
sion intervals vary independently of each other over time
Δa amplitude of the outlier (expressed algebraically), in the event an outlier is recorded
5 Preliminary technical analysis of the process
5.1 General
The preliminary analysis is designed to determine the intrinsic factors and their aspects, and thus, to
define the process states liable to be found.
For a process operation, an assumption should be made, per characteristic, on whether or not the process
produces a multimodal distribution. If it is assumed to be multimodal, then it will be necessary to define
the states liable to be found.
5.2 Identification of intrinsic factors
The analyst tasked with this upstream preliminary analysis shall first define the intrinsic factors liable
to act as sources of differentiation and thus generate different statistical distributions. The analyst shall
also define the various different aspects possible for each intrinsic factor identified.
EXAMPLES
— part positioning in relation to the machine (multi-station fixtures, heat treatment load);
— product-machine interface (different fixtures, different clampings, etc.);
6 © ISO 2014 – All rights reserved

— different mounting patterns (guide-slots, die cavities, positions on the conveyor, etc.).
5.3 Determination of process-specific states
The process analyst shall integrate different constraint factors (economic, organizational, etc.) so as to
shortlist only the specific states deemed representative of extreme process states.
EXAMPLES
— for a heat treatment process involving a batch furnace, where each load contains 300 parts, the
process analyst could, for example, select four positions from the 300 states possible: one at the
furnace gate, one near the back of the furnace, and two near the centre (one at load centre and one
at the top of the load), which the analyst’s knowledge of the furnace tells them when are the extreme
state effects;
— for a cylinder head machining process for which 400 fixtures (adapters) are used, the process
analyst could only select six fixtures. Based on an analysis of the geometric surveys taken on these
fixtures (defects tied to the support bases, defects tied to clamping quality, etc.), the analyst shall
select a series of occurrences tied to these surveys (extreme cases, possibly combined with some
intermediate cases).
One process operation can generate different observable characteristics. These characteristics are often
impacted differently in different process states. This can guide the analyst to select states according to
categories of characteristics.
At this point, the analyst shall arbitrate between the options to select the states. Their selection shall also
take into account the process knowledge needed in order to lead root cause analysis as a step toward
building a process tracking system.
The number of states envisaged, a priori, at this early stage can be revised when defining which sampling
plan to apply. The aim is to determine the best trade-off between number of states investigated and the
quality of the knowledge on each of these states.
Examples are presented in Annex A.
6 Preliminary verifications before calculating the machine performance indices
6.1 Measurement system
Regardless of the process to qualify and the characteristic, it is first necessary to start by verifying
that the measurement uncertainty is compatible with the pre-set capability objectives defining the
maximum permissible global intrinsic dispersion.
This is done by running an estimate of measurement uncertainty taking into account the various sources
of error: repeatability, reproducibility, bias error, etc.
This step can be determined using the GUM (Guide to the expression of uncertainty in measurement) and
the ISO 5725 series of International Standards. The analysts can turn to an approach of the measurement
uncertainty estimation set out, for example, in ISO 22514-7 or in the guide MSA (measurement systems
analysis).
In order to move on to qualify the process, the measurement uncertainty shall not be too high. Excessively
high measurement uncertainty impacts significantly on any estimates of real product dispersions,
making it difficult to differentiate between process states.
A necessary prerequisite is that the enlarged uncertainty shall be less, for example, than a sixth of the
maximum acceptable global intrinsic dispersion in order to make sure the judgement on the production
tool does not become overly biased.
6.2 Definition of the sampling plan for estimating global intrinsic dispersion
The sampling plan is dictated by the number N of parts, on which measurements will be realized. It is
often the case that N is set at around 30 or 50. In order to eliminate any time-related bias, the N parts
shall be manufactured under the most identical conditions possible (although obviously excluding state
switchovers), which therefore means in a short time span.
The number of states to be investigated is denoted as k. Number k can be different from the number
initially planned for in the preliminary analysis, as N is often imposed. For each state, the sample size
shall be identical and is equal to n. The n value shall never, under any circumstances, be less than 3 (5 is
the value most widely used). N is calculated as n × k.
If the production process simultaneously handles a set of products, then a sample is compiled of produced
parts through different production cycles, where only the outputs from one of the selected states is
studied. Since sample size is set at n, there will be n measurement campaigns with k measurements per
campaign.
EXAMPLE In the case of a batch-load furnace heat treatment, for the validation of intrinsic dispersion, n
= 6 parts per load will be sampled from k = 5 different loads. A sample of five parts is put together using parts
sampled from the same in-furnace location but from five different loads. Two of the samples will be taken from
the edges of the load but from opposite locations, plus two from the load centre and two from an intermediate
position. Where the process involves particularly voluminous loads, the analyst can opt to take a higher number
of samples but from a lower number of loads (parts per sample).
NOTE Definition of the sampling plan for estimating production dispersion (see ISO 3534-2).
Once global intrinsic dispersion has been estimated, the next step is to identify the process states leading
to distributions that present extreme dispersion widths or locations. These states will serve as the basis
for estimating production dispersion.
EXAMPLE In the case of a continuous furnace treating several parts in parallel or a batch-load furnace heat
treatment, the very first step is to validate the intrinsic dispersion. It is only when the intrinsic dispersion has
been validated that it becomes possible, if necessary, to validate production dispersion. The definition of the
sample for validating production dispersion is actually dependent on the results recorded during the intrinsic
dispersion validation step.
7 Estimation of global intrinsic dispersion and calculation of machine perfor-
mance indices
7.1 General
Global intrinsic dispersion results from a mixing of local intrinsic dispersions, integrating their locations
and widths plus the possibility that a value detected can be an outlier yet having a real physical effect.
Each local intrinsic dispersion linked to a given state is defined by its central tendency (location) and its
width. This makes it possible to define the upper and lower bounds of the local intrinsic dispersion of
each state. For each state indexed j, the following estimators should be calculated (see Figure 3):
— the location of the lower bound of the local intrinsic dispersion in state j: X ;
0,135 %,j
— the location of the upper bound of the local intrinsic dispersion in state j: X ;
99,865 %,j
— which gives the width of the local intrinsic dispersion, Di = X – X ;
j 99,865 %,j 0,135 %,j
— and the half-widths of dispersion:
— lower-bound local intrinsic dispersion, Di = X – X ;
l,j 50 %,j 0,135 %,j
— upper-bound local intrinsic dispersion, Di = X – X ;
u,j 99,865 %,j 50 %,j
8 © ISO 2014 – All rights reserved

Di
j
Di Di
inf,j sup,j
X
Figure 3 — Parameters estimated for each state in relation to each local intrinsic dispersion
The multi-state process has to be split up into a set of states before capability indices related to global
instantaneous dispersion can be determined (there is no indicator available for local instantaneous
dispersion).
In order to achieve this splitting up, it is first necessary to check that there are no outliers liable to corrupt
the later estimates produced. Next, the widths of local intrinsic dispersions shall be estimated before
their locations can be compared. Statistical hypothesis testing is performed for this cross-comparison
step.
The statistical tests applied in this part of ISO 22514 employ a default 5 % significance level. A 5 %
significance level corresponds to the risk to reject wrongly the hypothesis.
If the calculated value of the statistic is greater than the tabulated value at 5 % level of significance, then
the hypothesis is rejected, otherwise accepted.
7.2 Verification on the absence of outliers in the set of made measurement results
For each drawn sample on a process state, a Grubbs’ test for outliers is applied (see Annex B) and then
repeated a second time but on the full data set (all process states collected).
If an outlier is detected, it shall be eliminated from the sample, after which the Grubbs’ test is repeated
again and again if necessary, up until no more outliers are detected. Care needs to be taken that no more
than one third of the data gets eliminated in the process.
Whatever the results of this Grubbs’ test for outliers, it is important not to question the whole set of
values from all samples; instead, continue with the analysis.
Each time an outlier is detected, determine whether the outlier is in order by
— a data transcription error,
— a measurement error, and
— a physical reality.
Depending on the case (dealt with in order)
a) if the outlier is a data transcription error: if the original intended value is known, it shall be inserted
to replace the outlier value. Otherwise, the following rule (b) is applied.
b) if the outlier is a measurement error: if the part concerned can be re-measured, then the outlier value
shall be replaced by the new result of measurement; otherwise, it shall be excluded. Furthermore,
the measurement process shall need to be made reliable.
c) if the outlier is a physical reality: first, estimate the effect of the outlier by calculating the difference
between the outlier value and the mean of the other values for the state concerned. This difference
is given the symbol Δa. Second, this outlier value is excluded from the statistical treatments tied to
local intrinsic dispersion (width and location), but to end with, it is, nevertheless, integrated into the
estimation of global intrinsic dispersion.
If the test reveals several outliers related to a physical reality, then a more advanced analysis shall need
to be led on the causes of the outliers in order to be in a position to even consider estimating global
intrinsic dispersion.
7.3 Determination of the widths of local intrinsic dispersions
The width of intrinsic dispersion is estimated (via its reference interval) for each process state, on the
data for any one given sample. This width is split into two half-widths (upper and lower), which can be
different if the distributions are asymmetrical (see Figure 4).
Depending on the type of characteristic under analysis, it should be assigned an a priori distribution. The
same characteristic for a given production process is considered to share the same type of distribution,
regardless of process state.
Figure 4 — Illustrations of state distributions
These distribution selections are not tested for goodness-of-fit test, the size n of each sample is often too
low. The choices are thus made based on the type of characteristic under analysis and on the analyst’s
experience.
EXAMPLES
— for a dimensional characteristic, a normal distribution;
— for a geometric characteristic, a Rayleigh distribution, a non-uniform distribution, a Weibull
distribution, or a Galton distribution (log-normal off-centred);
— for a characteristic defined as the impurity burden in a solution, a Galton distribution.
Thus, the width of local intrinsic dispersion Di is then estimated for each process state j.
j
The various different estimations, each tied to a process state, are then cross-compared. The aim is
to answer the question, “Can we accept (within a specified risk) that the widths of the local intrinsic
dispersions are identical, regardless of the process state considered?”
To answer this question, it is recommended to cross-compare variances using a Bartlett’s test, if there
are more than two process states, or a Fisher’s test, if there are only two process states (see Annex B).
10 © ISO 2014 – All rights reserved

If this hypothesis can be accepted, then all the widths of local intrinsic dispersions are considered equal
to a value that is calculated according to the system given in Annex B.
If this hypothesis cannot be accepted, there are two possible scenarios:
— to identify the cause of the difference and eliminate this cause from the production process, in
which case the previous protocol should be repeated, either partially or in full depending on the
cause suggested (cylinder head, for example);
— to accept this cause as being inherent to the production process, in which case it is possible to
consider whether or not to pool together several different local intrinsic dispersions (that all share
the same causal effect). This makes it possible to define the final conclusive retained dispersion
widths, by providing a narrower confidence interval (see the example set out in Annex A.2).
NOTE 1 Annex B also gives the conventional limits for the Bartlett’s test.
NOTE 2 The Bartlett’s test can be dropped and replaced by a Levene’s test.
7.4 Determination of the locations of local intrinsic dispersions
The analysis of the locations of local intrinsic dispersions shall not be performed until the analyst has
first determined the widths of these dispersions and, if these widths are deemed non equal, led the
indispensable process investigations.

The location of local intrinsic dispersion X is estimated (via its mean x or its median x ) for each
50 %,j
jj
jj
process state, on the data for any one given sample. By default, this location is estimated via the median,
but where the distribution is symmetrical or close to symmetrical, the mean shall be preferred to the
median as location estimator.
The different location estimations, each in relation to a process state, are cross-compared if and only
if the widths of local dispersions have been deemed identical. If this is not the case, then the location
estimations are not cross-compared if there are more than two process states.
If the locations of dispersion intervals are compared by running a goodness of fit test, then the aim of the
fit-test is to answer the question, “Can we accept (within a specified significance level) that the locations
of the local intrinsic dispersions are identical, regardless of the process state considered?”
To answer this question, it is recommended to use the following:
— an F-test if more than two states are being tackled, and if the variances of the states have been
estimated to be the same;
— if only two states are being tackled, and if the variances of the states have been estimated to be:
— the same, then a t-test, and
— different, then an aspin-welch’s test (t-test with unequal variances, also called paired t-test).
Annex B describes these tests and the limits to their use.
If this hypothesis can be accepted, then all the locations of local intrinsic dispersions are considered
equal to the mean, in this case, the difference between the locations of local dispersion interval is
considered equal to zero (Δm = 0).
If this hypothesis can no longer be accepted, then the analyst should look to integrate the observed
differences between the extreme means or between the extreme medians into the estimation of the
range of extreme locations of local intrinsic dispersion intervals (Δm).
If the hypothesis of equal locations has not been tested (more than two states and unequal variances),
the range of extreme locations of local intrinsic dispersion intervals (Δm) is considered equal to the
range in the extreme locations of these states.
7.5 Global intrinsic dispersion: type and estimation
Global intrinsic dispersion corresponds to the range covered by all the local intrinsic dispersions
combined together (widths and locations), plus the effect of any outliers having a physical reality (see
Figure 5).
Figure 5 — Illustration of global intrinsic distribution based on local intrinsic distributions
The results on the homogeneity of the widths and the locations of local intrinsic dispersions, as obtained
via the previous sections, can be used to determine the type of global intrinsic dispersion that matches
the production process.
In cases where the locations of the local dispersion intervals are estimated as different (Δm ≠ 0), then
analysis should be conducted to decide whether this difference Δm is liable to vary quickly or, conversely,
whether is expected to remain stable over time. This analysis has an impact on how capability indices
will be calculated.
The different types of global intrinsic dispersion are defined in Table 1.
12 © ISO 2014 – All rights reserved

Table 1 — Definitions of different types of global intrinsic dispersion
Type of process Widths of local Estimation of the Type of global Illustration
intrinsic differences in intrinsic
dispersions locations of local production
(Di ) intrinsic dispersions dispersion
j
(Δm)
equal Δm = 0 See ISO 22514-3
Δm ≠ 0
and is deemed constant
Uni-modal Type 1
equal
Δm ≠ 0
and is deemed variable
Type 2
Δm = 0
Type 3
Δm ≠ 0
and is deemed constant
Multi-modal different Type 4
Δm ≠ 0
and is deemed variable
Type 5
NOTE The illustrations in this table show the distributions of two extreme states and, where appropriate, their variations
(variable differences in location).
The bounds of local intrinsic dispersion intervals shall be cross-compared on both bottom-slope side
and top-slope side in order to define the lowest-performance state on each side (denoted g on the bottom
slope and d on top slope).
If there are no outliers having a real physical effect, the global intrinsic dispersion is equal to the
interval between the extreme-left lower bound and the extreme-right upper bound (the extreme-left
and extreme-right locations of the points X and X ).
0,135 %,j 99,865 %,j
If there is an outlier having a real physical effect, the Δa value shall be integrated in the estimation of
global intrinsic dispersion.
There are two scenarios:
— either the outlier Δa can only occur in one direction, in which case:
— if Δa is negative, it shall be added as an absolute value, but only to all the Di values,
l,j
— if Δa is positive, it shall only be added to all the Di values;
u,j
— the outlier Δa can occur in both directions, in which case:
— the absolute value for Δa shall be added to all the Di values and to all the Di values.
l,j u,j
This operation modifies the widths of the local intrinsic dispersions of each state: Di = Di + Di . It is
j l,j u,j
these new estimations that shall be integrated into the calculation of the capability indicators.
7.6 Calculation of capability indices P and P
m mk
Estimations of multi-state process capability indices cannot be globalized without picturing all the
states in their entirety. These indices are therefore equally dependent on extreme states.
The standards in place today hinge around two types of indices (see ISO 22514-1):
— indications of potential, which compare the width of the dispersion with the width of the tolerances
limits (i.e. the tolerance interval), i.e. P ;
m
— indicators that also integrate the location of the dispersion: i.e. P ;
mk
Table 2 — Calculation of capability indicators
Type of global Estimation of P or P depending on the type Estimation of P or P depending on the
m p mk pk
intrinsic of production process observation type of production process observation
production disper- P = min (P ; P )
mk mk,l mk,u
sion
Type 1 Tm−Δ
UX−max
()
50%,j
Di +Di 1j≤≤k
lu
Δm ≠ 0 is constant
P =
mk,u
Di
u
Widths of local Di are
equal
T
Type 2
min XL−
()
50%,j
1j≤≤k
Di ++Di Δm*
lu
Δm ≠ 0 is variable
P =
mk,l
Di
l
Widths of local Di are
equal
Type 3
T
UX−
50%
P =
mku
Δm = 0
max Di
max Di
()
j ()
u,j
1j≤≤k
1≤≤jk
Widths of local Di are
unequal
XL−
50%
P =
mkl
max Di
()
l,j
1≤≤jk
Δm* When the relative locations of the various different local intrinsic dispersions are considered to vary independently of
each other over time, it is possible to overestimate the difference Δm observed in the calculation of Pm. This overestimation
is defined by the process analysts who use their experience to evaluate the maximum Δm liable to be encountered. This
deviation is deno
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