ISO 7870-8:2017

INTERNATIONAL ISO
STANDARD 7870-8
First edition
2017-04
Control charts —
Part 8:
Charting techniques for short runs
and small mixed batches
Cartes de contrôle —
Partie 8: Techniques de cartes pour petites séries et pour petits lots
combinés
Reference number
ISO 7870-8:2017(E)
©
ISO 2017

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ISO 7870-8:2017(E)

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© ISO 2017, Published in Switzerland
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ISO 7870-8:2017(E)

Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms, definitions and symbols . 1
3.1 Terms and definitions . 1
3.2 Symbols . 1
4 How to select the correct type of Shewhart control chart for continuous variables data .2
4.1 General . 2
4.2 How to select the correct type of Shewhart control chart for measured data generally . 2
4.3 How to select the Shewhart control chart when the characteristic does not have a
constant aim or process spread . 3
5 How to prepare for short run, small mixed batch control charting .5
5.1 Focus on the process . 5
5.2 Procedure for grouping similar processes . 5
5.3 Typical applications . 7
5.4 Preliminary process diagnosis . 8
5.5 Procedure to establish the correct initial set-up of a process characteristic . 8
5.5.1 Purpose . 8
5.5.2 Scope and limitations. 8
5.5.3 Reasons for need of procedure . 8
5.5.4 Method . 9
5.5.5 Example .10
5.6 Procedure to pre-establish control limits for SPC charts for short run, small
batch, processes .11
5.6.1 Purpose .11
5.6.2 Scope of application .11
5.6.3 Reasons for need of procedure .11
5.6.4 Method .11
5.6.5 Example .12
6 How to establish and apply short run, small mixed batch, control charts .15
6.1 General .15
6.2 Variable aim, individual and moving range chart .15
6.2.1 Purpose .15
6.2.2 Scope of application .16
6.2.3 Method .16
6.2.4 Example .16
6.3 Variable aim, moving mean and moving range chart .18
6.3.1 Purpose .18
6.3.2 Scope of application .18
6.3.3 Method .18
6.3.4 Example .19
6.4 Universal, individual and moving range chart .20
6.4.1 Purpose .20
6.4.2 Scope of application .20
6.4.3 Method .20
6.4.4 Example .21
6.5 Universal, moving mean and moving range chart .22
6.5.1 Purpose .22
6.5.2 Scope of application .23
6.5.3 Method .23
6.5.4 Example .24
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ISO 7870-8:2017(E)

Annex A (informative) Reproducible copies of control charts forms and normal
probability worksheet .25
Bibliography .31
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ISO 7870-8:2017(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.
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).
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. 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).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
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 World Trade Organization (WTO) principles in the
Technical Barriers to Trade (TBT) see the following URL: www . i so .org/ iso/ foreword .html.
The committee responsible for this document is ISO/TC 69, Applications of statistical methods,
Subcommittee SC 4, Applications of statistical methods in product and process management.
A list of parts in the ISO 7870 series can be found on the ISO website.
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ISO 7870-8:2017(E)

Introduction
It is generally recommended that at least 25 subgroups of data be collected, and plotted, before any
constructive analysis can take place to form the basis for establishing standard traditional variables
control charts. This represents best practice for the application of standard statistical process
control (SPC) charts to long production runs of a single product characteristic (for instance, a diameter)
or a process parameter (for instance, temperature). However, it presents a problem in many potential
applications of SPC.
In the business environment, there is an increasing need for versatility and flexibility in highly efficient
systems. These support just-in-time inventories and create greater product variety, with smaller
batches and shorter runs. The consequent ever-increasing resets, changeovers, die changes, and so
on, bring new challenges to the meaningful application of SPC. These occur at a critical time when the
pressure for continual performance improvement has never been greater.
Processes accommodate many part numbers, often of similar shape but different nominal sizes at best,
and part configurations having multiple characteristics with different specified nominal values, units
of measure and tolerances. For example, a bolt maker with short runs of various size bolts (diameter
and length), or a tube extruder with tubes of different size outside diameter, inside diameter and wall
thickness. The customary approach is to put a different standard control chart on each characteristic of
each part number. The consequences of this administratively cumbersome, product-focused, procedure
would include the generation of large numbers of run charts each containing data too sparse to be
useful, either for control or improvement.
In the same way that other functions have responded to the challenge, for instance, the introduction of
lean methods and single minute exchange of die (SMED) in production, so the SPC facilitating function
responds. This situation presents both a problem and an opportunity.
The problem arises because, in many organizations, production runs are often too small to generate
enough data to apply standard control charts. This can occur in two ways. Firstly, there is the case where
the batch, or lot, size itself is very small. Secondly, there is the situation where the run is very short; for
instance, the high speed stamping operation that may run only for a short period. It is frequently not
practicable, in either case, to generate enough subgroups to make the control chart meaningful.
The opportunity arises because much current statistical process control is actually statistical product
control, that is, SPC implementation is often product-focused rather than process-focused. Different
products that are generated by a single or similar process are looked upon as dissimilar entities.
Consequently, sources of process variation can be overlooked when analysing the product orientated
control chart. Due to the sparseness of product information in short run, small batch situations, the
focus has to be on the common element, the process. Short run SPC provides the means to transform a
succession of short run product-related jobs into a long term process. An example is the “jobbing” shop
that does not make many of the same part, but has a number of processes that are continually being
employed. They turn many shafts, drill many holes, etc., continually. The grouping of drilling, turning,
grinding processes and the like, or their corresponding facilities (for instance, machine tools) could
make good candidates for the application of short run SPC.
Some basic statistical concepts, terminology and symbols are introduced in this document; however,
these are kept to a minimum. The language chosen is that of the workplace rather than that of the
statistician. The aim is to make this document readily comprehensible to the extensive range of
prospective users and too facilitate widespread communication and understanding of the method.
It is advisable that those who are not familiar with the control chart technique read both ISO 7870-1
and ISO 7870-2 before reading this document.
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INTERNATIONAL STANDARD ISO 7870-8:2017(E)
Control charts —
Part 8:
Charting techniques for short runs and small mixed batches
1 Scope
This document describes ways of applying regular variables control charts to short runs and small
mixed batches where the sample size for monitoring is restricted to one. It provides a set of tools to
facilitate the understanding of sources of variation in such processes so that the processes can be better
managed.
The charts described are process-focused rather than product-focused. The user can plot, monitor and
control similar characteristics on different items, or different characteristics on an item, on a single
control chart.
NOTE 1 The terms short run and small batch size are not well defined. Here, short run and small batch size are
taken to mean only a few items are manufactured before a different item is then produced.
NOTE 2 For situations where the subgroup size is larger than one, other standards apply.
2 Normative references
There are no normative references in this document.
3 Terms, definitions and symbols
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 3534-2 apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http:// www .electropedia .org/
— ISO Online browsing platform: available at http:// www .iso .org/ obp
3.2 Symbols
C centre line of a control chart
L
L L , L and L are the lower control limits for individuals, mean and range,
CL CL CL CL
x x R
respectively
T target (aim) value
n subgroup size
R the difference between the maximum and minimum of the values
R the expected value of the range of a particular characteristic
exp
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R moving range, the difference between the maximum and minimum of the consecutive values
moving
S process standard deviation
s realized value of the process standard deviation
u test statistic for set-up acceptance
U U , U and U are the upper control limits for individuals, mean and range,
CL CL CL CL
x x R
respectively
general value of a quality characteristic of the process mean
X
realized value of a quality characteristic of the process mean
x
4 How to select the correct type of Shewhart control chart for continuous
variables data
4.1 General
The business aim of statistical process control (SPC) is to control and improve quality, increase
productivity and reduce cost. The principal graphical tool of SPC is the control chart. There are three
main classes of control charts: Shewhart, cumulative sum (cusum) and exponentially weighted moving
average (EWMA).
NOTE Cusum control charts are dealt with in ISO 7870-4 and EWMA in ISO 7870-6.
The Shewhart control chart provides a graphical representation of a process showing plotted values of
a representative statistic of a selected characteristic (for instance, the individual value, mean, range or
standard deviation), a centre line, and one or more control lines. The control line(s) and centre line are
used as a basis for judging the stability of the process, namely, whether or not the process is in a state of
statistical control. Control lines are derived from the actual performance of the process and are not to
be confused with specified limits or specified tolerances.
Shewhart control charts provide a common language for communicating technical information on the
performance of a process. Control charts are effective tools in understanding process behaviour. They
distinguish between special and common cause variation. When no special cause is present, the process
is said to be in a state of statistical control.
When a process is in statistical control, its capability is predictable and can be assessed. Reducing
common cause variation and improving process targeting can enhance process capability.
Potentially, the control chart has wide applicability throughout any organization.
4.2 How to select the correct type of Shewhart control chart for measured data
generally
The procedure for selecting a Shewhart type measured data control chart is as follows.
a) If the characteristic to be monitored is ongoing with a targeted constant aim and process spread,
refer to ISO 7870-2.
b) If the characteristics do not have a constant aim or process spread, and the sample size is limited to
one, see 4.3.
c) If the characteristics do not have a constant aim or process spread and the feasible sample size is
greater than one, specialist guidance should be sought.
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This selection procedure is illustrated in Figure 1.
Figure 1 — Shewhart control chart selection flow chart for “measured” data
4.3 How to select the Shewhart control chart when the characteristic does not have a
constant aim or process spread
There are a number of Shewhart type control charts available for handling short run and small batch
situations where there are expected changes in aim or process spread. These include the following:
a) not constant aim, individual and moving range charts;
b) not constant aim, moving mean and moving range charts;
c) universal, moving mean and moving range charts;
d) universal, individual and moving range charts.
The procedure for selecting the appropriate control chart is illustrated in Figure 2.
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ISO 7870-8:2017(E)

Figure 2 — Control chart selection flow chart for short runs and small batches
Table 1 assists in the interpretation of Figure 2.
Table 1 — Chart selection table for short runs and small batches (subgroup size, n = 1)
Clause Additional
Parameter or Process Process
Output Chart name refer- information:
characteristic aim spread
ence Result required
Variable aim,
Single Dissimilar Similar Normal individual and 6.2 Quick response to change
moving range
Variable aim,
Approximate- moving mean Detect trend; smooth
Single Dissimilar Similar 6.3
ly normal and moving data
range
Universal,
Approximate-
Multiple Dissimilar Dissimilar individual and 6.4 Quick response to change
ly normal
moving range
Universal, mov-
Detect trend; smooth
Multiple Dissimilar Dissimilar Non-normal ing mean and 6.5
data
moving range
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5 How to prepare for short run, small mixed batch control charting
5.1 Focus on the process
Shewhart-styled control charts are usually applied to high volume long run products. One of
the consequences of this is that SPC often focuses on statistical product control rather than the
indicated statistical process control. This is because process results that are after-the-event product
characteristics are frequently monitored and concentrated on rather than the process parameters
giving rise to them.
Short run and small batch processes typify the flexible strategy essential to meet world class levels of
performance. The key to successful short run and small mixed batch statistical process control is to
focus on the process rather than the product. While nominal product characteristics necessarily change
in both type and size, the process generating the product frequently stays the same, for instance:
a) the same drilling process produces different diameter and depth holes where the nominal values
are not the same;
b) the same heading machine produces bolts with various nominal size heads, lengths and diameters;
c) the same press produces stampings with various nominal slot widths;
d) the same mixing process produces different solutions with different chemical elements and
target ratios;
e) the same extruder extrudes tubes with different nominal outer and inner diameters and wall
thicknesses;
f) the same coiner produces blanks in multiple cavity dies;
g) the same soldering operation produces small batch size printed circuit board assemblies with
different nominal solder strengths per board.
NOTE The examples given relate to engineering processes.
SPC techniques are applicable to any short run or small batch process that is in any way repetitive.
Process knowledge transfer is feasible from one run or batch to another. SPC techniques provide the
means to transform a succession of short run product data into meaningful information in terms of
a single long term process. It achieves this by combining multiple product characteristics involving
dissimilar nominal sizes and units of measure, unlike characteristics and of different process spread,
into a single, process-based, Shewhart control chart.
Short run SPC usually provides a more informative, effective and efficient alternative to traditional
methods, for example:
— 100 % final inspection that is an expensive and after-the-event activity;
— first-off inspection based on a single measurement that provides limited set-up information and
does not take into account process changes over time;
— last-off inspection, that is a high-risk strategy, taken after the event, that provides too little
information and, too late.
If a separate control chart is produced for each feature and nominal dimension, it is not cost effective
and is administratively cumbersome to operate. This will lead to an excessive number of charts being
produced and often with too few data points to properly interpret them with no benefit.
5.2 Procedure for grouping similar processes
To effectively group characteristics, a procedure is required that prevents that data coming from
significantly different processes to be monitored by the same control chart. If the systematic influences
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are unknown and not compensated for, the unintended consequences are that two or more stable
processes create frequent false alarms when monitored in the same chart.
A procedure that combines expert knowledge and data analysis to create groups and adjust them if
needed is given in Figure 3.
Figure 3 — Procedure for identifying and grouping similar characteristics
a) Step 1: First, processes that are potentially “groupable” need to be identified. This can be
different processes that follow the same procedure but with varying characteristics, such as
nominal/target value, tolerance, material, measurement process, production machine, tool,
environmental conditions, etc. Characteristics that vary between processes are plotted in a cause-
effect diagram along with their respective parameter space (Figure 4).
Figure 4 — Cause and effect diagram to establish differences between similar processes
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ISO 7870-8:2017(E)

b) Step 2: The next step is to determine if a difference in certain characteristics causes two or more
processes to behave significantly different. This information can be obtained, for example, by
1) expert knowledge/workshops,
2) simulation,
3) preliminary experiments, and/or
4) statistical analysis of existing data about the processes.
If there are no significant differences or the differences are systematic and can be compensated by
normalization and no other practical reasons stand against it, the characteristics can be grouped
and joint control charts can be applied.
c) Step 3: In the course of the application of control charts, more data are collected and more
knowledge is gained about the processes. Therefore, it is wise to periodically recheck that the
grouping conditions are still valid. This is especially true if alarms are frequently raised where no
assignable cause can be found. To be able to flexibly group and re-group processes, it is important
to record the characteristics as metadata along with the measured data so that each measurement
value is associable with a group of processes.
EXAMPLE In Table 2, the grouping is done for the characteristics given in Figure 4. Without grouping, 360
combinations have to be monitored. With grouping, the number of combinations
...