Control charts

ISO 7870-8:2017 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.

Cartes de contrôle

General Information

Status
Published
Publication Date
03-Apr-2017
Current Stage
6060 - International Standard published
Start Date
25-Jan-2017
Completion Date
04-Apr-2017
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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
---------------------- Page: 1 ----------------------
ISO 7870-8:2017(E)
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© ISO 2017, Published in Switzerland

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ii © ISO 2017 – All rights reserved
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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

iv © ISO 2017 – All rights reserved
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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.
© ISO 2017 – All rights reserved v
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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.
vi © ISO 2017 – All rights reserved
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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 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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ISO 7870-8:2017(E)

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
realized value of a quality characteristic of the process mean
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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ISO 7870-8:2017(E)
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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ISO 7870-8:2017(E)
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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ISO 7870-8:2017(E)

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
...

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