ISO 7870-4:2021

INTERNATIONAL ISO
STANDARD 7870-4
Second edition
2021-09
Control charts —
Part 4:
Cumulative sum charts
Cartes de contrôle —
Partie 4: Cartes de contrôle à somme cumulée
Reference number
© ISO 2021
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Contents Page
Foreword .v
Introduction . vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions, abbreviated terms and symbols . 1
3.1 Terms and definitions . 1
3.2 Abbreviated terms . 2
3.3 Symbols . 2
4 Principal features of cumulative sum (CUSUM) charts . 3
5 Basic steps in the construction of CUSUM charts — Graphical representation .4
6 Example of a CUSUM plot — Motor voltages . 5
6.1 Process . 5
6.2 Simple plot of results . . 5
6.3 Standard control chart for individual results . 6
6.4 CUSUM chart construction . 7
7 Fundamentals of making CUSUM-based decisions . 8
7.1 Need for decision rules . 8
7.2 Basis for making decisions . 8
7.3 Measuring the effectiveness of a decision rule . 9
7.3.1 Basic concepts . 9
7.3.2 Example of calculation of ARL . 10
8 Types of CUSUM decision schemes .10
8.1 V-mask . 10
8.1.1 Configuration and dimensions. 10
8.1.2 Application of the V-mask . 11
8.1.3 Average run lengths . 14
8.1.4 General comments on average run lengths . 15
8.2 Fast-initial response (FIR) CUSUM . 16
8.3 Tabular CUSUM . 16
8.3.1 Rationale . 16
8.3.2 Deployment . 17
9 CUSUM methods for process and quality control .19
9.1 Nature of the changes to be detected . 19
9.1.1 Size of the changes to be detected . 19
9.1.2 ‘Step’ changes . 19
9.1.3 Drifting . 19
9.1.4 Cyclic . 19
9.1.5 Hunting . 19
9.2 Selecting target values . 19
9.2.1 General . 19
9.2.2 Standard (given) value as target . 20
9.2.3 Performance-based target . 20
9.3 CUSUM schemes for monitoring location . . 20
9.3.1 Standard schemes.20
9.3.2 Standard schemes — Limitations . 27
9.3.3 ‘Tailored’ CUSUM schemes . 27
9.4 CUSUM schemes for monitoring variation .28
9.4.1 General .28
9.4.2 CUSUM schemes for subgroup ranges .29
9.4.3 CUSUM schemes for subgroup standard deviations . 32
9.5 Special situations .36
iii
9.5.1 Large between-subgroup variation .36
9.5.2 ‘One-at-a-time’ data .36
9.5.3 Serial dependence between observations .36
9.5.4 Outliers. 37
9.6 CUSUM schemes for discrete data .38
9.6.1 Event count — Poisson data .38
9.6.2 Two classes data — Binomial data .40
Annex A (informative) Example of tabular CUSUM . 44
Annex B (informative) Estimation of the change point when a step change occurs .48
Bibliography .50
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Foreword
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electrotechnical standardization.
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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
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This document was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 4, Applications of statistical methods in process management.
This second edition of ISO 7870-4 cancels and replaces the first edition (ISO 7870-4: 2011), which has
been technical revised.
The main changes compared to the previous edition are as follows:
— Manhattan diagram removed (former 6.7);
— V-mask types in Types of CUSUM decision schemes reduced to one V-mask;
— von Neumann method removed (former Annex A).
A list of all parts in the ISO 7870 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
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