SIST-TP ISO/TR 18532:2010
Guidance on the application of statistical methods to quality and to industrial standardization
Guidance on the application of statistical methods to quality and to industrial standardization
This Technical Report describes a broad range of statistical methods applicable to the management, control and improvement of processes.
Lignes directrices pour l'application des méthodes statistiques à la qualité et à la normalisation industrielle
Napotek za uporabo statističnih metod na področju kakovosti in industrijske standardizacije
To tehnično poročilo opisuje širok razpon statističnih metod, ki se uporabljajo pri obvladovanju, kontroli in izboljšavi procesov.
General Information
Buy Standard
Standards Content (Sample)
SLOVENSKI STANDARD
SIST-TP ISO/TR 18532:2010
01-julij-2010
1DSRWHN]DXSRUDERVWDWLVWLþQLKPHWRGQDSRGURþMXNDNRYRVWLLQLQGXVWULMVNH
VWDQGDUGL]DFLMH
Guidance on the application of statistical methods to quality and to industrial
standardization
Lignes directrices pour l'application des méthodes statistiques à la qualité et à la
normalisation industrielle
Ta slovenski standard je istoveten z: ISO/TR 18532:2009
ICS:
03.120.30 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical
methods
SIST-TP ISO/TR 18532:2010 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
---------------------- Page: 1 ----------------------
SIST-TP ISO/TR 18532:2010
---------------------- Page: 2 ----------------------
SIST-TP ISO/TR 18532:2010
TECHNICAL ISO/TR
REPORT 18532
First edition
2009-04-15
Guidance on the application of statistical
methods to quality and to industrial
standardization
Lignes directrices pour l'application des méthodes statistiques à la
qualité et à la normalisation industrielle
Reference number
ISO/TR 18532:2009(E)
©
ISO 2009
---------------------- Page: 3 ----------------------
SIST-TP ISO/TR 18532:2010
ISO/TR 18532:2009(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
COPYRIGHT PROTECTED DOCUMENT
© ISO 2009
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2009 – All rights reserved
---------------------- Page: 4 ----------------------
SIST-TP ISO/TR 18532:2010
ISO/TR 18532:2009(E)
Contents Page
Foreword .ix
Introduction.x
1 Scope.1
2 Normative references.1
3 Terms and definitions .1
4 Illustration of value and role of statistical method through examples .1
4.1 Statistical method.1
4.2 Example 1: Strength of wire .2
4.2.1 General.2
4.2.2 Overall test results and lower specification limit.2
4.2.3 Initial analysis.3
4.2.4 Preliminary investigation.3
4.2.5 General discussion on findings.6
4.2.6 Explanation of statistical terms and tools used in this example.6
4.3 Example 2: Mass of fabric .7
4.3.1 General.7
4.3.2 Test results and specification limits .7
4.3.3 Discussion of specific results.10
4.3.4 Discussion on general findings .11
4.4 Example 3: Mass fraction of ash (in %) in a cargo of coal .11
4.4.1 General.11
4.4.2 Test results (reference ISO 11648-1: Statistical aspects of sampling from bulk materials).12
4.4.3 Initial graphical analysis of specific results .12
4.4.4 Benefits of a statistically sound sampling plan .14
4.4.5 General conclusions .16
5 Introduction to basic statistical tools.16
5.1 General.16
5.2 Basic statistical terms and measures .16
5.3 Presentation of data .19
5.3.1 Dot or line plot .19
5.3.2 Tally chart.19
5.3.3 Stem and leaf plot.19
5.3.4 Box plot.20
5.3.5 Multi-vari chart.22
5.3.6 Position-Dimension (P-D) diagram .23
5.3.7 Graphical portrayal of frequency distributions.25
5.3.8 The normal distribution .31
5.3.9 The Weibull distribution.35
5.3.10 Graphs.41
5.3.11 Scatter diagram and regression.41
5.3.12 Pareto (or Lorenz) diagram.43
5.3.13 Cause and effect diagram.44
6 Variation and sampling considerations .45
6.1 Statistical control and process capability .45
6.1.1 Statistical control .45
6.1.2 Erratic variation.47
6.1.3 Systematic variation.47
6.1.4 Systematic changes with time .48
6.1.5 Statistical indeterminacy.49
© ISO 2009 – All rights reserved iii
---------------------- Page: 5 ----------------------
SIST-TP ISO/TR 18532:2010
ISO/TR 18532:2009(E)
6.1.6 Non-normal variation. 49
6.1.7 Quality level and process capability. 49
6.2 Sampling considerations . 50
7 Methods of conformity assessment . 54
7.1 The statistical concept of a population . 54
7.2 The basis of securing conformity to specification. 55
7.2.1 The two principal methods . 55
7.2.2 Considerations of importance to the customer. 56
7.2.3 Considerations of importance to the supplier. 56
8 The statistical relationship between sample and population. 57
8.1 The variation of the mean and the standard deviation in samples . 57
8.1.1 General. 57
8.1.2 Variation of means. 58
8.1.3 Variation of standard deviations . 60
8.2 The reliability of a mean estimated from stratified and duplicate sampling . 64
8.2.1 Stratified sampling. 64
8.2.2 Duplicate sampling . 66
8.3 Illustration of the use of the mean mass, and the lowest mass, in a sample of prescribed
size of specimens of fabric. 67
8.4 Tests and confidence intervals for means and standard deviations . 69
8.4.1 Confidence intervals for means and standard deviations. 69
8.4.2 Tests for means and standard deviations. 71
8.4.3 Equivalence of methods of testing hypotheses .77
8.5 Simultaneous variation in the sample mean and in the sample standard deviation. 77
8.6 Tests and confidence intervals for proportions .80
8.6.1 Attributes. 80
8.6.2 Estimating a proportion . 80
8.6.3 Confidence intervals for a proportion . 81
8.6.4 Comparison of a proportion with a given value . 82
8.6.5 Comparison of two proportions . 82
8.6.6 Sample size determination. 83
8.7 Prediction intervals. 84
8.7.1 One-sided prediction interval for the next m observations . 84
8.7.2 Two-sided prediction interval for the next m observations . 85
8.7.3 One and two-sided prediction intervals for the mean of the next m observations . 85
8.8 Statistical tolerance intervals . 86
8.8.1 Statistical tolerance intervals for normal populations.86
8.8.2 Statistical tolerance intervals for populations of an unknown distributional type. 87
8.8.3 Tables for statistical tolerance intervals . 87
8.9 Estimation and confidence intervals for the Weibull distribution . 87
8.9.1 The Weibull distribution. 87
8.10 Distribution-free methods: estimation and confidence intervals for a median. 88
9 Acceptance sampling. 89
9.1 Methodology. 89
9.2 Rationale. 90
9.3 Some terminology of acceptance sampling.91
9.3.1 Acceptance quality limit (AQL). 91
9.3.2 Limiting quality (LQ). 91
9.3.3 Classical versus economic methods. 92
9.3.4 Inspection levels . 92
9.3.5 Inspection severity and switching rules. 92
9.3.6 Use of “non-accepted” versus “rejected”. 93
9.4 Acceptance sampling by attributes . 93
9.4.1 General. 93
9.4.2 Single sampling. 94
9.4.3 Double sampling . 96
9.4.4 Multiple sampling. 96
9.4.5 Sequential sampling. 99
iv © ISO 2009 – All rights reserved
---------------------- Page: 6 ----------------------
SIST-TP ISO/TR 18532:2010
ISO/TR 18532:2009(E)
9.4.6 Continuous sampling.100
9.4.7 Skip-lot sampling.101
9.4.8 Audit sampling.102
9.4.9 Sampling for parts per million.102
9.4.10 Isolated lots.103
9.4.11 Accept-zero plans.103
9.5 Acceptance sampling by variables — Single quality characteristic.104
9.5.1 General.104
9.5.2 Single sampling plans by variables for known process standard deviation — The “σ”
method.105
9.5.3 Single sampling plans by variables for unknown process standard deviation — The “s”
method.106
9.5.4 Double sampling plans by variables .109
9.5.5 Sequential sampling plans by variables for known process standard deviation.110
9.5.6 Accept-zero plans by variables.110
9.6 Multiple quality characteristics.111
9.6.1 Classification of quality characteristics.111
9.6.2 Unifying theme.111
9.6.3 Inspection by attributes for nonconforming items .111
9.6.4 Inspection by attributes for nonconformities.112
9.6.5 Independent variables.113
9.6.6 Dependent variables.113
9.6.7 Attributes and variables.113
10 Statistical process control (SPC).113
10.1 Process focus.113
10.2 Essence of SPC.116
10.3 Statistical process control or statistical product control? .117
10.4 Over-control, under-control and control of processes .118
10.4.1 General.118
10.4.2 Scenario 1: Operator reacts to each individual sample giving rise to process over-control.119
10.4.3 Scenario 2: Operator monitors a process using a run chart giving rise to haphazard
control.120
10.4.4 Scenario 3: Monitoring using SPC chart with a potential for effective control .121
10.5 Key statistical steps in establishing a standard performance-based control chart.122
10.5.1 General.122
10.5.2 Monitoring strategy .122
10.5.3 Construction of a standard control chart .125
10.6 Interpretation of standard Shewhart-type control charts.127
10.7 Selection of an appropriate control chart for a particular use .128
10.7.1 Overview.128
10.7.2 Shewhart-type control charts.129
10.7.3 Cumulative sum (cusum) charts.129
11 Process capability.130
11.1 Overview.130
11.2 Process performance versus process capability.131
11.3 Process capability for measured (i.e. variables) data .132
11.3.1 General.132
11.3.2 Estimation of process capability (normally distributed data).132
11.3.3 Estimation of process capability (non-normally distributed data).133
11.4 Process capability indices.138
11.4.1 General.138
11.4.2 The C index.138
p
11.4.3 The C family of indices.139
pk
11.4.4 The C index .142
pm
11.5 Process capability for attribute data .145
12 Statistical experimentation and standards.148
12.1 Basic concepts.148
12.1.1 What is involved in experimentation?.148
© ISO 2009 – All rights reserved v
---------------------- Page: 7 ----------------------
SIST-TP ISO/TR 18532:2010
ISO/TR 18532:2009(E)
12.1.2 Why experiment?. 148
12.1.3 Where does statistics come in? . 149
12.1.4 What types of standard experimental designs are there and how does one make a choice
of which to use?. 149
13 Measuring systems. 164
13.1 Measurements and standards . 164
13.2 Measurements, result quality and statistics . 165
13.3 Examples of statistical methods to ensure quality of measured data . 166
13.3.1 Example 1: Resolution . 166
13.3.2 Example 2: Bias and precision. 169
13.3.3 Precision — Repeatability. 171
13.3.4 Precision — Reproducibility. 172
Annex A (informative) Measured data control charts: Formulae and constants. 177
Bibliography . 181
Index. 188
Figure 1 — Dot plot of breaking strength of 64 test specimens .2
Figure 2 — Basic cause and effect diagram for variation in wire strength (due to possible changes of
material and process parameters within specified tolerances). 3
Figure 3 — Line plots showing patterns of results after division into rational groups . 4
Figure 4 — Diagram indicating the effect of the interrelationship between oil quench temperature and
steel temperature on wire strength. 5
Figure 5 — Means of masses plotted against sample number (illustrating decreasing variation in the
mean with the sample size increase).
...
TECHNICAL ISO/TR
REPORT 18532
First edition
2009-04-15
Guidance on the application of statistical
methods to quality and to industrial
standardization
Lignes directrices pour l'application des méthodes statistiques à la
qualité et à la normalisation industrielle
Reference number
ISO/TR 18532:2009(E)
©
ISO 2009
---------------------- Page: 1 ----------------------
ISO/TR 18532:2009(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
COPYRIGHT PROTECTED DOCUMENT
© ISO 2009
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2009 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/TR 18532:2009(E)
Contents Page
Foreword .ix
Introduction.x
1 Scope.1
2 Normative references.1
3 Terms and definitions .1
4 Illustration of value and role of statistical method through examples .1
4.1 Statistical method.1
4.2 Example 1: Strength of wire .2
4.2.1 General.2
4.2.2 Overall test results and lower specification limit.2
4.2.3 Initial analysis.3
4.2.4 Preliminary investigation.3
4.2.5 General discussion on findings.6
4.2.6 Explanation of statistical terms and tools used in this example.6
4.3 Example 2: Mass of fabric .7
4.3.1 General.7
4.3.2 Test results and specification limits .7
4.3.3 Discussion of specific results.10
4.3.4 Discussion on general findings .11
4.4 Example 3: Mass fraction of ash (in %) in a cargo of coal .11
4.4.1 General.11
4.4.2 Test results (reference ISO 11648-1: Statistical aspects of sampling from bulk materials).12
4.4.3 Initial graphical analysis of specific results .12
4.4.4 Benefits of a statistically sound sampling plan .14
4.4.5 General conclusions .16
5 Introduction to basic statistical tools.16
5.1 General.16
5.2 Basic statistical terms and measures .16
5.3 Presentation of data .19
5.3.1 Dot or line plot .19
5.3.2 Tally chart.19
5.3.3 Stem and leaf plot.19
5.3.4 Box plot.20
5.3.5 Multi-vari chart.22
5.3.6 Position-Dimension (P-D) diagram .23
5.3.7 Graphical portrayal of frequency distributions.25
5.3.8 The normal distribution .31
5.3.9 The Weibull distribution.35
5.3.10 Graphs.41
5.3.11 Scatter diagram and regression.41
5.3.12 Pareto (or Lorenz) diagram.43
5.3.13 Cause and effect diagram.44
6 Variation and sampling considerations .45
6.1 Statistical control and process capability .45
6.1.1 Statistical control .45
6.1.2 Erratic variation.47
6.1.3 Systematic variation.47
6.1.4 Systematic changes with time .48
6.1.5 Statistical indeterminacy.49
© ISO 2009 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO/TR 18532:2009(E)
6.1.6 Non-normal variation. 49
6.1.7 Quality level and process capability. 49
6.2 Sampling considerations . 50
7 Methods of conformity assessment . 54
7.1 The statistical concept of a population . 54
7.2 The basis of securing conformity to specification. 55
7.2.1 The two principal methods . 55
7.2.2 Considerations of importance to the customer. 56
7.2.3 Considerations of importance to the supplier. 56
8 The statistical relationship between sample and population. 57
8.1 The variation of the mean and the standard deviation in samples . 57
8.1.1 General. 57
8.1.2 Variation of means. 58
8.1.3 Variation of standard deviations . 60
8.2 The reliability of a mean estimated from stratified and duplicate sampling . 64
8.2.1 Stratified sampling. 64
8.2.2 Duplicate sampling . 66
8.3 Illustration of the use of the mean mass, and the lowest mass, in a sample of prescribed
size of specimens of fabric. 67
8.4 Tests and confidence intervals for means and standard deviations . 69
8.4.1 Confidence intervals for means and standard deviations. 69
8.4.2 Tests for means and standard deviations. 71
8.4.3 Equivalence of methods of testing hypotheses .77
8.5 Simultaneous variation in the sample mean and in the sample standard deviation. 77
8.6 Tests and confidence intervals for proportions .80
8.6.1 Attributes. 80
8.6.2 Estimating a proportion . 80
8.6.3 Confidence intervals for a proportion . 81
8.6.4 Comparison of a proportion with a given value . 82
8.6.5 Comparison of two proportions . 82
8.6.6 Sample size determination. 83
8.7 Prediction intervals. 84
8.7.1 One-sided prediction interval for the next m observations . 84
8.7.2 Two-sided prediction interval for the next m observations . 85
8.7.3 One and two-sided prediction intervals for the mean of the next m observations . 85
8.8 Statistical tolerance intervals . 86
8.8.1 Statistical tolerance intervals for normal populations.86
8.8.2 Statistical tolerance intervals for populations of an unknown distributional type. 87
8.8.3 Tables for statistical tolerance intervals . 87
8.9 Estimation and confidence intervals for the Weibull distribution . 87
8.9.1 The Weibull distribution. 87
8.10 Distribution-free methods: estimation and confidence intervals for a median. 88
9 Acceptance sampling. 89
9.1 Methodology. 89
9.2 Rationale. 90
9.3 Some terminology of acceptance sampling.91
9.3.1 Acceptance quality limit (AQL). 91
9.3.2 Limiting quality (LQ). 91
9.3.3 Classical versus economic methods. 92
9.3.4 Inspection levels . 92
9.3.5 Inspection severity and switching rules. 92
9.3.6 Use of “non-accepted” versus “rejected”. 93
9.4 Acceptance sampling by attributes . 93
9.4.1 General. 93
9.4.2 Single sampling. 94
9.4.3 Double sampling . 96
9.4.4 Multiple sampling. 96
9.4.5 Sequential sampling. 99
iv © ISO 2009 – All rights reserved
---------------------- Page: 4 ----------------------
ISO/TR 18532:2009(E)
9.4.6 Continuous sampling.100
9.4.7 Skip-lot sampling.101
9.4.8 Audit sampling.102
9.4.9 Sampling for parts per million.102
9.4.10 Isolated lots.103
9.4.11 Accept-zero plans.103
9.5 Acceptance sampling by variables — Single quality characteristic.104
9.5.1 General.104
9.5.2 Single sampling plans by variables for known process standard deviation — The “σ”
method.105
9.5.3 Single sampling plans by variables for unknown process standard deviation — The “s”
method.106
9.5.4 Double sampling plans by variables .109
9.5.5 Sequential sampling plans by variables for known process standard deviation.110
9.5.6 Accept-zero plans by variables.110
9.6 Multiple quality characteristics.111
9.6.1 Classification of quality characteristics.111
9.6.2 Unifying theme.111
9.6.3 Inspection by attributes for nonconforming items .111
9.6.4 Inspection by attributes for nonconformities.112
9.6.5 Independent variables.113
9.6.6 Dependent variables.113
9.6.7 Attributes and variables.113
10 Statistical process control (SPC).113
10.1 Process focus.113
10.2 Essence of SPC.116
10.3 Statistical process control or statistical product control? .117
10.4 Over-control, under-control and control of processes .118
10.4.1 General.118
10.4.2 Scenario 1: Operator reacts to each individual sample giving rise to process over-control.119
10.4.3 Scenario 2: Operator monitors a process using a run chart giving rise to haphazard
control.120
10.4.4 Scenario 3: Monitoring using SPC chart with a potential for effective control .121
10.5 Key statistical steps in establishing a standard performance-based control chart.122
10.5.1 General.122
10.5.2 Monitoring strategy .122
10.5.3 Construction of a standard control chart .125
10.6 Interpretation of standard Shewhart-type control charts.127
10.7 Selection of an appropriate control chart for a particular use .128
10.7.1 Overview.128
10.7.2 Shewhart-type control charts.129
10.7.3 Cumulative sum (cusum) charts.129
11 Process capability.130
11.1 Overview.130
11.2 Process performance versus process capability.131
11.3 Process capability for measured (i.e. variables) data .132
11.3.1 General.132
11.3.2 Estimation of process capability (normally distributed data).132
11.3.3 Estimation of process capability (non-normally distributed data).133
11.4 Process capability indices.138
11.4.1 General.138
11.4.2 The C index.138
p
11.4.3 The C family of indices.139
pk
11.4.4 The C index .142
pm
11.5 Process capability for attribute data .145
12 Statistical experimentation and standards.148
12.1 Basic concepts.148
12.1.1 What is involved in experimentation?.148
© ISO 2009 – All rights reserved v
---------------------- Page: 5 ----------------------
ISO/TR 18532:2009(E)
12.1.2 Why experiment?. 148
12.1.3 Where does statistics come in? . 149
12.1.4 What types of standard experimental designs are there and how does one make a choice
of which to use?. 149
13 Measuring systems. 164
13.1 Measurements and standards . 164
13.2 Measurements, result quality and statistics . 165
13.3 Examples of statistical methods to ensure quality of measured data . 166
13.3.1 Example 1: Resolution . 166
13.3.2 Example 2: Bias and precision. 169
13.3.3 Precision — Repeatability. 171
13.3.4 Precision — Reproducibility. 172
Annex A (informative) Measured data control charts: Formulae and constants. 177
Bibliography . 181
Index. 188
Figure 1 — Dot plot of breaking strength of 64 test specimens .2
Figure 2 — Basic cause and effect diagram for variation in wire strength (due to possible changes of
material and process parameters within specified tolerances). 3
Figure 3 — Line plots showing patterns of results after division into rational groups . 4
Figure 4 — Diagram indicating the effect of the interrelationship between oil quench temperature and
steel temperature on wire strength. 5
Figure 5 — Means of masses plotted against sample number (illustrating decreasing variation in the
mean with the sample size increase). 9
Figure 6 — Ranges of masses within each sample vs sample number [illustrating increasing (range)
variation within a sample with sample size increase] .9
Figure 7 — Averages of mass fraction of ash (in %) of coal by lot from cargo . 13
Figure 8 — Progressive averages of mass fraction of ash (in %) in terms of lot. 13
Figure 9 — Schematic diagram showing plan for sampling percentage ash from cargo of ship. 14
Figure 10 — Mass fraction of ash (in %) plotted against test number for lots 19 and 20 (illustrating
relative consistency of percentage ash within each of these lots) . 15
Figure 11 — Mass fraction of ash (in %) plotted against test number for lots 9 and 10 (
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.