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 2009
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ii © ISO 2009 – All rights reserved

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
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

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
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 (illustrating
rogue pairs in both lots) . 15
Figure 12 — Line plot of breaking strength of wire (Table 1 data) . 19
Figure 13 — Typical tally charts. 19
Figure 14 — Stem and leaf plot for data . 20
Figure 15 — Box plot . 21
Figure 16 — Box plot for Delta E panel shade variation between supply sources. 21
Figure 17 — Multi-vari chart as a tool for process variation analysis. 23
Figure 18 — Measurements on cylinder to determine nominal size, ovality and taper . 23
Figure 19 — Measurement on cylinder — P-D diagrams showing ideal diameter values, pure taper and
pure ovality. 24
Figure 20 — Measurement on cylinder — P-D diagrams indicating progressive decrease of mean and
increase in geometric form variation and the beneficial effects of overhaul. 25
Figure 21 — Frequency histogram for immersion times in Table 6 . 27
Figure 22 — Percentage frequency histogram for immersion times in Table 6. 27
Figure 23 — Cumulative percentage frequency histogram for immersion times in Table 6 . 28
Figure 24 — Cumulative percentage frequency diagram for immersion times in Table 6. 29
Figure 25 — Normal curve overlaid on the immersion time histogram (mean = 6,79; standard
deviation = 1,08). 30
Figure 26 — Straight line plot on normal probability paper indicating normality of data in Table 6. 31
Figure 27 — Percentages of normal distribution in relation to distances from the mean in terms of
standard deviations. 32
Figure 28 — Standard normal probability density with indications of percentage expected beyond a
value, U or L, that is z standard deviation units from the mean . 33
Figure 29 — Comparison with Weibull distributions, all with α = 1. 37
vi © ISO 2009 – All rights reserved

Figure 30 — Q-Q plot to assess the fit of days between accidents (data in column one of Table 8) to a
Weibull distribution.39
Figure 31 — Weibull probability plot of days between accidents (data in column one of Table 8).40
Figure 32 — Scatter diagrams of four data sets that all have the same correlation coefficients (r) and
fitted regression lines.43
Figure 33 — Relative contribution of different types of in-process paint faults.44
Figure 34 — Process cause and effect diagram for cracks in a casting .45
Figure 35 — Diagram indicating types of variation in samples.47
Figure 36 — Contrast of the capabilities of two filling machines.50
Figure 37 — Illustration of one-sided test.73
Figure 38 — Scatter chart for sample means and standard deviations in canned tomatoes data .78
Figure 39 — Standardized control chart for mean and standard deviation .79
Figure 40 — Type A and B OC curves for n = 32, Ac = 2, N = 100.94
Figure 41 — Type B OC curves for Ac = 0, 1/3,1/2 and 1.95
Figure 42 — OC curves for single, double and multiple sampling size code letter L and AQL 2,5 %.97
Figure 43 — Average sample size (ASSI) curves for single, double and multiple sampling plans for
sample size code letter L and AQL 2,5 % .98
Figure 44 — Curves for the double and multiple sampling plans for sample size code letter L and AQL
2,5 % showing the probability of needing to inspect significantly more sample items than under
single sampling .99
Figure 45 — Example of sequential sampling by attributes for percent nonconforming.100
Figure 46 — Acceptance chart for a lower specification limit .106
Figure 47 — Acceptance charts for double specification limits with separate control .107
Figure 48 — Standardized acceptance chart for sample size 18 for double specification limits with
combined control at an AQL of 4 % under normal inspection .107
Figure 49 — Standardized acceptance chart for sample size 18 for double specification limits with
combined control at an AQL of 1 % for the upper limit and an AQL of 4 % overall under normal
inspection .108
Figure 50 — ISO 9001:2008 Model of a process-based quality management system.114
Figure 51 — Control chart for nonconforming underwear.117
Figure 52 — Outline of process of applying a topcoat to a photographic film.118
Figure 53 — Probability of setter/operator observing a single mass value when mean = 45 .119
Figure 54 — Example of process run chart with variation, but with no guidance on how to interpret and
deal with variation.121
Figure 55 — Example of process control chart with criteria for “out-of-control” signals.122
Figure 56 — A two factor nested design is the basis of an XR chart (illustrated with a subgroup size
of 3).123
Figure 57 — Effect of subgroup size on ability to detect changes in process mean (process
nominal = 5,00, process standard deviation = 0,01) .124
Figure 58 — Mean and range chart for masses of standard specimens of fabric.126
Figure 59 — Graphical comparison of process capability with specified tolerance.133
Figure 60 — Illustration of the estimation of capability with a skew distribution (equivalent to a range
of ± 3σ in a normal distribution).134
Figure 61 — Dot plot for percent of silicon data showing overall pattern of variation.135
Figure 62 — Probability plot for percent of silicon data showing overall pattern of variation .136
Figure 63 — Probability plot for the logarithm of percent of silicon data showing overall pattern of
variation.137
Figure 64 — Individuals control chart of ln percent of silicon with limits.137
Figure 65 — Relationship between C C and C for two sets of process variability and
and
p pkU pkL
locations of specification limits.141
Figure 66 — Comparison of conformance to toleranced specification with optimal value approach .144
Figure 67 — Printed circuit board faults SPC chart and cumulative faults per unit (FPU) chart.147
Figure 68 — Effect of lubrication, speed, surface finish and density on push-off strength .154
Figure 69 — Interaction between squeegee speed and ink viscosity.155
Figure 70 — Central composite design of the face-centred cube variety for 3 factors .156
Figure 71 — Computer-generated contour plot for oxide uniformity in terms of power and pulse of the
etching process for gas ratio fixed at its coded level 0 .158
Figure 72 — Illustration of the fundamental difference in designs for two independent factors as
compared with a two-component mixture.159
Figure 73 — Illustration of the fundamental difference in designs for three independent factors as
compared with a three-component mixture. 160
Figure 74 — Ten-point augmented simplex centroid three-component design. 160
Figure 75 — Response surface contours for mean burn rate in terms of fuel (X1), oxidize (X2) and
binder (X3) blend components. 161
Figure 76 — Response surface contours for standard deviation of burn rate in terms of fuel (X1),
oxidize (X2) and binder (X3) blend components . 161
Figure 77 — Factors A and B set at nominal to give a process yield of 68 %. 162
Figure 78 — First stage optimisation using Box EVOP . 163
Figure 79 — First stage Box EVOP as local optimum has been found. 163
Figure 80 — Incomplete 5 stage simplex maximization experiment for two factors in terms of yield . 164
Figure 81 — Recommended resolution for process control and determination of compliance with
specified tolerance . 167
Figure 82 — Range charts showing adequate and inadequate resolutions. 168
Figure 83 — Bias and precision . 169
Figure 84 — Effect of measuring systems uncertainty on compliance decision. 170
Figure 85 — Establishing bias and precision for a pressure gauge . 171
Figure 86 — Individuals and moving range chart for pressure to check for stability of results prior to
performing a bias and precision test. 172

viii © ISO 2009 – All rights reserved

Foreword
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longer valid or useful.
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.
ISO/TR 18532 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods.
Introduction
This Technical Report demonstrates the advantages in the application of statistical methods in as simple and
efficient a manner as possible so that they become accessible to the many rather than to the few.
As an introduction to the subject
...