1、 Reference number ISO/TR 18532:2009(E) ISO 2009TECHNICAL REPORT ISO/TR 18532 First edition 2009-04-15 Guidance on the application of statistical methods to quality and to industrial standardization Lignes directrices pour lapplication des mthodes statistiques la qualit et la normalisation industriel
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7、9 All rights reserved iiiContents Page Foreword ix Introduction.x 1 Scope1 2 Normative references1 3 Terms and definitions .1 4 Illustration of value and role of statistical method through examples 1 4.1 Statistical method1 4.2 Example 1: Strength of wire .2 4.2.1 General.2 4.2.2 Overall test result
8、s and lower specification limit.2 4.2.3 Initial analysis3 4.2.4 Preliminary investigation3 4.2.5 General discussion on findings.6 4.2.6 Explanation of statistical terms and tools used in this example6 4.3 Example 2: Mass of fabric 7 4.3.1 General.7 4.3.2 Test results and specification limits .7 4.3.
9、3 Discussion of specific results10 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
10、 results .12 4.4.4 Benefits of a statistically sound sampling plan .14 4.4.5 General conclusions .16 5 Introduction to basic statistical tools16 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
11、 plot19 5.3.4 Box plot20 5.3.5 Multi-vari chart.22 5.3.6 Position-Dimension (P-D) diagram 23 5.3.7 Graphical portrayal of frequency distributions25 5.3.8 The normal distribution 31 5.3.9 The Weibull distribution35 5.3.10 Graphs41 5.3.11 Scatter diagram and regression.41 5.3.12 Pareto (or Lorenz) dia
12、gram.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 variation47 6.1.4 Systematic changes with time .48 6.1.5 Statistical indeterminacy49 ISO/TR
13、 18532:2009(E) iv ISO 2009 All rights reserved6.1.6 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
14、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
15、 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 pres
16、cribed 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 variat
17、ion 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
18、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 8
19、5 8.8 Statistical tolerance intervals 86 8.8.1 Statistical tolerance intervals for normal populations86 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 Weibu
20、ll 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 Limit
21、ing 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 .
22、96 9.4.4 Multiple sampling 96 9.4.5 Sequential sampling. 99 ISO/TR 18532:2009(E) ISO 2009 All rights reserved v9.4.6 Continuous sampling100 9.4.7 Skip-lot sampling.101 9.4.8 Audit sampling.102 9.4.9 Sampling for parts per million102 9.4.10 Isolated lots103 9.4.11 Accept-zero plans103 9.5 Acceptance
23、sampling by variables Single quality characteristic104 9.5.1 General.104 9.5.2 Single sampling plans by variables for known process standard deviation The “ ” method105 9.5.3 Single sampling plans by variables for unknown process standard deviation The “s” method106 9.5.4 Double sampling plans by va
24、riables .109 9.5.5 Sequential sampling plans by variables for known process standard deviation.110 9.5.6 Accept-zero plans by variables110 9.6 Multiple quality characteristics111 9.6.1 Classification of quality characteristics111 9.6.2 Unifying theme.111 9.6.3 Inspection by attributes for nonconform
25、ing 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 variables113 10 Statistical process control (SPC).113 10.1 Process focus113 10.2 Essence of SPC.116 10.3 Statistical process control or statistical
26、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-control119 10.4.3 Scenario 2: Operator monitors a process using a run chart giving rise to haphazard contro
27、l.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 Interp
28、retation of standard Shewhart-type control charts127 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) charts129 11 Process capability.130 11.1 Overview.130 11.2 Process performance versu
29、s 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 indices138 11.4.1 Ge
30、neral.138 11.4.2 The C pindex.138 11.4.3 The C pkfamily of indices139 11.4.4 The C pmindex .142 11.5 Process capability for attribute data .145 12 Statistical experimentation and standards.148 12.1 Basic concepts148 12.1.1 What is involved in experimentation?.148 ISO/TR 18532:2009(E) vi ISO 2009 All
31、 rights reserved12.1.2 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
32、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
33、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 showin
34、g 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
35、 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 fr
36、action 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
37、 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 Fig
38、ure 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 diamet
39、er 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
40、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
41、,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
42、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 = 1 37 ISO/TR 18532:2009(E) ISO 2009 All rights reserved viiFigure 30 Q-Q plot to assess the fit of days between accidents (da
43、ta 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
44、 contribution of different types of in-process paint faults44 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 machines50 Figure 37 Illustration of one-sided test7
45、3 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 195 Figure 42 OC c
46、urves 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 co
47、de 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 Accept
48、ance 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 s
49、pecification 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 film118 Figure 53 Probability of setter/operator observing a single mass value when mean = 45 119
