1、| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BRITISH STANDARD BS 600:2000 ICS 03.120.30
2、 NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAW A guide to the application of statistical methods to quality and standardizationThis British Standard, having been prepared under the direction of the Management Systems Sector Committee, was published under the authority of the
3、 Standards Committee and comes into effect on 15 October 2000 BSI 10-2000 The following BSI references relate to the work on this standard: Committee reference SS/3 Draft for comment 99/404263 DC ISBN 0 580 33227 6 BS 600:2000 Amendments issued since publication Amd. No. Date Comments Committees res
4、ponsible for this British Standard The preparation of this British Standard was entrusted by Technical Committee SS/3, Application of statistical methods in standardization, upon which the following bodies were represented: Institute of Quality Assurance Laboratory of the Government Chemist National
5、 Physical Laboratory Royal Statistical SocietyBS 600:2000 BSI 10-2000 i Contents Page Committees responsible Inside front cover Foreword ii Introduction 1 1 Scope 2 2 Normative references 2 3 Terms and definitions 2 4 Illustration of value and role of statistical method through examples 2 4.1 Statis
6、tical method 2 4.2 Example 1: Strength of wire 2 4.2.1 General 2 4.2.2 Overall test results and minimum specified value 3 4.2.3 Initial analysis 3 4.2.4 Preliminary investigation 4 4.2.5 General discussion on findings 7 4.2.6 Explanation of statistical terms and tools used in this example 7 4.3 Exam
7、ple 2: Weight of fabric 8 4.3.1 General 8 4.3.2 Test results and specification limits 8 4.3.3 Discussion of specific results 10 4.3.4 Discussion on general findings 11 4.4 Example 3: Percentage ash content of cargo of coal 11 4.4.1 General 11 4.4.2 Test results 12 4.4.3 Initial graphical analysis of
8、 specific results 12 4.4.4 Benefits of a statistically sound sampling plan 14 4.4.5 General conclusions 16 5 Introduction to the simpler statistical tools 16 5.1 General 16 5.2 Basic statistical terms and measures 16 5.3 Presentation of data 18 5.3.1 Dot or line plot 18 5.3.2 Tally chart 19 5.3.3 St
9、em and leaf plot 19 5.3.4 Box plot 19 5.3.5 Multi-vari chart 21 5.3.6 Position-dimension (P-D) diagram 21 5.3.7 Graphical portrayal of frequency distributions 23 5.3.8 The normal distribution 28 5.3.9 The Weibull distribution 31 5.3.10 Graphs 33 5.3.11 Scatter diagram and regression 33 5.3.12 “Paret
10、o” (or Lorenz) diagram 34 5.3.13 Cause and effect diagram 35BS 600:2000 ii BSI 10-2000 Page 6 Variation and sampling considerations 36 6.1 Statistical control and process capability 36 6.1.1 Statistical control 36 6.1.2 Erratic variation 39 6.1.3 Systematic variation 39 6.1.4 Systematic changes with
11、 time 40 6.1.5 Statistical indeterminacy 40 6.1.6 Non-normal variation 40 6.1.7 Quality level and process capability 40 6.2 Sampling considerations 41 7 Methods of conformity assessment 43 7.1 The statistical concept of a population 43 7.2 The basis of securing conformity to specification 44 7.2.1 T
12、he two principal methods 44 7.2.2 Considerations of importance to the customer 45 7.2.3 Considerations of importance to the supplier 45 8 The statistical relationship between sample and population 46 8.1 The variation of the mean and the standard deviation in samples 46 8.1.1 General 46 8.1.2 Variat
13、ion of means 47 8.1.3 Variation of standard deviations 47 8.2 The reliability of a mean estimated from representative and duplicate sampling 51 8.2.1 Representative sampling 51 8.2.2 Duplicate sampling 53 8.3 Illustration of the use of the mean weight, and the lowest weight, in a sample of prescribe
14、d size of standard specimens of fabric 54 8.4 Tests and confidence intervals for means and standard deviations 56 8.4.1 Confidence intervals for means and standard deviations 56 8.4.2 Tests for means and standard deviations 57 8.4.2.1 Terminology 57 8.4.2.2 Test of a population mean against a given
15、value 58 8.4.2.3 Test of the difference between two population means; degrees of freedom 59 8.4.2.4 Power of the test 60 8.4.2.5 Comparison of two means in the case of paired observations 60 8.4.2.6 Comparison of standard deviations 61 8.5 Simultaneous variation in the sample mean and in the sample
16、standard deviation 61 8.6 Tests and confidence intervals for proportions 64 8.6.1 Attributes 64 8.6.2 Estimating a proportion 64 8.6.3 Confidence intervals for a proportion 65 8.6.4 Comparison of a proportion with a given value 65 8.6.5 Comparison of two proportions 66 8.6.6 Sample size determinatio
17、n 66 BSI 10-2000 iii BS 600:2000 Page 8.7 Prediction intervals 67 8.7.1 One-sided prediction interval for the next m observations 67 8.7.2 Two-sided prediction interval for the next m observations 68 8.7.3 One and two-sided prediction intervals for the mean of the next m observations 68 8.8 Statisti
18、cal tolerance intervals 69 8.8.1 Statistical tolerance intervals for normal populations 69 8.8.2 Statistical tolerance intervals for populations of an unknown distributional type 69 8.9 Estimation and confidence intervals for the Weibull distribution 70 8.9.1 The Weibull distribution 70 8.9.2 Goodne
19、ss-of-fit tests 71 8.9.3 Parameter estimation 71 8.9.4 Confidence intervals 71 8.10 Distribution-free methods: estimation and confidence intervals for a median 72 9 Acceptance sampling 73 9.1 Methodology 73 9.2 Rationale 74 9.3 Some terminology of acceptance sampling 74 9.3.1 The AQL 74 9.3.2 Limiti
20、ng quality (LQ) 74 9.3.3 Classical versus economic methods 75 9.3.4 Inspection levels 75 9.3.5 Inspection severity and switching rules 75 9.3.6 Use of “non-accepted” versus “rejected” 76 9.4 Acceptance sampling by attributes 76 9.4.1 General 76 9.4.2 Single sampling 77 9.4.3 Double sampling 79 9.4.4
21、 Multiple sampling 79 9.4.5 Sequential sampling 82 9.4.6 Continuous sampling 83 9.4.7 Skip-lot sampling 84 9.4.8 Audit sampling 85 9.4.9 Sampling for parts per million 85 9.4.10 Isolated lots 85 9.4.11 Accept-zero plans 85 9.5 Acceptance sampling by variables Single quality characteristic 86 9.5.1 G
22、eneral 86 9.5.2 Single sampling plans by variables for known process standard deviation: the “s” method 87 9.5.3 Single sampling plans by variables for unknown process standard deviation: the “s” method 87 9.5.4 Double sampling plans by variables 90 9.5.5 Sequential sampling plans by variables for k
23、nown process standard deviation 91 9.5.6 Accept-zero plans by variables 91BS 600:2000 iv BSI 10-2000 Page 9.6 Multiple quality characteristics 91 9.6.1 Classification of quality characteristics 91 9.6.2 Unifying theme 92 9.6.3 Inspection by attributes for non-conforming items 92 9.6.3.1 Independent
24、attributes 92 9.6.3.2 Dependent attributes 92 9.6.3.3 Example 92 9.6.4 Inspection by attributes for nonconformities 92 9.6.5 Independent variables 93 9.6.6 Dependent variables 93 9.6.7 Attributes and variables 93 10 Statistical process control (SPC) 93 10.1 Process focus 93 10.2 Essence of statistic
25、al process control (SPC) 95 10.3 Statistical process control or statistical product control? 97 10.4 Over-control, under-control and control of processes 98 10.5 Key statistical steps in establishing a standard performance based control chart 101 10.5.1 General 101 10.5.2 Monitoring strategy 101 10.
26、5.2.1 Subgroup constitution 101 10.5.2.2 Subgroup size 102 10.5.2.3 Frequency of sampling 104 10.5.3 Construction of a standard control chart 104 10.5.3.1 Common features 104 10.5.3.2 Example of typical mean and range control chart for measured data 104 10.5.3.3 Rationale for control limits 105 10.6
27、 Interpretation of standard Shewhart type control charts 106 10.7 Selection of an appropriate control chart for a particular use 106 10.7.1 Overview 106 10.7.2 Shewhart type control charts 106 10.7.3 Cumulative sum (cusum) charts 109 10.7.3.1 Principal features of cusum charts 109 10.7.3.2 Construct
28、ion of cusum charts 109 10.7.3.3 Application: fractional horse-power motor voltage 109 11 Process capability 113 11.1 Overview 113 11.2 Process performance v process capability 113 11.3 Process capability for measured data 113 11.3.1 Estimation of process capability (normally distributed data) 113 1
29、1.3.2 Estimation of process capability (non-normally distributed data) 114 11.3.3 Estimation of process capability (non-normally distributed data) 115 11.4 Process capability indices 117 11.4.1 General 117 11.4.2 The Cp index 120 11.4.3 The Cpk family of indices 121 BSI 10-2000 v BS 600:2000 Page 11
30、.4.4 The Cpm index 123 11.4.4.1 Current specification practice v optimal design values 123 11.4.4.2 Expression for Cpm index 124 11.4.4.3 Basis of Cpm index 124 11.5 Process capability for attribute data 126 12 Statistical experimentation and standards 129 12.1 Basic concepts 129 12.1.1 What is invo
31、lved in experimentation? 129 12.1.2 Why experiment? 129 12.1.3 Where does statistics come in? 129 12.1.4 What types of standard experimental designs are there and how does one make a choice of which to use? 130 12.1.4.1 Full factorial experiments 130 12.1.4.2 Fractional factorial experiments 130 12.
32、1.4.3 Nested or hierarchical design 134 12.1.4.4 Composite response surface designs 135 12.1.4.5 Mixture designs 137 12.1.4.6 Evolutionary operation (EVOP) designs 140 13 Measurement systems 143 13.1 Measurements and standards 143 13.2 Measurements, quality and statistics 143 13.3 Examples of statis
33、tical methods to ensure quality of measured data 144 13.3.1 Example 1: Resolution 144 13.3.2 Example 2: Bias and precision 146 13.3.3 Precision Repeatability 148 13.3.4 Precision Reproducibility 149 Annex A (informative) Measured data control charts: formulae and constants 153 Annex B (informative)
34、Percentage points of the t-distribution 156 Bibliography 157 Figure 1 Line plot of breaking strength of 64 test specimens 3 Figure 2 Basic cause and effect diagram for variation in wire strength (due to possible changes of material and process parameters within specified tolerances) 4 Figure 3 Line
35、plots showing pattern of results after division into rational subgroups 5 Figure 4 Diagram indicating the effect of the inter-relationship between oil quench temperature and steel temperature on wire strength 6 Figure 5 Plot of means of weights v sample number (illustrating decreasing variation in t
36、he mean with sample size increase) 9 Figure 6 Plot of ranges of weights within each sample v sample number illustrating increasing (range) variation within a sample with sample size increase 10 Figure 7 Plot of averages of percentage ash content of coal by lot from cargo 13 Figure 8 Plot of progress
37、ive averages of percentage ash content in terms of lot 13 Figure 9 Schematic diagram showing plan for sampling percentage ash from cargo of ship 14 Figure 10 Plot of percentage ash v test number for lots 19 and 20 (illustrating relative consistency of percentage ash within each of these lots) 15 Fig
38、ure 11 Plot of percentage ash v test number for lots 9 and 10 (illustrating rogue pairs in both lots) 15BS 600:2000 vi BSI 10-2000 Page Figure 12 Dot plot of breaking strength of wire (Table 1 data) 18 Figure 13 Typical tally charts 19 Figure 14 Stem and leaf plot for data 19 Figure 15 Basic box plo
39、t 20 Figure 16 Box plot for Delta E panel shade variation between supply sources 20 Figure 17 Multi-vari chart as a tool for process variation analysis 21 Figure 18a) Measurements on cylinder to determine nominal size, ovality and taper 22 Figure 18b) P-D diagrams showing ideal diameter values, pure
40、 taper and pure ovality 22 Figure 18c) P-D diagrams indicating progressive decrease of mean and increase in geometric form variation and the beneficial effects of overhaul 22 Figure 19a) Frequency histogram for immersion times 24 Figure 19b) Percentage frequency histogram for immersion times 25 Figu
41、re 19c) Cumulative percentage frequency histogram for immersion times 25 Figure 19d) Cumulative percentage frequency diagram for immersion times 26 Figure 19e) Normal curve overlaid on the immersion time histogram (mean = 6.79: standard deviation = 1.08) 27 Figure 19f) Straight line plot on normal p
42、robability paper indicating normality of data 28 Figure 20 Percentages of normal distribution (in terms of standard deviations) 29 Figure 21 Weibull probability plot for hybrid unit on life test 33 Figure 22 Scatter diagram for flexing life of rubber in terms of material age 34 Figure 23 Relative co
43、ntribution of different types of in-process paint faults 35 Figure 24 Process cause and effect diagram for cracks in a casting 36 Figure 25 Diagram indicating types of variation in samples 38 Figure 26 Contrast of the capabilities of two filling machines 41 Figure 27 Illustration of one-sided test 5
44、8 Figure 28 Scatter chart for canned tomatoes data 62 Figure 29 Standardized control chart for mean and standard deviation 63 Figure 30 Comparison of Weibull distributions all with a =1 7 0 Figure 31 Type A and B OC curves for n = 32, Ac = 2, N = 100 77 Figure 32 Type B OC curves for Ac = 0, , and 1
45、 78 Figure 33 OC curves for single, double and multiple sampling plans for sample size code letter L and AQL 2%8 0 Figure 34 ASN curves for single, double and multiple sampling plans for sample size code letter L and AQL 2%8 1 Figure 35 Curves for the double and multiple sampling plans for sample si
46、ze code leter L and AQL 2 % showing the probability of needing to inspect significantly more sample items than under single sampling 82 Figure 36 Example of sequential sampling by attributes for percent nonconforming 83 Figure 37 Acceptance chart for a lower specification limit 88 Figure 38 Acceptan
47、ce chart for double specification limits with separate control 88 Figure 39 Standardized acceptance chart for sample size 18 for double specification limits with combined control at an AQL of 4 % under normal inspection 89 BSI 10-2000 vii BS 600:2000 Page Figure 40 Standardized acceptance chart for
48、sample size 18 for double specification limits with complex control at an AQL of 1 % for the upper limit and an AQL of 4% overall under normal inspection 89 Figure 41 ISO 9001:2000 Quality management process model 94 Figure 42 Control chart for nonconforming underwear 96 Figure 43 Outline of process
49、 of applying a top coat to a photographic film 97 Figure 44 Likelihood of setter/operator observing a single weight value when mean = 45 98 Figure 45 Process run chart with no guidance on how to deal with variation 100 Figure 46 Process control chart with criteria for “out-of control” signals 101 Figure 47 A two factor nested design is the basis of an X.R chart (illustrated with a subgroup size of 3) 102 Figure 48 Effect of subgroup size on ability to detect c
