BS 6002-1:2007
$215.11
Sampling procedures for inspection by variables – Guide to single sampling plans indexed by acceptance quality limit (AQL) for lot-by-lot inspection for a single quality characteristic and a single AQL
Published By | Publication Date | Number of Pages |
BSI | 2007 | 118 |
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PDF Pages | PDF Title |
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3 | Contents Introduction 1 1 Scope 3 2 Normative references 3 3 Terms and definitions 4 4 Symbols 6 5 Acceptance quality limit (AQL) 8 6 Switching rules for normal, tightened and reduced inspection 9 7 Relation to BS 6001-1 9 8 Limiting quality protection 11 9 Planning 12 10 Choice between variables and attributes 12 11 Choice between the “s” and “s” methods 13 12 Choice of inspection level and AQL 14 13 Choice of sampling plan 14 14 Preliminary operations 15 15 Standard procedure for the “s” method 16 16 Standard procedure for the “s” method 26 17 Procedure during continuing inspection 29 18 Normality and outliers 30 19 Records 30 20 Operation of switching rules 31 21 Discontinuation and resumption of inspection 31 22 Switching between the “s” and “s” methods 32 23 Chart A – Sample size code letters of standard single sampling plans for specified qualities at 95% and 10% probabilities of acceptance 33 24 Charts B to R – Operating characteristic curves and tabulated values for single sampling plans, normal inspection: “s” method 34 25 Charts s-D to s-R – Acceptance curves for combined control of double specifications limits: “s” method 64 Annexes Annex A (normative) Table for determining the sample size code letter 77 Annex B (normative) Form k “s” method single sampling plans 78 Annex C (normative) Form k “s” method single sampling plans 81 Annex D (normative) Values of fs for maximum sample standard deviation (MSSD) 84 Annex E (normative) Values of fs for maximum process standard deviation (MPSD) 87 Annex F (normative) Estimating the process fraction nonconforming for sample size 3: “s” method 88 Annex G (normative) Type p* single sampling plans 91 Annex H (normative) Values of cu for upper control limit on the sample standard deviation 92 Annex I (normative) Supplementary acceptability constants for qualifying towards reduced inspection 93 Annex J (normative) Procedures for obtaining s and s 94 Annex K (informative) Consumer’s risk qualities 96 Annex L (informative) Producer’s risks 100 |
4 | Annex M (informative) Operating characteristics for the “s” method 104 Annex N (informative) Estimating the process fraction nonconforming for sample sizes 3 and 4: “s” method 105 Bibliography 107 List of figures Figure 1 – Example of the use of an acceptance chart for a single specification limit: “s” method 19 Figure 2 – Example of the use of an acceptance chart for a combined of double specification limits: “s” method with actual scales 25 Figure 3 – Example of the use of an acceptance chart for combined control of double specification limits: “s” method with normalized scales 26 List of tables Table A.1 – Sample size code letters and inspection levels 77 Table B.1 – Single sampling plans of Form k for normal inspection: “s” method 79 Table B.2 – Single sampling plans of Form k for tightened inspection: “s” method 79 Table B.3 – Single sampling plans of Form k for reduced inspection: “s” method 80 Table C.1 – Single sampling plans of Form k for normal inspection: “s” method 81 Table C.2 – Single sampling plans of Form k for tightened inspection: “s” method 82 Table C.3 – Single sampling plans of Form k for reduced inspection: “s” method 83 Table D.1 – Values of fs for maximum sample standard deviation for combined control of double specification limits: normal inspection, “s” method 84 Table D.2 – Values of fs for maximum sample standard deviation for combined control of double specification limits: tightened inspection, “s” method 85 Table D.3 – Values of fs for maximum sample standard deviation for combined control of double specification limits: reduced inspection, “s” method 86 Table E.1 – Values of fs for maximum process standard deviation for combined control of double specification limits: “s” method 87 Table F.1 – Estimated process fraction nonconforming, , as a function of the quality statistic Q 88 Table G.1 – Maximum allowable values, p*, of the estimated process fraction nonconforming for sample sizes 3 and 4: “s” method 91 Table H.1 – Values of cu for upper control limit on the sample standard deviation 92 Table I.1 – Supplementary acceptability constants for qualifying towards reduced inspection 93 Table K.1.s – Consumer’s risk quality (in percent) for normal inspection: “s” method 97 Table K.1.s – Consumer’s risk quality (in percent) for normal inspection: “s” method 97 |
5 | Table K.2.s – Consumer’s risk quality (in percent) under tightened inspection: “s” method 98 Table K.2.s – Consumer’s risk quality (in percent) for tightened inspection: “s” method 98 Table K.3.s – Consumer’s risk quality (in percent) under reduced inspection: “s” method 99 Table K.3.s – Consumer’s risk quality (in percent) for reduced inspection: “s” method 99 Table L.1.s – Producer’s risk (in percent) for normal inspection: “s” method 101 Table L.1.s – Producer’s risk (in percent) for normal inspection: “s” method 101 Table L.2.s – Producer’s risk (in percent) for tightened inspection: “s” method 102 Table L.2.s – Producer’s risk (in percent) for tightened inspection: “s” method 102 Table L.3.s – Producer’s risk (in percent) for reduced inspection: “s” method 103 Table L.3.s – Producer’s risk (in percent) for reduced inspection: “s” method 103 |
7 | Foreword |
9 | Introduction a) automatic protection to the consumer (by means of a switch to tightened inspection or discontinuation of sampling inspection) should a deterioration in quality be detected; b) an incentive (at the discretion of the responsible authority) to reduce inspection costs (by means of a switch to a smaller sample size) should consistently good quality be achieved. |
10 | Summary table |
11 | 1 Scope a) where the inspection procedure is to be applied to a continuing series of lots of discrete products all supplied by one producer using one production process; b) where only a single quality characteristic x of these products is taken into consideration, which must be measurable on a continuous scale; c) where the measurement error is negligible, i.e. with a standard deviation no more than 10% of the process standard deviation; d) where production is stable (under statistical control) and the quality characteristic x is distributed according to a normal distribution or a close approximation to the normal distribution; e) where a contract or standard defines a lower specification limit L, an upper specification limit U, or both; an item is quali… 2) x u U (i.e. the upper specification limit is not violated); 3) x W L and x u U (i.e. neither the lower nor the upper specification limit is violated). 2 Normative references |
12 | 3 Terms and definitions 3.1 inspection by variables 3.2 sampling inspection 3.3 acceptance sampling inspection acceptance sampling 3.4 acceptance sampling inspection by variables 3.5 process fraction nonconforming 3.6 acceptance quality limit AQL NOTE See Clause 5. 3.7 quality level 3.8 limiting quality LQ NOTE See 13.1. 3.9 nonconformity |
13 | 3.10 nonconforming unit 3.11 “s” method acceptance sampling plan NOTE See Clause 15. 3.12 “s” method acceptance sampling plan NOTE See Clause 16. 3.13 specification limit 3.14 lower specification limit 3.15 upper specification limit U 3.16 combined control NOTE See 5.3. 3.17 acceptability constant k NOTE See 15.2 and 16.2. 3.18 quality statistic Q NOTE See 15.2 and 16.2. 3.19 lower quality statistic QL NOTE See Clause 4, 15.2 and 16.2. |
14 | 3.20 upper quality statistic QU NOTE See Clause 4, 15.2 and 16.2. 3.21 maximum sample standard deviation MSSD smax NOTE See 15.4. 3.22 maximum process standard deviation MPSD smax NOTE See 16.3. 3.23 switching rule NOTE See Clause 20. 3.24 measurement 4 Symbols |
16 | 5 Acceptance quality limit (AQL) 5.1 Concept 5.2 Use 5.3 Specifying AQLs 5.4 Preferred AQLs 5.5 Caution 5.6 Limitation |
17 | 6 Switching rules for normal, tightened and reduced inspection 7 Relation to BS 6001-1 7.1 Similarities a) This British Standard is complementary to BS 6001-1; the two standards share a common philosophy and, as far as possible, their procedures and vocabulary are the same. b) Both use the AQL to index the sampling plans and the preferred values used in this document are identical with those given for percent nonconforming in BS 6001-1 (i.e. from 0.01% to 10%). c) In both British Standards, lot size and inspection level (inspection level II in default of other instructions) determine a s… d) The switching rules are essentially equivalent. |
18 | 7.2 Differences a) Determination of acceptability. Acceptability for a BS 6001-1 attributes sampling plan for percent nonconforming is determine… b) Normality. In BS 6001-1, there is no requirement relating to the distribution of the characteristics. However, in this Britis… c) Operating characteristic curves (OC curves). The OC curves of the variables plans in this standard are not identical to those… d) Producer’s risk. For process quality precisely at the AQL, the producer’s risk that a lot will not be accepted tends to decre… e) Sample sizes. The variables sample sizes for given combinations of sample size code letter and AQL are usually smaller than t… f) Double sampling plans. Double sampling plans by variables are presented separately, in BS 6002-3. g) Multiple sampling plans. No multiple sampling plans by variables are given in this British Standard. |
19 | h) Average outgoing quality limit (AOQL). The AOQL concept is mainly of value when 100% inspection and rectification is feasible… 8 Limiting quality protection 8.1 Use of individual plans 8.2 Consumer’s risk quality tables 8.3 Producer’s risk tables |
20 | 8.4 Operating characteristic curves 9 Planning 10 Choice between variables and attributes a) In terms of economics, it is necessary to compare the total cost of the relatively simple inspection of a larger number of it… b) In terms of the knowledge gained, the advantage lies with inspection by variables, as the information obtained indicates more precisely how good the product is. Earlier warning may therefore be given if the quality is slipping. c) An attributes scheme can be more readily understood and accepted; for example, it may at first be difficult to accept that, w… |
21 | d) From a comparison of the size of the samples required for the same AQL from standard plans for inspection by attributes, such… e) Inspection by variables is particularly appropriate in conjunction with the use of control charts for variables. f) Variables sampling has a substantial advantage when the inspection process is expensive, for example in the case of destructive testing. g) A variables scheme becomes relatively more complicated to operate as the number of measurements to be taken on each item increases. (For two or more quality characteristics, this part of BS 6002 does not apply. See Part 2 for details.) h) The use of this British Standard is only applicable when there is reason to believe that the distribution of measurements of the quality characteristic is normal. In case of doubt, the responsible authority should be consulted. 11 Choice between the “s” and “s” methods |
22 | 12 Choice of inspection level and AQL 13 Choice of sampling plan 13.1 Standard plans |
23 | 13.2 Special plans 14 Preliminary operations a) check that production is considered to be continuing and that the distribution of the quality characteristic can be considered to be normal; b) check whether the “s” method is to be used initially or whether the standard deviation is stable and known, in which case the “s” method should be used; c) check that the inspection level to be used has been designated. If none has been given, inspection level II should be used; d) check, for a quality characteristic with double specification limits, that nonconformities beyond each limit are of equal importance. If this is not the case, refer to BS 6002-2; e) check that an AQL has been designated, and that it is one of the preferred AQLs for use with this British Standard. If it is not, then the tables are not applicable. |
24 | 15 Standard procedure for the “s” method 15.1 Obtaining a plan, sampling and preliminary calculations a) With the inspection level given (normally this will be II) and with the lot size, obtain the sample size code letter using Table A.1. b) For a single specification limit, enter Table B.1, B.2 or B.3 as appropriate with this code letter and the AQL, and obtain th… c) Take a random sample of size n, measure the characteristic x in each item and then calculate the sample mean, and s, the samp… 15.2 Acceptability criteria for single specification limits |
26 | 15.3 Graphical method for a single specification limit |
27 | Figure 1 Example of the use of an acceptance chart for a single specification limit: “s” method 15.4 Acceptability criterion for combined control of double specification limits 15.4.1 General |
28 | 15.4.2 Procedure for sample size 3 |
30 | 15.4.3 Procedure for sample size 4 |
31 | 15.4.4 Procedure for sample sizes greater than 4 |
33 | Figure 2 Example of the use of an acceptance chart for a combined of double specification limits: “s” method with actual scales |
34 | Figure 3 Example of the use of an acceptance chart for combined control of double specification limits: “s” method with normalized scales 16 Standard procedure for the “s” method 16.1 Obtaining a plan, sampling and preliminary calculations |
35 | 16.2 Acceptability criteria for a single specification limit |
36 | 16.3 Acceptability criterion for combined control of double specification limits a) Before sampling, enter Table E.1 with the AQL to determine the value of the factor fs. b) Calculate the maximum allowable value of the process standard deviation, using the formula smax = (U – L)fs for the MPSD. c) Compare the value of the process standard deviation s with smax. If s exceeds smax, the process is unacceptable and sampling inspection is pointless until it is demonstrated that the process variability has been adequately reduced. d) If s u smax, use the lot size and given inspection level to determine the sample size code letter from Table A.1. e) From the sample size code letter and inspection severity (i.e. whether inspection is normal, tightened or reduced) determine the sample size, n, and acceptability constant, k, from Table C.1, C.2 or C.3. f) Calculate the upper allowable bound, , to sample means from the formula = U – ks, and the lower allowable bound from the formula = L + ks. g) Select a random sample of size n from the lot and calculate the sample mean . The acceptability criterion is: If u u , the lot is acceptable; if , the lot is not acceptable. |
37 | 17 Procedure during continuing inspection a) the characteristic being inspected is normally distributed; b) records are kept; c) the switching rules are obeyed; |
38 | 18 Normality and outliers 18.1 Normality 18.2 Outliers 19 Records 19.1 Control charts 19.2 Lots that are not accepted |
39 | 20 Operation of switching rules a) these lots would have been acceptable if the AQL had been one step tighter; b) production is in statistical control; c) reduced inspection is considered desirable by the responsible authority. a) a lot is not accepted; b) production becomes irregular or delayed; c) reduced inspection is no longer considered desirable by the responsible authority. 21 Discontinuation and resumption of inspection |
40 | 22 Switching between the “s” and “s” methods 22.1 Estimating the process standard deviation 22.2 State of statistical control 22.3 Switching from the “s” method to the “s” method 22.4 Switching from the “s” method to the “s” method |
41 | 23 Chart A – Sample size code letters of standard single sampling plans for specified qualities at 95% and 10% probabilities of acceptance |
42 | 24 Charts B to R – Operating characteristic curves and tabulated values for single sampling plans, normal inspection: “s” method 24.1 Operating characteristic curves and tabulated values for sample size code letter B: “s” method Chart B – Operating characteristic curves and sample size code letter B, normal inspection (except where otherwise indicated) |
43 | Tabulated values for operating characteristic curves for single sampling plans |
44 | 24.2 Operating characteristic curves and tabulated values for sample size code letter C: “s” method Chart C – Operating characteristic curves and sample size code letter C, normal inspection (except where otherwise indicated) |
45 | Tabulated values for operating characteristic curves for single sampling plans |
46 | 24.3 Operating characteristic curves and tabulated values for sample size code letter D: “s” method Chart D – Operating characteristic curves and sample size code letter D, normal inspection (except where otherwise indicated) |
47 | Tabulated values for operating characteristic curves for single sampling plans |
48 | 24.4 Operating characteristic curves and tabulated values for sample size code letter E: “s” method Chart E – Operating characteristic curves and sample size code letter E, normal inspection (except where otherwise indicated) |
49 | Tabulated values for operating characteristic curves for single sampling plans |
50 | 24.5 Operating characteristic curves and tabulated values for sample size code letter F: “s” method Chart F – Operating characteristic curves and sample size code letter F, normal inspection (except where otherwise indicated) |
51 | Tabulated values for operating characteristic curves for single sampling plans |
52 | 24.6 Operating characteristic curves and tabulated values for sample size code letter G: “s” method Chart G – Operating characteristic curves and sample size code letter G, normal inspection (except where otherwise indicated) |
53 | Tabulated values for operating characteristic curves for single sampling plans |
54 | 24.7 Operating characteristic curves and tabulated values for sample size code letter H: “s” method Chart H – Operating characteristic curves and sample size code letter H, normal inspection (except where otherwise indicated) |
55 | Tabulated values for operating characteristic curves for single sampling plans |
56 | 24.8 Operating characteristic curves and tabulated values for sample size code letter J: “s” method Chart J – Operating characteristic curves and sample size code letter J, normal inspection (except where otherwise indicated) |
57 | Tabulated values for operating characteristic curves for single sampling plans |
58 | 24.9 Operating characteristic curves and tabulated values for sample size code letter K: “s” method Chart K – Operating characteristic curves and sample size code letter K, normal inspection (except where otherwise indicated) |
59 | Tabulated values for operating characteristic curves for single sampling plans |
60 | 24.10 Operating characteristic curves and tabulated values for sample size code letter L: “s” method Chart L – Operating characteristic curves and sample size code letter L, normal inspection (except where otherwise indicated) |
61 | Tabulated values for operating characteristic curves for single sampling plans |
62 | 24.11 Operating characteristic curves and tabulated values for sample size code letter M: “s” method Chart M – Operating characteristic curves and sample size code letter M, normal inspection (except where otherwise indicated) |
63 | Tabulated values for operating characteristic curves for single sampling plans |
64 | 24.12 Operating characteristic curves and tabulated values for sample size code letter N: “s” method Chart N – Operating characteristic curves and sample size code letter N, normal inspection (except where otherwise indicated) |
65 | Tabulated values for operating characteristic curves for single sampling plans |
66 | 24.13 Operating characteristic curves and tabulated values for sample size code letter P: “s” method Chart P – Operating characteristic curves and sample size code letter P, normal inspection (except where otherwise indicated) |
67 | Tabulated values for operating characteristic curves for single sampling plans |
68 | 24.14 Operating characteristic curves and tabulated values for sample size code letter Q: “s” method Chart Q – Operating characteristic curves and sample size code letter Q, normal inspection (except where otherwise indicated) |
69 | Tabulated values for operating characteristic curves for single sampling plans |
70 | 24.15 Operating characteristic curves and tabulated values for sample size code letter R: “s” method Chart R – Operating characteristic curves and sample size code letter R, normal inspection (except where otherwise indicated) |
71 | Tabulated values for operating characteristic curves for single sampling plans |
72 | 25 Charts s-D to s-R – Acceptance curves for combined control of double specifications limits: “s” method 25.1 Charts s-D – Acceptance curves for combined control of double specifications limits for sample size code letter D under normal and tightened inspection and for sample size code letter F under reduced inspection |
73 | 25.2 Charts s-E – Acceptance curves for combined control of double specifications limits for sample size code letter E under normal and tightened inspection and for sample size code letter G under reduced inspection |
74 | 25.3 Charts s-F – Acceptance curves for combined control of double specifications limits for sample size code letter F under normal and tightened inspection and for sample size code letter H under reduced inspection |
75 | 25.4 Charts s-G – Acceptance curves for combined control of double specifications limits for sample size code letter G under normal and tightened inspection and for sample size code letter J under reduced inspection |
76 | 25.5 Charts s-H – Acceptance curves for combined control of double specifications limits for sample size code letter H under normal and tightened inspection and for sample size code letter K under reduced inspection |
77 | 25.6 Charts s-J – Acceptance curves for combined control of double specifications limits for sample size code letter J under normal and tightened inspection and for sample size code letter L under reduced inspection |
78 | 25.7 Charts s-K – Acceptance curves for combined control of double specifications limits for sample size code letter K under normal and tightened inspection and for sample size code letter M under reduced inspection |
79 | 25.8 Charts s-L – Acceptance curves for combined control of double specifications limits for sample size code letter L under normal and tightened inspection and for sample size code letter N under reduced inspection |
80 | 25.9 Charts s-M – Acceptance curves for combined control of double specifications limits for sample size code letter M under normal and tightened inspection and for sample size code letter P under reduced inspection |
81 | 25.10 Charts s-N – Acceptance curves for combined control of double specifications limits for sample size code letter N under normal and tightened inspection and for sample size code letter Q under reduced inspection |
82 | 25.11 Charts s-P – Acceptance curves for combined control of double specifications limits for sample size code letter P under normal and tightened inspection and for sample size code letter R under reduced inspection |
83 | 25.12 Charts s-Q – Acceptance curves for combined control of double specifications limits for sample size code letter Q under normal and tightened |
84 | 25.13 Charts s-R – Acceptance curves for combined control of double specifications limits for sample size code letter R under normal and tightened |
85 | Annex A (normative) Table for determining the sample size code letter Table A.1 Sample size code letters and inspection levels |
86 | Annex B (normative) Form k “s” method single sampling plans Table B.1 Single sampling plans of Form k for normal inspection: “s” method |
87 | Table B.2 Single sampling plans of Form k for tightened inspection: “s” method |
88 | Table B.3 Single sampling plans of Form k for reduced inspection: “s” method |
89 | Annex C (normative) Form k “s” method single sampling plans Table C.1 Single sampling plans of Form k for normal inspection: “s” method |
90 | Table C.2 Single sampling plans of Form k for tightened inspection: “s” method |
91 | Table C.3 Single sampling plans of Form k for reduced inspection: “s” method |
92 | Annex D (normative) Values of fs for maximum sample standard deviation (MSSD) Table D.1 Values of fs for maximum sample standard deviation for combined control of double specification limits: normal inspection, “s” method |
93 | Table D.2 Values of fs for maximum sample standard deviation for combined control of double specification limits: tightened inspection, “s” method |
94 | Table D.3 Values of fs for maximum sample standard deviation for combined control of double specification limits: reduced inspection, “s” method |
95 | Annex E (normative) Values of fs for maximum process standard deviation (MPSD) Table E.1 Values of fs for maximum process standard deviation for combined control of double specification limits: “s” method |
96 | Annex F (normative) Estimating the process fraction nonconforming for sample size 3: “s” method Table F.1 Estimated process fraction nonconforming, pˆ, as a function of the quality statistic Q |
97 | Table F.1 Estimated process fraction nonconforming, pˆ, as a function of the quality statistic Q (continued) |
98 | Table F.1 Estimated process fraction nonconforming, pˆ, as a function of the quality statistic Q (concluded) |
99 | Annex G (normative) Type p* single sampling plans Table G.1 Maximum allowable values, p*, of the estimated process fraction nonconforming for sample sizes 3 and 4: “s” method |
100 | Annex H (normative) Values of cu for upper control limit on the sample standard deviation Table H.1 Values of cu for upper control limit on the sample standard deviation |
101 | Annex I (normative) Supplementary acceptability constants for qualifying towards reduced inspection Table I.1 Supplementary acceptability constants for qualifying towards reduced inspection |
102 | Annex J (normative) Procedures for obtaining s and s J.1 Procedure for obtaining s |
103 | J.2 Procedure for obtaining s |
104 | Annex K (informative) Consumer’s risk qualities |
105 | Table K.1.s Consumer’s risk quality (in percent) for normal inspection: “s” method Table K.1.s Consumer’s risk quality (in percent) for normal inspection: “s” method |
106 | Table K.2.s Consumer’s risk quality (in percent) under tightened inspection: “s” method Table K.2.s Consumer’s risk quality (in percent) for tightened inspection: “s” method |
107 | Table K.3.s Consumer’s risk quality (in percent) under reduced inspection: “s” method Table K.3.s Consumer’s risk quality (in percent) for reduced inspection: “s” method |
108 | Annex L (informative) Producer’s risks |
109 | Table L.1.s Producer’s risk (in percent) for normal inspection: “s” method Table L.1.s Producer’s risk (in percent) for normal inspection: “s” method |
110 | Table L.2.s Producer’s risk (in percent) for tightened inspection: “s” method Table L.2.s Producer’s risk (in percent) for tightened inspection: “s” method |
111 | Table L.3.s Producer’s risk (in percent) for reduced inspection: “s” method Table L.3.s Producer’s risk (in percent) for reduced inspection: “s” method |
112 | Annex M (informative) Operating characteristics for the “s” method M.1 Formula for probability of acceptance M.2 Example M.3 Comparison with tabulated value for the “s” method |
113 | Annex N (informative) Estimating the process fraction nonconforming for sample sizes 3 and 4: “s” method N.1 General formula for sample size n N.2 Formula for sample size 3 |
114 | N.3 Formula for sample size 4 |
115 | Bibliography [1] MELGAARD, H. and THYREGOD, P. (2001). Acceptance Sampling by Variables under Measurement Uncertainty, pp. 47-60. In: Lenz, H.J. and Wilrich, P.-Th. [Editors]. Frontiers in Statistical Quality Control 6, Physica-Verlag, Heidelberg; New York [2] GÖB, R. (2001). Methodological Foundations of Statistical Lot Inspection, pp. 3-24. In: Lenz, H.J. and Wilrich, P.-Th. [Editors]. Frontiers in Statistical Quality Control 6, Physica-Verlag, Heidelberg; New York |