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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
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
BS 6002-1:2007
$215.11