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BS 6002-3:2005

BS 6002-3:2005

$215.11

Sampling procedures for inspection by variables – Guide to double sampling schemes indexed by acceptance quality limit (AQL) for lot-by-lot inspection

Published By Publication Date Number of Pages
BSI 2005 110
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This British Standard specifies an acceptance sampling system of double sampling schemes for inspection by variables for percent nonconforming. It is indexed in terms of the acceptance quality limit (AQL).

The objectives of the methods laid down in this British Standard are to ensure that lots of acceptable quality have a high probability of acceptance and that the probability of non-accepting inferior lots is as high as practicable. This is achieved by means of the switching rules, which provide:

  1. 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;
  2. 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.

In this British Standard, the acceptability of a lot is implicitly or explicitly determined from an estimate of the percentage of nonconforming items in the process, based on either one or two random samples of items from the lot.

This British Standard is primarily designed for use under the following conditions:

  1. 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. If there are different producers or production processes, this British Standard shall be applied to each one separately;
  2. where the items of product have a single quality characteristic (for multiple quality characteristics, see Annex A, Annex B and Annex C, which are all informative);
  3. where the quality characteristic is measurable on a continuous scale;
  4. where the measurement error is negligible (i.e. with a standard deviation no more than 10 % of the corresponding process standard deviation);
  5. where production is stable (under statistical control) and the quality characteristic is distributed, at least to a close approximation, according to a normal distribution;

CAUTION. The procedures in this British Standard are not suitable for application to lots that have been screened previously for nonconforming items.

  1. where the possibility of having to select and inspect a second sample is administratively acceptable;
  2. where a contract or standard defines an upper specification limit U, a lower specification limit L, or both on the quality characteristic. An item is deemed to conform if its measured quality characteristic x satisfies the appropriate one of the following inequalities:
    1. x ≤ U (i.e. the upper specification limit is not violated);
    2. x ≥ L (i.e. the lower specification limit is not violated);
    3. x ≤ U and x ≥ L (i.e. neither the upper nor the lower specification limit is violated).

NOTE Inequalities i) and ii) are called cases with a “single specification limit”, and iii) is the case with “double specification limits”.

For double specification limits, a further distinction is made between combined control, separate control and complex control, as follows:

  • combined control is where a single AQL applies to nonconformity beyond both limits;
  • separate control is where separate AQLs apply to nonconformity beyond each of the limits;
  • complex control is where one AQL applies to nonconformity beyond the limit that is of greater seriousness, and a larger AQL applies to the total nonconformity beyond both limits.

PDF Catalog

PDF Pages PDF Title
1 BRITISH STANDARD
2 Committees responsible for this British�Standard
3 Contents
9 Introduction
1 Scope
10 2 Normative references
3 Terms and definitions
inspection by variables
sampling inspection
acceptance sampling inspection
11 double sampling inspection
acceptance sampling inspection by variables
process average
acceptance quality limit
quality level
limiting quality
nonconformity
nonconforming unit
“s” method acceptance sampling plan
“Ö” method acceptance sampling plan
12 specification limit
lower specification limit
upper specification limit
combined control
separate control
complex control
acceptability constant
quality statistic
lower quality statistic
upper quality statistic
13 maximum sample standard deviation
maximum process standard deviation
switching rule
measurement
average sample number
4 Symbols and abbreviations
14 5 Acceptance quality limit (AQL)
5.1 Concept
15 5.2 Use
5.3 Specifying AQLs
5.4 Preferred AQLs
5.5 Caution
5.6 Limitation
6 Switching rules for normal, tightened and reduced inspection
16 7 Relation to BS�6001-1
7.1 Similarities to BS�6001-1
7.2 Differences from BS�6001-1
17 8 Limiting quality protection
8.1 Use of individual plans
8.2 Consumer’s risk quality tables
8.3 Producer’s risk tables
8.4 Operating characteristic curves
9 Planning
18 10 Choice between variables and attributes
11 Choice of method
12 Choice between single and double sampling plans
19 13 Choice of inspection level and AQL
14 Choice of sampling scheme
14.1 Standard schemes
20 14.2 Special schemes
15 Preliminary operations
16 Standard univariate “
16.1 Obtaining a plan, sampling and preliminary calculations
21 16.2 Form
23 16.3 Form
24 16.4 Form
29 16.5 Form
17 Standard univariate “÷” method procedures
17.1 Obtaining a plan, sampling and preliminary calculations
30 17.2 Form
32 17.3 Form
33 17.4 Form
34 17.5 Form
35 18 Procedure during continuing inspection
19 Normality and outliers
19.1 Normality
19.2 Outliers
36 20 Records
20.1 Control charts
20.2 Lots that are non-accepted
21 Operation of switching rules
21.1 Normal inspection
21.2 Tightened inspection
21.3 Reduced inspection
37 22 Discontinuation and resumption of inspection
23 Switching between the “
23.1 Estimating the process standard deviation
23.2 State of statistical control
23.3 Switching from the “
23.4 Switching from the “÷” method to the “
Table 1 — Sample size code letters and inspection levels BS 6002-1.
38 Table 2.1 — Form k double sampling plans for normal inspection (master table) — “s” method
39 Table 2.2 — Form k double sampling plans for tightened inspection (master table) — “s” method
40 Table 2.3 — Form k double sampling plans for reduced inspection (master table) — “s” method
41 Table 3.1 — Form k double sampling plans for normal inspection (master table) — “Ö” method
42 Table 3.2 — Form k double sampling plans for tightened inspection (master table) — “Ö” method
43 Table 3.3 — Form k double sampling plans for reduced inspection (master table) — “Ö” method
44 Table 4.1 — Values of fs for maximum sample standard deviation (MSSD) for combined control of double specification limits — Normal inspection, “s” method
45 Table 4.2 — Values of fs for maximum sample standard deviation (MSSD) for combined control of double specification limits — Tightened inspection, “s” method
46 Table 4.3 — Values of fs for maximum sample standard deviation (MSSD) for combined control of double specification limits — Reduced inspection, “s” method E 1.3303 .6494 F
Table 5.1 — Values of fÖ for maximum process standard deviation (MPSD) for combined control of double specification limits — “Ö” method
47 Table 5.2 — Values of fÖ for maximum process standard deviation ( MPSD) for separate control of double specification limits — “ Ö” method
48 Table 5.3 — Values of fÖ for maximum process standard deviation ( MPSD) for complex control of double specification limits — “ Ö” method
49 Table 6 — Estimated process average, , as a function of the quality statistic Q for sample size 3 — “s” method pˆ
51 Table 7.1 — Form p* double sampling plans for normal inspection (master table) — “s” method
52 Table 7.2 — Form p* double sampling plans for tightened inspection (master table) — “s” method
53 Table 7.3 — Form p* double sampling plans for reduced inspection (master table) — “s” method
54 Table 8.1 — Form p* double sampling plans for normal inspection (master table) — “Ö” method
55 Table 8.2 — Form p* double sampling plans for tightened inspection (master table) — “Ö” method
56 Table 8.3 — Form p* double sampling plans for reduced inspection (master table) — “O” method
57 Table 9 — Values of cU for upper control limit of sample standard deviation
58 Chart A — Sample size code letters of standard double sampling plans for specified qualities at 95 % and 50 % probabilities of acceptance
59 Chart C — Operating characteristic curves for double sampling plans, normal inspection — Sample size code letter C, “s” method
60 Chart D — Operating characteristic curves for double sampling plans, normal inspection — Sample size code letter D, “s” method
61 Chart E — Operating characteristic curves for double sampling plans, normal inspection — Sample size code letter E, “s” method
62 Chart F — Operating characteristic curves for double sampling plans, normal inspection — Sample size code letter F, “s” method
63 Chart G — Operating characteristic curves for double sampling plans, normal inspection — Sample size code letter G, “s” method
64 Chart H — Operating characteristic curves for double sampling plans, normal inspection — Sample size code letter H, “s” method
65 Chart J — Operating characteristic curves for double sampling plans, normal inspection — Sample size code letter J, “s” method
66 Chart K — Operating characteristic curves for double sampling plans, normal inspection — Sample size code letter K, “s” method
67 Chart L — Operating characteristic curves for double sampling plans, normal inspection — Sample size code letter L, “s” method
68 Chart M — Operating characteristic curves for double sampling plans, normal inspection — Sample size code letter M, “s” method
69 Chart N — Operating characteristic curves for double sampling plans, normal inspection — Sample size code letter N, “s” method
70 Chart P — Operating characteristic curves for double sampling plans, normal inspection — Sample size code letter P, “s” method
71 Chart Q — Operating characteristic curves for double sampling plans, normal inspection — Sample size code letter Q, “s” method
72 Chart R — Operating characteristic curves for double sampling plans, normal inspection — Sample size code letter R, “s” method
73 Annex A (informative)
A.1 Standard multivariate “s” method procedures for double sampling with independent quality characteristics
A.2 Procedure for a single class of nonconformity
A.3 Procedure for more than one class of nonconformity
74 Annex B informative)
B.1 Standard multivariate “O” method procedures for double sampling with independent qu…
B.2 Procedure for a single class of nonconformity
75 B.3 Procedure for more than one class of nonconformity
76 Annex C (informative)
Standard multivariate combined “s” and “Ö” method procedures for double sampling with independent quality characteristics
C.1 General
C.2 Procedure for a single class of nonconformity
C.3 Procedure for more than one class of nonconformity
77 Annex D (informative)
Location of text on key features
78 Annex E (normative)
Estimating the process fraction nonconforming
E.1 General
E.2 Notation
E.3 Exact formulae for a single sample of size
The exact MVUE estimator of p for the “
79 The exact MVUE estimator of p for the “B” method
E.4 Exact formulae for a double sample with each sample of size
The exact MVUE estimator of
80 The exact MVUE estimator of
E.5 Approximative procedure for the “
81 Table E.1 — Values of an
82 E.6 Simplified exact formula for�
83 E.7 Simplified exact formula for�
84 Annex F (informative)
(informative) Form k “s” method single sampling plans matched to the corresponding
single sampling plans by attributes
Table F.1 Matched single sampling plans of Form
85 Table F.2 Matched single sampling plans of Form
86 Table F.3 Matched single sampling plans of Form
87 Annex G (informative)
Form k “Ö” method single sampling plans matched to the corresponding
single sampling plans by attributes
Table G.1 Matched single sampling plans of Form
88 Table G.2 Matched single sampling plans of Form
89 Table G.3 Matched single sampling plans of Form
90 Annex H (informative)
Average sample numbers for double sampling by variables:�—�“
Table H.1 Average sample numbers for double sampling under normal inspection — “
91 Table H.2 Average sample numbers for double sampling under tightened�inspection — “
92 Table H.3 Average sample numbers for double sampling under reduced�inspection — “
93 Annex I (informative)
Producer’s risks under normal inspection (in percent) — “s” method
Table I.1 Producer’s risks under normal inspection (in percent) — “
94 Table I.2 Producer’s risks under tightened inspection (in percent) — “
95 Table I.3 Producer’s risks under reduced inspection (in percent) — “
96 Annex J (informative)
Tabulated operating characteristics for double sampling plans with known process st…
Table J.1 Tabulated “÷” method OCs for code letter C (normal and tightened inspection) and�E (reduced inspe…
Table J.2Tabulated “÷” method OCs for code letter D (normal and tightened inspection) and�F (reduced inspe…
97 Table J.3 Tabulated “÷” method OCs for code letter E (normal and tightened inspection) and�G (reduced inspe…
Table J.4 Tabulated “÷” method OCs for code letter F (normal and tightened inspection) and�H (reduced inspe…
98 Table J.5 Tabulated “÷” method OCs for code letter G (normal and tightened inspection) and�J (reduced inspe…
Table J.6 Tabulated “÷” method OCs for code letter H (normal and tightened inspection) and�K (reduced inspe…
99 Table J.7 Tabulated “÷” method OCs for code letter J (normal and tightened inspection) and�L (reduced inspe…
Table J.8 Tabulated “÷” method OCs for code letter K (normal and tightened inspection) and�M (reduced inspe…
100 Table J.9 Tabulated “÷” method OCs for code letter L (normal and tightened inspection) and�N (reduced inspe…
Table J.10 Tabulated “÷” method OCs for code letter M (normal and tightened inspection) and�P (reduced inspe…
101 Table J.11 Tabulated “÷” method OCs for code letter N (normal and tightened inspection) and�Q (reduced inspe…
Table J.12 Tabulated “÷” method OCs for code letter P (normal and tightened inspection) and�R (reduced inspe…
102 Table J.13 Tabulated “÷” method OCs for code letter Q (normal and tightened inspection)
Table J.14 Tabulated “÷” method OCs for code letter R (normal and tightened inspection)
103 Annex K (informative)
Ratios of ASNs of double sampling plans under normal inspection to the sample�size …
Table K.1 Minimum and maximum values of the ratios of the ASNs —� “
104 Table K.2 Minimum and maximum values of the ratios of the ASNs —� “
105 Annex L (informative)
Ratios of the ASNs of double sampling plans by variables to the ASNs of correspondin…
Table L.1 Minimum and maximum ASN ratios for normal inspection
106 Table L.2 Minimum and maximum ASN ratios for tightened inspection
107 Table L.3 Minimum and maximum ASN ratios for reduced inspection
109 Bibliography

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BS 6002-3:2005
$215.11