Operating Characteristic (OC) curves for on-line sampling and inspection.

  1. Law
  2. CFR 7
  3. Agriculture
  4. Regulations of the Department of Agriculture
  5. Agricultural Marketing Service (Standards, Inspections, Marketing Practices), Department of Agriculture
  6. Commodity Standards and Container Requirements
  7. Standards for Condition of Food Containers
  8. Miscellaneous
  9. Operating Characteristic (OC) curves for on-line sampling and inspection.

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§ 42.140 Operating Characteristic (OC) curves for on-line sampling and inspection.

(a) This section contains the Operating Characteristic (OC) curve for each of the sampling plans given in Tables I, I-A, II, II-A, III, and III-A. The OC curve and the corresponding sampling plans are listed by AQL.

(b) Different acceptance and rejection criteria are provided for each AQL. The criteria for each AQL must be obtained from the applicable sampling plan tables.

(c) The curves show the ability of the various sampling plans to distinguish between good and bad lots. This can be illustrated by examining OC curve 6 for an AQL of 0.25 defects per hundred units in the Reduced and Normal Inspection Plans. If the quality of the lots submitted for inspection is poorer than the AQL of 0.25 defects per hundred units, fewer lots will be accepted. For example, OC curve 6 shows that when the quality of lots submitted for inspection is 1.0 defects per hundred units, only 26 percent of the lots are expected to be accepted. Conversely when the quality of the lots submitted for inspection is better than the AQL of 0.25 defects per hundred units, most lots are expected to be accepted. For example, the same OC curve 6 shows that when the quality of lots submitted for inspection is 0.10 defects per hundred units, about 99 percent of the lots are expected to be accepted.

(d) The table of sampling plans that correspond to OC curve 6 can be found over the curves for an AQL of 0.25 defects per hundred units in the Reduced and Normal Inspection Plan. An examination of this table reveals that there is one single and one double sampling plan that have OC curves comparable to OC curve 6. The first plan listed is a single plan requiring the inspection of 500 individual containers. Under this plan the lot is accepted as meeting the requirements for an AQL of 0.25 if there are 3 or less defects in the sample or rejected if there are 4 or more defects in the sample.

(e) The next plan that is listed in the column headed 6 for an AQL of 0.25 is a double sampling plan that requires the initial inspection of 228 individual containers. The lot will be accepted as meeting the requirements of an AQL of 0.25 if there are no defects in the sample, and rejected if there are 3 or more defects in the sample. In the event that the number of defects is between the acceptance (0) and rejection (3) numbers, additional containers must be inspected. In this case, the table indicates that a total of 516 containers must be inspected before a decision can be made to either accept or reject the lot. This will require the inspection of 288 more containers (516 − 228 = 288).

If there are 3 or less defects in the total sample, the lot will be accepted. If there are 4 or more defects in the total sample, the lot will be rejected. The other double sampling plans operate in a similar manner with the only differences being the sample sizes and acceptance and rejection numbers.

Expand Table

Reduced and Normal Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 0.15 Defects per Hundred Units

[Sampling plans - AQL = 0.15]

Comparable sampling plans Identification number of OC curve
R1 R2 R3 R4 N4 N5 N6 N7 N8
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 29 1 2 84 1 2 126 0 1 315 1 2 168 1 2 264 1 2 500 2 3 800 3 4 1,250 4 5
Double 18 0 2 36 0 2 120 0 2 174 0 2 252 0 3 456 0 4
36 1 2 96 1 2 180 1 2 336 1 2 540 2 3 864 3 4

nc = Cumulative sample size. Ac = Acceptance number. Re = Rejection number.

Expand Table

Tightened Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 0.15 Defects per Hundred Units

[Sampling plans - AQL = 0.15]

Comparable sampling plans Identification number of OC curves
1 2 3 4
nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 264 0 1 500 1 2 800 2 3 1,250 3 4
Double 360 0 2 456 0 3 576 0 3
516 1 2 864 2 3 1,296 3 4

nc = Cumulative sample size. Ac = Acceptance number. Re = Rejection number.

Expand Table

Reduced and Normal Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 0.25 Defects per Hundred Units

[Sampling plans - AQL = 0.25]

Comparable sampling plans Identification number OC curves
R1 N2 R3 N and R4 N and R5 N6 N7
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 29 1 2 84 0 1 84 1 2 168 1 2 315 2 3 500 3 4 800 4 5
Double 18 0 2 36 0 2 120 0 2 168 0 3 228 0 3
18 1 2 96 1 2 180 1 2 348 2 3 516 3 4

nc = Cumulative sample size. Ac = Acceptance number. Re = Rejection number.

Expand Table

Tightened Inspection Plans - Sampling Plans and Operation Characteristics (OC) Curves for AQL = 0.25 Defects per Hundred Units

[Sampling plans - AQL = 0.25]

Comparable sampling plans Identification number of OC curves
1 2 3 4 5
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 168 0 1 315 1 2 500 2 3 800 3 4 1,250 4 5
Double 168 0 2 228 0 3 456 0 4
348 1 2 516 2 3 864 3 4

nc = Cumulative sample size. Ac = Acceptance number. Re = Rejection number.

Expand Table

Reduced and Normal Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 0.50 Defects per Hundred Units

[Sampling plans - AQL = 0.50]

Comparable sampling plans Identification number of OC curves
R1 N and R2 N and R3 N and R4 N5 N6
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 29 1 2 84 1 2 168 2 3 315 3 4 500 5 6 800 7 8
Double 18 0 2 36 0 2 120 0 3 168 0 4 228 0 5
36 1 2 96 1 2 180 2 3 348 3 4 516 5 6

nc = Cumulative sample size. Ac = Acceptance number. Re = Rejection number.

Expand Table

Tightened Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 0.50 Defects per Hundred Units

[Sampling plans - AQL = 0.50]

Comparable sampling plans Identification number of OC curves
1 2 3 4 5
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 168 1 2 315 2 3 500 3 4 800 4 5 1,250 6 7
Double 120 0 2 168 0 3 228 0 3 456 1 5
180 1 2 348 2 3 516 3 4 864 4 5

nc = Cumulative sample size. Ac = Acceptance number. Re = Rejection number.

Expand Table

Reduced and Normal Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 1.00 Defects per Hundred Units

[Sampling plans - AQL = 1.00]

Comparable sampling plans Identification number of OC curves
R1 N and R2 N and R3 N and R4 N5 N6
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 29 1 2 84 2 3 168 4 5 315 6 7 500 9 10 800 13 14
Double 18 0 2 36 0 3 120 2 5 168 1 5 228 2 7
36 1 2 96 2 3 180 4 5 348 7 8 516 9 10

nc = Cumulative sample size. Ac = Acceptance number. Re = Rejection number.

Expand Table

Tightened Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 1.00 Defects per Hundred Units

[Sampling plans - AQL = 1.00]

Comparable sampling plans Identification number of OC curves
1 2 3 4 5
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 168 2 3 315 3 4 500 5 6 800 7 8 1,250 10 11
Double 120 0 3 168 0 4 228 0 5 456 2 6
180 2 3 348 3 4 516 5 6 864 8 9

nc = Cumulative sample size Ac = Acceptance number. Re = Rejection number.

Expand Table

Reduced and Normal Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 1.50 Defects per Hundred Units

[Sampling plans - AQL = 1.50]

Comparable sampling plans Identification number of OC curves
R1 N and R2 N and R3 N and R4 N5 N6
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 29 1 2 84 3 4 168 5 6 315 8 9 500 12 13 800 18 19
Double 18 0 2 36 0 4 120 2 6 168 2 7 228 3 9
36 1 2 96 3 4 180 5 6 348 9 10 516 12 13

nc = Cumulative sample size. Ac = Acceptance number. Re = Rejection number.

Expand Table

Tightened Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 1.50 Defects per Hundred Units

[Sampling plans - AQL = 1.50]

Comparable sampling plans Identification number of OC curves
1 2 3 4 5
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 168 4 5 315 6 7 500 9 10 800 13 14 1,250 19 20
Double 120 2 5 168 1 5 228 2 7 456 5 10
180 4 5 348 7 8 516 9 10 864 14 15

nc = Cumulative sample size. Ac = Acceptance number. Re = Rejection number.

Expand Table

Reduced and Normal Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 2.50 Defects per Hundred Units

[Sampling plans - AQL = 2.50]

Comparable sampling plans Identification number of OC curves
R1 N and R2 N and R3 N and R4 N5 N6
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 29 2 3 84 4 5 168 7 8 315 13 14 500 18 19 800 27 28
Double 18 0 3 36 0 4 120 3 7 168 5 10 228 5 11
36 2 3 96 4 5 180 8 9 348 14 15 516 19 20

nc = Cumulative sample size. Ac = Acceptance number. Re = Rejection number.

Expand Table

Tightened Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 2.50 Defects per Hundred Units

[Sampling plans - AQL = 2.50]

Comparable sampling plans Identification number of OC curves
1 2 3 4 5
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 168 5 6 315 8 9 500 12 13 800 18 19 1,250 26 27
Double 120 2 6 168 2 7 228 3 9 456 8 13
180 5 6 348 9 10 516 12 13 864 19 20

nc = Cumulative sample size. Ac = Acceptance number. Re = Rejection number.

Expand Table

Reduced and Normal Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 4.00 Defects per Hundred Units

[Sampling plans - AQL = 4.00]

Comparable sampling plans Identification number of OC curves
R1 N and R2 N and R3 N and R4 N5 N6
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 29 3 4 84 6 7 168 11 12 315 19 20 500 28 29 800 42 43
Double 18 1 3 36 0 5 120 6 10 168 7 13 228 8 17
36 4 5 96 7 8 180 12 13 348 21 22 516 29 30

nc = Cumulative sample size. Ac = Acceptance number. Re = Rejection number.

Expand Table

Tightened Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 4.00 Defects per Hundred Units

[Sampling plans - AQL = 4.00]

Comparable sampling plans Identification number of OC curves
1 2 3 4 5
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 168 7 8 315 13 14 500 18 19 800 27 28 1,250 41 42
Double 120 3 7 168 5 10 228 5 11 456 12 19
180 8 9 348 14 15 516 19 20 864 29 30

nc = Cumulative sample size. Ac = Acceptance number. Re = Rejection number.

Expand Table

Reduced and Normal Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 2.50 Defects per Hundred Units

[Sampling plans - AQL = 6.50]

Comparable sampling plans Identification number of OC curves
R1 N and R2 N and R3 N and R4 N5 N6
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 29 4 5 84 9 10 168 16 17 315 28 29 500 42 43 800 64 65
Double 18 1 4 36 2 7 120 10 14 168 12 18 228 15 24
36 5 6 96 10 11 180 17 18 348 31 32 516 43 44

nc = Cumulative sample size. Ac = Acceptance number. Re = Rejection number.

Expand Table

Tightened Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 6.50 Defects per Hundred Units

[Sampling plans - AQL = 6.50]

Comparable sampling plans Identification number of OC curves
1 2 3 4 5
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 168 11 12 315 19 20 500 28 29 800 42 43 1,250 63 64
Double 120 6 10 168 7 13 228 8 17 456 21 28
180 12 13 348 21 22 516 29 30 864 44 45

nc = Cumulative sample size. Ac = Acceptance number. Re = Rejection number.

Expand Table

Reduced and Normal Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 10.00 Defects per Hundred Units

[Sampling plans - AQL = 10.00]

Comparable sampling plans Identification number of OC curves
R1 N and R2 N and R3 N and R4 N5 N6
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 29 5 6 84 13 14 168 23 24 315 41 42 500 62 63 800 95 96
Double 18 2 5 36 3 9 120 14 19 168 19 26 228 23 34
36 6 7 96 15 16 180 25 26 348 45 46 516 64 65

nc = Cumulative sample size. Ac = Acceptance number. Re = Rejection number.

Expand Table

Tightened Inspection Plans - Sampling Plans and Operating Characteristic (OC) Curves for AQL = 10.00 Defects per Hundred Units

[Sampling plans - AQL = 10.00]

Comparable sampling plans Identification number of OC curves
1 2 3 4 5
nc Ac Re nc Ac Re nc Ac Re nc Ac Re nc Ac Re
Single 168 16 17 315 28 29 500 42 43 800 64 65 1,250 96 97
Double 120 10 14 168 12 18 228 15 24 456 32 41
180 17 18 348 31 32 516 43 44 864 69 70

nc = Cumulative sampling size. Ac = Acceptance number. Re = Rejection number.

[31 FR 4687, Mar. 19, 1966; 31 FR 4949, Mar. 25, 1966, as amended at 36 FR 18457, Sept. 15, 1971. Redesignated at 41 FR 42640, Sept. 28, 1976 and 42 FR 32514, June 27, 1977, further redesignated at 45 FR 69424, Oct. 21, 1980 and 46 FR 63203, Dec. 31, 1981]


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