Title 7

SECTION 42.140

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

§ 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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]