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a. . AQL LTPD. Supplement J - Acceptance Sampling Plans. Sequential Sampling Chart. 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 – 0 –. Number of defectives. | | | | | | | 10 20 30 40 50 60 70. Cumulative sample size. Figure J.1. Sequential Sampling Chart. 8 – 7 –

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Supplement j acceptance sampling plans

a

AQL LTPD

Supplement J -Acceptance SamplingPlans



Sequential sampling chart1

8

7 –

6 –

5 –

4 –

3 –

2 –

1 –

0 –

Number of defectives

| | | | | | |

10 20 30 40 50 60 70

Cumulative sample size

Figure J.1

Sequential Sampling Chart


Sequential sampling chart2

8

7 –

6 –

5 –

4 –

3 –

2 –

1 –

0 –

Number of defectives

Continue sampling

| | | | | | |

10 20 30 40 50 60 70

Cumulative sample size

Figure J.1

Sequential Sampling Chart


Sequential sampling chart3

8

7 –

6 –

5 –

4 –

3 –

2 –

1 –

0 –

Reject

Number of defectives

Continue sampling

Accept

| | | | | | |

10 20 30 40 50 60 70

Cumulative sample size

Figure J.1

Sequential Sampling Chart


Sequential sampling chart4

8

7 –

6 –

5 –

4 –

3 –

2 –

1 –

0 –

Decision to reject

Reject

Number of defectives

Continue sampling

Accept

| | | | | | |

10 20 30 40 50 60 70

Cumulative sample size

Figure J.1

Sequential Sampling Chart



Operating characteristic curve1

Probability of acceptance

Proportion defective

Figure J.2

Operating Characteristic Curve


Operating characteristic curve2

Ideal OC curve

Probability of acceptance

Proportion defective

Figure J.2

Operating Characteristic Curve


Operating characteristic curve3

Ideal OC curve

Probability of acceptance

Typical OC curve

Proportion defective

Figure J.2

Operating Characteristic Curve


Operating characteristic curve4

1.0

Ideal OC curve

a

Probability of acceptance

Typical OC curve

AQL LTPD

Proportion defective

Figure J.2

Operating Characteristic Curve



Operating characteristic curve6

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1


Operating characteristic curve7

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability

Proportion of c or less

defective defects

(p) np (Pa) Comments

n = 60

c = 1

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1


Operating characteristic curve8

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

np 0 1 2

.05 .951 .999 1.000

.10 .905 .995 1.000

.15 .861 .990 .999

.20 .819 .982 .999

.25 .779 .974 .998

.30 .741 .963 .996

.35 .705 .951 .994

.40 .670 .938 .992

.45 .638 .925 .989

.50 .607 .910 .986

.55 .577 .894 .982

.60 .549 .878 .977

.65 .522 .861 .972

Probability

Proportion of c or less

defective defects

(p) np (Pa) Comments

n = 60

c = 1

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1


Operating characteristic curve9

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

np 0 1 2

.05 .951 .999 1.000

.10 .905 .995 1.000

.15 .861 .990 .999

.20 .819 .982 .999

.25 .779 .974 .998

.30 .741 .963 .996

.35 .705 .951 .994

.40 .670 .938 .992

.45 .638 .925 .989

.50 .607 .910 .986

.55 .577 .894 .982

.60 .549 .878 .977

.65 .522 .861 .972

Probability

Proportion of c or less

Defective defects

(p) np (Pa) Comments

n = 60

c = 1

0.01 (AQL) 0.6

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1


Operating characteristic curve10

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

np 0 1 2

.05 .951 .999 1.000

.10 .905 .995 1.000

.15 .861 .990 .999

.20 .819 .982 .999

.25 .779 .974 .998

.30 .741 .963 .996

.35 .705 .951 .994

.40 .670 .938 .992

.45 .638 .925 .989

.50 .607 .910 .986

.55 .577 .894 .982

.60 .549 .878 .977

.65 .522 .861 .972

Probability

Proportion of c or less

defective defects

(p) np (Pa) Comments

n = 60

c = 1

0.01 (AQL) 0.6

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1


Operating characteristic curve11

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

np 0 1 2

.05 .951 .999 1.000

.10 .905 .995 1.000

.15 .861 .990 .999

.20 .819 .982 .999

.25 .779 .974 .998

.30 .741 .963 .996

.35 .705 .951 .994

.40 .670 .938 .992

.45 .638 .925 .989

.50 .607 .910 .986

.55 .577 .894 .982

.60 .549 .878 .977

.65 .522 .861 .972

Probability

Proportion of c or less

defective defects

(p) np (Pa) Comments

n = 60

c = 1

0.01 (AQL) 0.6 0.878

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1


Operating characteristic curve12

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

np 0 1 2

.05 .951 .999 1.000

.10 .905 .995 1.000

.15 .861 .990 .999

.20 .819 .982 .999

.25 .779 .974 .998

.30 .741 .963 .996

.35 .705 .951 .994

.40 .670 .938 .992

.45 .638 .925 .989

.50 .607 .910 .986

.55 .577 .894 .982

.60 .549 .878 .977

.65 .522 .861 .972

Probability

Proportion of c or less

defective defects

(p) np (Pa) Comments

n = 60

c = 1

0.01 (AQL) 0.6 0.878

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1


Operating characteristic curve13

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability

Proportion of c or less

defective defects

(p) np (Pa) Comments

n = 60

c = 1

0.01 (AQL) 0.6 0.878

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1


Operating characteristic curve14

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability

Proportion of c or less

defective defects

(p) np (Pa) Comments

n = 60

c = 1

0.663

0.01 (AQL) 0.6 0.878 a = 1.000 – 0.878 = 0.122

0.02 1.2 0.663

0.03 1.8 0.463

0.04 2.4 0.308

0.05 3.0 0.199

0.06 (LTPD) 3.6 0.126 b = 0.126

0.07 4.2 0.078

0.08 4.8 0.048

0.09 5.4 0.029

0.10 6.0 0.017

Probability of acceptance

0.308

0.199

0.048

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1


Operating characteristic curve15

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

0.878

0.663

Probability of acceptance

0.463

0.308

0.199

0.126

0.078

0.048

0.029

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

0.017

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1


Operating characteristic curve16

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

a = 0.122

0.878

0.663

Probability of acceptance

0.463

0.308

0.199

0.126

0.078

0.048

0.029

b = 0.126

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

0.017

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Figure J.3



Operating characteristic curve18

Operating Characteristic Curve

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.4


Operating characteristic curve19

Producer’s Consumer’s

Risk Risk

n (p = AQL) (p = LTPD)

Operating Characteristic Curve

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.4


Operating characteristic curve20

Producer’s Consumer’s

Risk Risk

n (p = AQL) (p = LTPD)

60 0.122 0.126

Operating Characteristic Curve

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.4


Operating characteristic curve21

Producer’s Consumer’s

Risk Risk

n (p = AQL) (p = LTPD)

60 0.122 0.126

80 0.191 0.048

Operating Characteristic Curve

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.4


Operating characteristic curve22

Producer’s Consumer’s

Risk Risk

n (p = AQL) (p = LTPD)

60 0.122 0.126

80 0.191 0.048

100 0.264 0.017

Operating Characteristic Curve

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.4


Operating characteristic curve23

Producer’s Consumer’s

Risk Risk

n (p = AQL) (p = LTPD)

60 0.122 0.126

80 0.191 0.048

100 0.264 0.017

120 0.332 0.006

Operating Characteristic Curve

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.4


Operating characteristic curve24

Operating Characteristic Curve

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

n = 60, c = 1

n = 80, c = 1

n = 100, c = 1

Probability of acceptance

n = 120, c = 1

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.4



Operating characteristic curve26

Operating Characteristic Curve

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.5


Operating characteristic curve27

Producer’s Consumer’s

Risk Risk

c (p = AQL) (p = LTPD)

Operating Characteristic Curve

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.5


Operating characteristic curve28

Producer’s Consumer’s

Risk Risk

c (p = AQL) (p = LTPD)

1 0.122 0.126

Operating Characteristic Curve

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.5


Operating characteristic curve29

Producer’s Consumer’s

Risk Risk

c (p = AQL) (p = LTPD)

1 0.122 0.126

2 0.023 0.303

Operating Characteristic Curve

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.5


Operating characteristic curve30

Producer’s Consumer’s

Risk Risk

c (p = AQL) (p = LTPD)

1 0.122 0.126

2 0.023 0.303

3 0.003 0.515

Operating Characteristic Curve

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.5


Operating characteristic curve31

Producer’s Consumer’s

Risk Risk

c (p = AQL) (p = LTPD)

1 0.122 0.126

2 0.023 0.303

3 0.003 0.515

4 0.000 0.726

Operating Characteristic Curve

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.5


Operating characteristic curve32

Operating Characteristic Curve

n = 60, c = 1

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

n = 60, c = 2

n = 60, c = 3

n = 60, c = 4

Probability of acceptance

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.5



Acceptance sampling plan1

AQL Based LTPD Based

Acceptance Expected Sample Expected Sample

Number Defectives Size Defectives Size

0 0.0509 5 2.2996 38

1 0.3552 36 3.8875 65

2 0.8112 81 5.3217 89

3 1.3675 137 6.6697 111

4 1.9680 197 7.9894 133

5 2.6256 263 9.2647 154

6 3.2838 328 10.5139 175

7 3.9794 398 11.7726 196

8 4.6936 469 12.9903 217

9 5.4237 542 14.2042 237

10 6.1635 616 15.4036 257

Acceptance Sampling Plan



Operating characteristic curve34

1.6 –

1.2 –

0.8 –

0.4 –

0 –

Average outgoing quality (percent)

| | | | | | | |

1 2 3 4 5 6 7 8

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2


Operating characteristic curve35

1.6 –

1.2 –

0.8 –

0.4 –

0 –

Proportion Probability

Defective of Acceptance

(p) np (Pa)

Average outgoing quality (percent)

| | | | | | | |

1 2 3 4 5 6 7 8

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2


Operating characteristic curve36

1.6 –

1.2 –

0.8 –

0.4 –

0 –

Proportion Probability

Defective of Acceptance

(p) np (Pa)

0.01 1.10 0.974

0.02 2.20 0.819

0.03 3.30 0.581 = (0.603 + 0.558)/2

0.04 4.40 0.359

0.05 5.50 0.202 = (0.213 + 0.191)/2

0.06 6.60 0.105

0.07 7.70 0.052 = (0.055 + 0.048)/2

0.08 8.80 0.024

Average outgoing quality (percent)

| | | | | | | |

1 2 3 4 5 6 7 8

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2


Operating characteristic curve37

1.6 –

1.2 –

0.8 –

0.4 –

0 –

Proportion Probability

Defective of Acceptance

(p) np (Pa)

0.01 1.10 0.974

0.02 2.20 0.819

0.03 3.30 0.581 = (0.603 + 0.558)/2

0.04 4.40 0.359

0.05 5.50 0.202 = (0.213 + 0.191)/2

0.06 6.60 0.105

0.07 7.70 0.052 = (0.055 + 0.048)/2

0.08 8.80 0.024

For p = 0.01:

Average outgoing quality (percent)

| | | | | | | |

1 2 3 4 5 6 7 8

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2


Operating characteristic curve38

1.6 –

1.2 –

0.8 –

0.4 –

0 –

Proportion Probability

Defective of Acceptance

(p) np (Pa)

0.01 1.10 0.974

0.02 2.20 0.819

0.03 3.30 0.581 = (0.603 + 0.558)/2

0.04 4.40 0.359

0.05 5.50 0.202 = (0.213 + 0.191)/2

0.06 6.60 0.105

0.07 7.70 0.052 = (0.055 + 0.048)/2

0.08 8.80 0.024

For p = 0.01: 0.01(0.974)(1000 – 110)/1000 = 0.0087

Average outgoing quality (percent)

| | | | | | | |

1 2 3 4 5 6 7 8

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2


Operating characteristic curve39

1.6 –

1.2 –

0.8 –

0.4 –

0 –

Proportion Probability

Defective of Acceptance

(p) np (Pa)

0.01 1.10 0.974

0.02 2.20 0.819

0.03 3.30 0.581 = (0.603 + 0.558)/2

0.04 4.40 0.359

0.05 5.50 0.202 = (0.213 + 0.191)/2

0.06 6.60 0.105

0.07 7.70 0.052 = (0.055 + 0.048)/2

0.08 8.80 0.024

For p = 0.01: 0.01(0.974)(1000 – 110)/1000 = 0.0087

Average outgoing quality (percent)

| | | | | | | |

1 2 3 4 5 6 7 8

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2


Operating characteristic curve40

1.6 –

1.2 –

0.8 –

0.4 –

0 –

Proportion Probability

Defective of Acceptance

(p) np (Pa)

0.01 1.10 0.974

0.02 2.20 0.819

0.03 3.30 0.581 = (0.603 + 0.558)/2

0.04 4.40 0.359

0.05 5.50 0.202 = (0.213 + 0.191)/2

0.06 6.60 0.105

0.07 7.70 0.052 = (0.055 + 0.048)/2

0.08 8.80 0.024

For p = 0.01: 0.01(0.974)(1000 – 110)/1000 = 0.0087

For p = 0.02: 0.02(0.819)(1000 – 110)/1000 = 0.0146

For p = 0.03: 0.03(0.581)(1000 – 110)/1000 = 0.0155

For p = 0.04: 0.04(0.359)(1000 – 110)/1000 = 0.0128

For p = 0.05: 0.05(0.202)(1000 – 110)/1000 = 0.0090

For p = 0.06: 0.06(0.105)(1000 – 110)/1000 = 0.0056

For p = 0.07: 0.07(0.052)(1000 – 110)/1000 = 0.0032

For p = 0.08: 0.08(0.024)(1000 – 110)/1000 = 0.0017

Average outgoing quality (percent)

| | | | | | | |

1 2 3 4 5 6 7 8

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2


Operating characteristic curve41

1.6 –

1.2 –

0.8 –

0.4 –

0 –

Proportion Probability

Defective of Acceptance

(p) np (Pa)

0.01 1.10 0.974

0.02 2.20 0.819

0.03 3.30 0.581 = (0.603 + 0.558)/2

0.04 4.40 0.359

0.05 5.50 0.202 = (0.213 + 0.191)/2

0.06 6.60 0.105

0.07 7.70 0.052 = (0.055 + 0.048)/2

0.08 8.80 0.024

Average outgoing quality (percent)

| | | | | | | |

1 2 3 4 5 6 7 8

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2


Operating characteristic curve42

Operating Characteristic Curve

1.6 –

1.2 –

0.8 –

0.4 –

0 –

Average outgoing quality (percent)

| | | | | | | |

1 2 3 4 5 6 7 8

Defectives in lot (percent)

Example J.2


Operating characteristic curve43

Operating Characteristic Curve

1.6 –

1.2 –

0.8 –

0.4 –

0 –

AOQL

Average outgoing quality (percent)

| | | | | | | |

1 2 3 4 5 6 7 8

Defectives in lot (percent)

Figure J.6


Solved problem

1.000

0.996

1.0 —

0.9 —

0.8 —

0.7 —

0.6 —

0.5 —

0.4 —

0.3 —

0.2 —

0.1 —

0 —

 = 0.049

0.951

0.810

0.587

Probability of acceptance (Pa)

0.363

0.194

0.092

0.039

 = 0.092

0.015

| | | | | | | | | |

1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)

Proportion defective (hundredths)(p)

Solved Problem


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