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## PowerPoint Slideshow about 'Supplement J - Acceptance Sampling Plans' - solana

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### Operating Characteristic Curve

### Operating Characteristic Curve

### Operating Characteristic Curve

### Operating Characteristic Curve

### Operating Characteristic Curve

### Operating Characteristic Curve

8 –### Sequential Sampling Chart

7 –

6 –

5 –

4 –

3 –

2 –

1 –

0 –

Number of defectives

| | | | | | |

10 20 30 40 50 60 70

Cumulative sample size

Figure J.1

8 –### Sequential Sampling Chart

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

8 –### Sequential Sampling Chart

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

8 –### Sequential Sampling Chart

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

Ideal OC curve### Operating Characteristic Curve

Probability of acceptance

Typical OC curve

Proportion defective

Figure J.2

1.0### Operating Characteristic Curve

Ideal OC curve

a

Probability of acceptance

Typical OC curve

AQL LTPD

Proportion defective

Figure J.2

1.0 –### Operating Characteristic Curve

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)

Example J.1

1.0 –### Operating Characteristic Curve

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)

Example J.1

1.0 –### Operating Characteristic Curve

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)

Example J.1

1.0 –### Operating Characteristic Curve

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)

Example J.1

1.0 –### Operating Characteristic Curve

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)

Example J.1

1.0 –### Operating Characteristic Curve

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)

Example J.1

1.0 –### Operating Characteristic Curve

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)

Example J.1

1.0 –### Operating Characteristic Curve

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)

Example J.1

1.0 –### Operating Characteristic Curve

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)

Example J.1

1.0 –### Operating Characteristic Curve

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)

Example J.1

1.0 –### Operating Characteristic Curve

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)

Figure J.3

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

Producer’s Consumer’s### Operating Characteristic Curve

Risk Risk

n (p = AQL) (p = LTPD)

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

Producer’s Consumer’s### Operating Characteristic Curve

Risk Risk

n (p = AQL) (p = LTPD)

60 0.122 0.126

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

Producer’s Consumer’s### Operating Characteristic Curve

Risk Risk

n (p = AQL) (p = LTPD)

60 0.122 0.126

80 0.191 0.048

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

Producer’s Consumer’s### Operating Characteristic Curve

Risk Risk

n (p = AQL) (p = LTPD)

60 0.122 0.126

80 0.191 0.048

100 0.264 0.017

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

Producer’s Consumer’s### Operating Characteristic Curve

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

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

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

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

Producer’s Consumer’s### Operating Characteristic Curve

Risk Risk

c (p = AQL) (p = LTPD)

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

Producer’s Consumer’s### Operating Characteristic Curve

Risk Risk

c (p = AQL) (p = LTPD)

1 0.122 0.126

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

Producer’s Consumer’s### Operating Characteristic Curve

Risk Risk

c (p = AQL) (p = LTPD)

1 0.122 0.126

2 0.023 0.303

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

Producer’s Consumer’s### Operating Characteristic Curve

Risk Risk

c (p = AQL) (p = LTPD)

1 0.122 0.126

2 0.023 0.303

3 0.003 0.515

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

Producer’s Consumer’s### Operating Characteristic Curve

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

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

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

AQL Based LTPD Based### Acceptance Sampling Plan

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

1.6 –### Operating Characteristic Curve

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

1.6 –### Operating Characteristic Curve

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)

Example J.2

1.6 –### Operating Characteristic Curve

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)

Example J.2

1.6 –### Operating Characteristic Curve

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)

Example J.2

1.6 –### Operating Characteristic Curve

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)

Example J.2

1.6 –### Operating Characteristic Curve

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)

Example J.2

1.6 –### Operating Characteristic Curve

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)

Example J.2

1.6 –### Operating Characteristic Curve

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)

Example J.2

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

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

1.000### Solved Problem

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)

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