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Supplement J - Acceptance Sampling Plans

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a

AQL LTPD

Supplement J -Acceptance SamplingPlans

Sequential Sampling Chart

8 –

7 –

6 –

5 –

4 –

3 –

2 –

1 –

0 –

Number of defectives

|||||||

10203040506070

Cumulative sample size

Figure J.1

Sequential Sampling Chart

8 –

7 –

6 –

5 –

4 –

3 –

2 –

1 –

0 –

Number of defectives

Continue sampling

|||||||

10203040506070

Cumulative sample size

Figure J.1

Sequential Sampling Chart

8 –

7 –

6 –

5 –

4 –

3 –

2 –

1 –

0 –

Reject

Number of defectives

Continue sampling

Accept

|||||||

10203040506070

Cumulative sample size

Figure J.1

Sequential Sampling Chart

8 –

7 –

6 –

5 –

4 –

3 –

2 –

1 –

0 –

Decision to reject

Reject

Number of defectives

Continue sampling

Accept

|||||||

10203040506070

Cumulative sample size

Figure J.1

Sequential Sampling Chart

Operating Characteristic Curve

Probability of acceptance

Proportion defective

Figure J.2

Operating Characteristic Curve

Ideal OC curve

Probability of acceptance

Proportion defective

Figure J.2

Operating Characteristic Curve

Ideal OC curve

Probability of acceptance

Typical OC curve

Proportion defective

Figure J.2

Operating Characteristic Curve

1.0

Ideal OC curve

a

Probability of acceptance

Typical OC curve

AQL LTPD

Proportion defective

Figure J.2

Operating Characteristic Curve

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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability

Proportionof c or less

defectivedefects

(p)np(Pa)Comments

n = 60

c = 1

Probability of acceptance

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

np012

.05.951.9991.000

.10.905.9951.000

.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

Proportionof c or less

defectivedefects

(p)np(Pa)Comments

n = 60

c = 1

Probability of acceptance

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

np012

.05.951.9991.000

.10.905.9951.000

.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

Proportionof c or less

Defectivedefects

(p)np(Pa)Comments

n = 60

c = 1

0.01 (AQL)0.6

Probability of acceptance

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

np012

.05.951.9991.000

.10.905.9951.000

.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

Proportionof c or less

defectivedefects

(p)np(Pa)Comments

n = 60

c = 1

0.01 (AQL)0.6

Probability of acceptance

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

np012

.05.951.9991.000

.10.905.9951.000

.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

Proportionof c or less

defectivedefects

(p)np(Pa)Comments

n = 60

c = 1

0.01 (AQL)0.60.878

Probability of acceptance

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

np012

.05.951.9991.000

.10.905.9951.000

.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

Proportionof c or less

defectivedefects

(p)np(Pa)Comments

n = 60

c = 1

0.01 (AQL)0.60.878

Probability of acceptance

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability

Proportionof c or less

defectivedefects

(p)np(Pa)Comments

n = 60

c = 1

0.01 (AQL)0.60.878

Probability of acceptance

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1

1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

Probability

Proportionof c or less

defectivedefects

(p)np(Pa)Comments

n = 60

c = 1

0.663

0.01 (AQL)0.60.878a = 1.000 – 0.878 = 0.122

0.021.20.663

0.031.80.463

0.042.40.308

0.053.00.199

0.06 (LTPD)3.60.126b = 0.126

0.074.20.078

0.084.80.048

0.095.40.029

0.106.00.017

Probability of acceptance

0.308

0.199

0.048

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1

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

||||||||||

12345678910

0.017

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Example J.1

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

||||||||||

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0.017

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Figure J.3

Operating Characteristic Curve

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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.4

Producer’sConsumer’s

RiskRisk

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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.4

Producer’sConsumer’s

RiskRisk

n (p = AQL)(p = LTPD)

600.1220.126

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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.4

Producer’sConsumer’s

RiskRisk

n (p = AQL)(p = LTPD)

600.1220.126

800.1910.048

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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.4

Producer’sConsumer’s

RiskRisk

n (p = AQL)(p = LTPD)

600.1220.126

800.1910.048

1000.2640.017

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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.4

Producer’sConsumer’s

RiskRisk

n (p = AQL)(p = LTPD)

600.1220.126

800.1910.048

1000.2640.017

1200.3320.006

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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.4

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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.4

Operating Characteristic Curve

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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.5

Producer’sConsumer’s

RiskRisk

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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.5

Producer’sConsumer’s

RiskRisk

c (p = AQL)(p = LTPD)

10.1220.126

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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.5

Producer’sConsumer’s

RiskRisk

c (p = AQL)(p = LTPD)

10.1220.126

20.0230.303

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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.5

Producer’sConsumer’s

RiskRisk

c (p = AQL)(p = LTPD)

10.1220.126

20.0230.303

30.0030.515

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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.5

Producer’sConsumer’s

RiskRisk

c (p = AQL)(p = LTPD)

10.1220.126

20.0230.303

30.0030.515

40.0000.726

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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.5

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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.5

Acceptance Sampling Plan

AQL BasedLTPD Based

AcceptanceExpectedSampleExpectedSample

NumberDefectivesSizeDefectivesSize

00.050952.299638

10.3552363.887565

20.8112815.321789

31.36751376.6697111

41.96801977.9894133

52.62562639.2647154

63.283832810.5139175

73.979439811.7726196

84.693646912.9903217

95.423754214.2042237

106.163561615.4036257

Acceptance Sampling Plan

Operating Characteristic Curve

1.6 –

1.2 –

0.8 –

0.4 –

0 –

Average outgoing quality (percent)

||||||||

12345678

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2

1.6 –

1.2 –

0.8 –

0.4 –

0 –

ProportionProbability

Defectiveof Acceptance

(p)np(Pa)

Average outgoing quality (percent)

||||||||

12345678

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2

1.6 –

1.2 –

0.8 –

0.4 –

0 –

ProportionProbability

Defectiveof Acceptance

(p)np(Pa)

0.011.100.974

0.022.200.819

0.033.300.581= (0.603 + 0.558)/2

0.044.400.359

0.055.500.202= (0.213 + 0.191)/2

0.066.600.105

0.077.700.052= (0.055 + 0.048)/2

0.088.800.024

Average outgoing quality (percent)

||||||||

12345678

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2

1.6 –

1.2 –

0.8 –

0.4 –

0 –

ProportionProbability

Defectiveof Acceptance

(p)np(Pa)

0.011.100.974

0.022.200.819

0.033.300.581= (0.603 + 0.558)/2

0.044.400.359

0.055.500.202= (0.213 + 0.191)/2

0.066.600.105

0.077.700.052= (0.055 + 0.048)/2

0.088.800.024

For p = 0.01:

Average outgoing quality (percent)

||||||||

12345678

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2

1.6 –

1.2 –

0.8 –

0.4 –

0 –

ProportionProbability

Defectiveof Acceptance

(p)np(Pa)

0.011.100.974

0.022.200.819

0.033.300.581= (0.603 + 0.558)/2

0.044.400.359

0.055.500.202= (0.213 + 0.191)/2

0.066.600.105

0.077.700.052= (0.055 + 0.048)/2

0.088.800.024

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

Average outgoing quality (percent)

||||||||

12345678

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2

1.6 –

1.2 –

0.8 –

0.4 –

0 –

ProportionProbability

Defectiveof Acceptance

(p)np(Pa)

0.011.100.974

0.022.200.819

0.033.300.581= (0.603 + 0.558)/2

0.044.400.359

0.055.500.202= (0.213 + 0.191)/2

0.066.600.105

0.077.700.052= (0.055 + 0.048)/2

0.088.800.024

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

Average outgoing quality (percent)

||||||||

12345678

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2

1.6 –

1.2 –

0.8 –

0.4 –

0 –

ProportionProbability

Defectiveof Acceptance

(p)np(Pa)

0.011.100.974

0.022.200.819

0.033.300.581= (0.603 + 0.558)/2

0.044.400.359

0.055.500.202= (0.213 + 0.191)/2

0.066.600.105

0.077.700.052= (0.055 + 0.048)/2

0.088.800.024

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)

||||||||

12345678

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2

1.6 –

1.2 –

0.8 –

0.4 –

0 –

ProportionProbability

Defectiveof Acceptance

(p)np(Pa)

0.011.100.974

0.022.200.819

0.033.300.581= (0.603 + 0.558)/2

0.044.400.359

0.055.500.202= (0.213 + 0.191)/2

0.066.600.105

0.077.700.052= (0.055 + 0.048)/2

0.088.800.024

Average outgoing quality (percent)

||||||||

12345678

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2

Operating Characteristic Curve

1.6 –

1.2 –

0.8 –

0.4 –

0 –

Average outgoing quality (percent)

||||||||

12345678

Defectives in lot (percent)

Example J.2

Operating Characteristic Curve

1.6 –

1.2 –

0.8 –

0.4 –

0 –

AOQL

Average outgoing quality (percent)

||||||||

12345678

Defectives in lot (percent)

Figure J.6

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

||||||||||

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(AQL)(LTPD)

Proportion defective (hundredths)(p)

Solved Problem