Supplement j acceptance sampling plans
This presentation is the property of its rightful owner.
Sponsored Links
1 / 53

Supplement J - Acceptance Sampling Plans PowerPoint PPT Presentation


  • 102 Views
  • Uploaded on
  • Presentation posted in: General

a. . AQL LTPD. Supplement J - Acceptance Sampling Plans. 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 –

Download Presentation

Supplement J - Acceptance Sampling Plans

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Supplement j acceptance sampling plans

a

AQL LTPD

Supplement J -Acceptance SamplingPlans


Sequential sampling chart

Sequential Sampling Chart


Sequential sampling chart1

8 –

7 –

6 –

5 –

4 –

3 –

2 –

1 –

0 –

Number of defectives

|||||||

10203040506070

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

|||||||

10203040506070

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

|||||||

10203040506070

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

|||||||

10203040506070

Cumulative sample size

Figure J.1

Sequential Sampling Chart


Operating characteristic curve

Operating Characteristic Curve


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 curve5

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

||||||||||

12345678910

(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

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


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 –

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


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 –

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


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 –

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


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 –

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


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 –

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


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

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


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

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


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

||||||||||

12345678910

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

||||||||||

12345678910

0.017

(AQL) (LTPD)

Proportion defective (hundredths)

Operating Characteristic Curve

Figure J.3


Operating characteristic curve17

Operating Characteristic Curve


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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.4


Operating characteristic curve19

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


Operating characteristic curve20

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


Operating characteristic curve21

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


Operating characteristic curve22

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


Operating characteristic curve23

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 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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.4


Operating characteristic curve25

Operating Characteristic Curve


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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.5


Operating characteristic curve27

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


Operating characteristic curve28

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


Operating characteristic curve29

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


Operating characteristic curve30

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


Operating characteristic curve31

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 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

||||||||||

12345678910

(AQL) (LTPD)

Proportion defective (hundredths)

Figure J.5


Acceptance sampling plan

Acceptance Sampling Plan


Acceptance sampling plan1

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 curve33

Operating Characteristic Curve


Operating characteristic curve34

1.6 –

1.2 –

0.8 –

0.4 –

0 –

Average outgoing quality (percent)

||||||||

12345678

Defectives in lot (percent)

Operating Characteristic Curve

Example J.2


Operating characteristic curve35

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


Operating characteristic curve36

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 curve37

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


Operating characteristic curve38

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


Operating characteristic curve39

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


Operating characteristic curve40

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


Operating characteristic curve41

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 curve42

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 curve43

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


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

||||||||||

12345678910

(AQL)(LTPD)

Proportion defective (hundredths)(p)

Solved Problem


  • Login