To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

α

β

AQL LTPD

Supplement J Supplement J --

Acceptance Acceptance SamplingSamplingPlansPlans

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Sequential Sampling ChartSequential Sampling Chart

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Sequential Sampling ChartSequential Sampling Chart8 –

7 –

6 –

5 –

4 –

3 –

2 –

1 –

0 –

Cumulative sample size

| | | | | | |10 20 30 40 50 60 70

Num

ber o

f def

ectiv

es

Figure J.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Sequential Sampling ChartSequential Sampling Chart8 –

7 –

6 –

5 –

4 –

3 –

2 –

1 –

0 –

Continue sampling

Cumulative sample size

| | | | | | |10 20 30 40 50 60 70

Num

ber o

f def

ectiv

es

Figure J.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Sequential Sampling ChartSequential Sampling Chart8 –

7 –

6 –

5 –

4 –

3 –

2 –

1 –

0 –

Reject

Continue sampling

Accept

Cumulative sample size

| | | | | | |10 20 30 40 50 60 70

Num

ber o

f def

ectiv

es

Figure J.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Sequential Sampling ChartSequential Sampling Chart8 –

7 –

6 –

5 –

4 –

3 –

2 –

1 –

0 –

RejectDecision to reject

Continue sampling

Accept

Cumulative sample size

| | | | | | |10 20 30 40 50 60 70

Num

ber o

f def

ectiv

es

Figure J.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve

Prob

abili

ty o

f acc

epta

nce

Proportion defectiveFigure J.2

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve

Ideal OC curve

Prob

abili

ty o

f acc

epta

nce

Proportion defectiveFigure J.2

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Operating Characteristic CurveOperating Characteristic Curve

Ideal OC curve

Typical OC curve

Prob

abili

ty o

f acc

epta

nce

Proportion defectiveFigure J.2

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve

α

1.0

β

Ideal OC curve

Typical OC curve

AQL LTPD

Prob

abili

ty o

f acc

epta

nce

Proportion defectiveFigure J.2

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

Example J.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic CurveProbability

Proportion of c or lessdefective defects

(p) np (Pa) Comments

n = 60c = 11.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

Example J.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic CurveProbability

Proportion of c or lessdefective defects

(p) np (Pa) Comments

n = 60c = 11.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

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

Example J.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic CurveProbability

Proportion of c or lessDefective defects

(p) np (Pa) Comments0.01 (AQL) 0.6

n = 60c = 11.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

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

Example J.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic CurveProbability

Proportion of c or lessdefective defects

(p) np (Pa) Comments0.01 (AQL) 0.6

n = 60c = 11.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

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

Example J.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic CurveProbability

Proportion of c or lessdefective defects

(p) np (Pa) Comments0.01 (AQL) 0.6 0.878

n = 60c = 11.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

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

Example J.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic CurveProbability

Proportion of c or lessdefective defects

(p) np (Pa) Comments0.01 (AQL) 0.6 0.878

n = 60c = 11.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

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

Example J.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic CurveProbability

Proportion of c or lessdefective defects

(p) np (Pa) Comments0.01 (AQL) 0.6 0.878

n = 60c = 11.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

Example J.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 –

0.663

| | | | | | | | | |1 2 3 4 5 6 7 8 9 10

0.308

0.199

0.048

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

ProbabilityProportion of c or lessdefective defects

(p) np (Pa) Comments

0.01 (AQL) 0.6 0.878 α = 1.000 – 0.878 = 0.1220.02 1.2 0.6630.03 1.8 0.4630.04 2.4 0.3080.05 3.0 0.1990.06 (LTPD) 3.6 0.126 β = 0.1260.07 4.2 0.0780.08 4.8 0.0480.09 5.4 0.0290.10 6.0 0.017

n = 60c = 1

Example J.1

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Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

0.878

0.663

0.463

0.308

0.1990.126 0.078

0.048 0.0290.017

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

Example J.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve

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 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

0.878

0.663

0.463

0.308

0.1990.126 0.078

0.048 0.0290.017

α = 0.122

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

β = 0.126

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Operating Characteristic CurveOperating Characteristic Curve

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

Figure J.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce Producer’s Consumer’s

Risk Riskn (p = AQL) (p = LTPD)

Figure J.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce Producer’s Consumer’s

Risk Riskn (p = AQL) (p = LTPD)

60 0.122 0.126

Figure J.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce Producer’s Consumer’s

Risk Riskn (p = AQL) (p = LTPD)

60 0.122 0.12680 0.191 0.048

Figure J.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce Producer’s Consumer’s

Risk Riskn (p = AQL) (p = LTPD)

60 0.122 0.12680 0.191 0.048

100 0.264 0.017

Figure J.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

Figure J.4

Producer’s Consumer’sRisk Risk

n (p = AQL) (p = LTPD)

60 0.122 0.12680 0.191 0.048

100 0.264 0.017120 0.332 0.006

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce n = 60, c = 1

n = 80, c = 1

n = 100, c = 1

n = 120, c = 1

Figure J.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

Figure J.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

Producer’s Consumer’sRisk Risk

c (p = AQL) (p = LTPD)

Figure J.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

Producer’s Consumer’sRisk Risk

c (p = AQL) (p = LTPD)

1 0.122 0.126

Figure J.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

Producer’s Consumer’sRisk Risk

c (p = AQL) (p = LTPD)

1 0.122 0.1262 0.023 0.303

Figure J.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

Producer’s Consumer’sRisk Risk

c (p = AQL) (p = LTPD)

1 0.122 0.1262 0.023 0.3033 0.003 0.515

Figure J.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

Producer’s Consumer’sRisk Risk

c (p = AQL) (p = LTPD)

1 0.122 0.1262 0.023 0.3033 0.003 0.5154 0.000 0.726

Figure J.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve1.0 –

0.9 –

0.8 –

0.7 –

0.6 –

0.5 –

0.4 –

0.3 –

0.2 –

0.1 –

0.0 – | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

(AQL) (LTPD)Proportion defective (hundredths)

Prob

abili

ty o

f acc

epta

nce

n = 60, c = 1n = 60, c = 2

n = 60, c = 3n = 60, c = 4

Figure J.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Acceptance Sampling Plan

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Acceptance Sampling Plan

AQL Based LTPD Based

0 0.0509 5 2.2996 381 0.3552 36 3.8875 652 0.8112 81 5.3217 893 1.3675 137 6.6697 1114 1.9680 197 7.9894 1335 2.6256 263 9.2647 1546 3.2838 328 10.5139 1757 3.9794 398 11.7726 1968 4.6936 469 12.9903 2179 5.4237 542 14.2042 237

10 6.1635 616 15.4036 257

Acceptance Expected Sample Expected SampleNumber Defectives Size Defectives Size

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Operating Characteristic CurveOperating Characteristic Curve

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Operating Characteristic CurveOperating Characteristic Curve

1.6 –

1.2 –

0.8 –

0.4 –

0 – | | | | | | | |1 2 3 4 5 6 7 8

Defectives in lot (percent)

Ave

rage

out

goin

g qu

ality

(per

cent

)

Example J.2

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve

1.6 –

1.2 –

0.8 –

0.4 –

0 – | | | | | | | |1 2 3 4 5 6 7 8

Defectives in lot (percent)

Ave

rage

out

goin

g qu

ality

(per

cent

)

Proportion ProbabilityDefective of Acceptance

(p) np (Pa)

Example J.2

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve

1.6 –

1.2 –

0.8 –

0.4 –

0 – | | | | | | | |1 2 3 4 5 6 7 8

Defectives in lot (percent)

Ave

rage

out

goin

g qu

ality

(per

cent

)

Proportion ProbabilityDefective of Acceptance

(p) np (Pa)

0.01 1.10 0.9740.02 2.20 0.8190.03 3.30 0.581 = (0.603 + 0.558)/20.04 4.40 0.3590.05 5.50 0.202 = (0.213 + 0.191)/20.06 6.60 0.1050.07 7.70 0.052 = (0.055 + 0.048)/20.08 8.80 0.024

Example J.2

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve

1.6 –

1.2 –

0.8 –

0.4 –

0 – | | | | | | | |1 2 3 4 5 6 7 8

Defectives in lot (percent)

Ave

rage

out

goin

g qu

ality

(per

cent

)

Proportion ProbabilityDefective of Acceptance

(p) np (Pa)

0.01 1.10 0.9740.02 2.20 0.8190.03 3.30 0.581 = (0.603 + 0.558)/20.04 4.40 0.3590.05 5.50 0.202 = (0.213 + 0.191)/20.06 6.60 0.1050.07 7.70 0.052 = (0.055 + 0.048)/20.08 8.80 0.024

For p = 0.01:

Example J.2

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve

1.6 –

1.2 –

0.8 –

0.4 –

0 – | | | | | | | |1 2 3 4 5 6 7 8

Defectives in lot (percent)

Ave

rage

out

goin

g qu

ality

(per

cent

)

Proportion ProbabilityDefective of Acceptance

(p) np (Pa)

0.01 1.10 0.9740.02 2.20 0.8190.03 3.30 0.581 = (0.603 + 0.558)/20.04 4.40 0.3590.05 5.50 0.202 = (0.213 + 0.191)/20.06 6.60 0.1050.07 7.70 0.052 = (0.055 + 0.048)/20.08 8.80 0.024

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

Example J.2

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve

1.6 –

1.2 –

0.8 –

0.4 –

0 – | | | | | | | |1 2 3 4 5 6 7 8

Defectives in lot (percent)

Ave

rage

out

goin

g qu

ality

(per

cent

)

Proportion ProbabilityDefective of Acceptance

(p) np (Pa)

0.01 1.10 0.9740.02 2.20 0.8190.03 3.30 0.581 = (0.603 + 0.558)/20.04 4.40 0.3590.05 5.50 0.202 = (0.213 + 0.191)/20.06 6.60 0.1050.07 7.70 0.052 = (0.055 + 0.048)/20.08 8.80 0.024

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

Example J.2

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve

1.6 –

1.2 –

0.8 –

0.4 –

0 – | | | | | | | |1 2 3 4 5 6 7 8

Defectives in lot (percent)

Ave

rage

out

goin

g qu

ality

(per

cent

)

Proportion ProbabilityDefective of Acceptance

(p) np (Pa)

0.01 1.10 0.9740.02 2.20 0.8190.03 3.30 0.581 = (0.603 + 0.558)/20.04 4.40 0.3590.05 5.50 0.202 = (0.213 + 0.191)/20.06 6.60 0.1050.07 7.70 0.052 = (0.055 + 0.048)/20.08 8.80 0.024

For p = 0.01: 0.01(0.974)(1000 – 110)/1000 = 0.0087For p = 0.02: 0.02(0.819)(1000 – 110)/1000 = 0.0146For p = 0.03: 0.03(0.581)(1000 – 110)/1000 = 0.0155For p = 0.04: 0.04(0.359)(1000 – 110)/1000 = 0.0128For p = 0.05: 0.05(0.202)(1000 – 110)/1000 = 0.0090For p = 0.06: 0.06(0.105)(1000 – 110)/1000 = 0.0056For p = 0.07: 0.07(0.052)(1000 – 110)/1000 = 0.0032For p = 0.08: 0.08(0.024)(1000 – 110)/1000 = 0.0017

Example J.2

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve

1.6 –

1.2 –

0.8 –

0.4 –

0 – | | | | | | | |1 2 3 4 5 6 7 8

Defectives in lot (percent)

Ave

rage

out

goin

g qu

ality

(per

cent

)

Proportion ProbabilityDefective of Acceptance

(p) np (Pa)

0.01 1.10 0.9740.02 2.20 0.8190.03 3.30 0.581 = (0.603 + 0.558)/20.04 4.40 0.3590.05 5.50 0.202 = (0.213 + 0.191)/20.06 6.60 0.1050.07 7.70 0.052 = (0.055 + 0.048)/20.08 8.80 0.024

Example J.2

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve

1.6 –

1.2 –

0.8 –

0.4 –

0 – | | | | | | | |1 2 3 4 5 6 7 8

Defectives in lot (percent)

Ave

rage

out

goin

g qu

ality

(per

cent

)

Example J.2

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Operating Characteristic CurveOperating Characteristic Curve

AOQL1.6 –

1.2 –

0.8 –

0.4 –

0 – | | | | | | | |1 2 3 4 5 6 7 8

Defectives in lot (percent)

Ave

rage

out

goin

g qu

ality

(per

cent

)

Figure J.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved.

Solved Problem1.0 —

0.9 —

0.8 —

0.7 —

0.6 —

0.5 —

0.4 —

0.3 —

0.2 —

0.1 —

0 — | | | | | | | | | |1 2 3 4 5 6 7 8 9 10

Proportion defective (hundredths)(p)

Prob

abili

ty o

f acc

epta

nce

(Pa)

(AQL) (LTPD)

1.000 0.996

0.9510.810

0.587

0.363

0.1940.092

0.0390.015β = 0.092

α = 0.049