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