1. Acceptance Sampling Plans
Supplement I a 
AQL LTPD
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2. Sequential Sampling Chart
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3. Sequential Sampling Chart
8 –
7 –
6 –
5 –
4 –
3 –
2 –
1 –
0 –
Cumulative sample size
| | | | | | |
Number of defectives
Figure I.1
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4. Sequential Sampling Chart
8 –
7 –
6 –
5 –
4 –
3 –
2 –
1 –
0 –
Continue sampling
Cumulative sample size
| | | | | | |
Number of defectives
Figure I.1
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5. Sequential Sampling Chart
8 –
7 –
6 –
5 –
4 –
3 –
2 –
1 –
0 –
Reject
Continue sampling
Accept
Cumulative sample size
| | | | | | |
Number of defectives
Figure I.1
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6. Sequential Sampling Chart
8 –
7 –
6 –
5 –
4 –
3 –
2 –
1 –
0 –
Reject
Decision to reject
Continue sampling
Accept
Cumulative sample size
| | | | | | |
Number of defectives
Figure I.1
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7. Operating Characteristic Curve
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8. Operating Characteristic Curve
Probability of acceptance
Proportion defective
Figure I.2
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9. Operating Characteristic Curve
Ideal OC curve
Probability of acceptance
Proportion defective
Figure I.2
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10. Operating Characteristic Curve
Ideal OC curve
Typical OC curve
Probability of acceptance
Proportion defective
Figure I.2
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11. Operating Characteristic Curve
1.0 
Ideal OC curve
Typical OC curve
AQL LTPD
Probability of acceptance
Proportion defective
Figure I.2
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12. Operating Characteristic Curve
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13. 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 –
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Probability of acceptance
Example I.1
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14. Operating Characteristic Curve
Probability
Proportion of c or less
defective defects
(p) np (Pa) Comments
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 –
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Probability of acceptance
Example I.1
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15. Operating Characteristic Curve
Probability
Proportion of c or less
defective defects
(p) np (Pa) Comments
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 –
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Probability of acceptance
np 0 1 2
Example I.1
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16. Operating Characteristic Curve
Probability
Proportion of c or less
Defective defects
(p) np (Pa) Comments
0.01 (AQL) 0.6
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 –
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Probability of acceptance
np 0 1 2
Example I.1
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17. Operating Characteristic Curve
Probability
Proportion of c or less
defective defects
(p) np (Pa) Comments
0.01 (AQL) 0.6
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 –
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Probability of acceptance
np 0 1 2
Example I.1
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18. Operating Characteristic Curve
Probability
Proportion of c or less
defective defects
(p) np (Pa) Comments
0.01 (AQL)
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 –
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Probability of acceptance
np 0 1 2
Example I.1
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19. Operating Characteristic Curve
Probability
Proportion of c or less
defective defects
(p) np (Pa) Comments
0.01 (AQL)
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 –
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Probability of acceptance
np 0 1 2
Example I.1
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20. Operating Characteristic Curve
Probability
Proportion of c or less
defective defects
(p) np (Pa) Comments
0.01 (AQL)
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 –
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Probability of acceptance
Example I.1
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21. Operating Characteristic Curve
Probability
Proportion of c or less
defective defects
(p) np (Pa) Comments
0.01 (AQL) a = – = 0.122
0.06 (LTPD) b = 0.126
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 –
0.663
| | | | | | | | | |
0.308
0.199
0.048
(AQL) (LTPD)
Proportion defective (hundredths)
Probability of acceptance
Example I.1
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22. 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 –
| | | | | | | | | |
0.878
0.663
0.463
0.308
0.199
0.126
0.078
0.048
0.029
0.017
(AQL) (LTPD)
Proportion defective (hundredths)
Probability of acceptance
Example I.1
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23. 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 –
| | | | | | | | | |
0.878
0.663
0.463
0.308
0.199
0.126
0.078
0.048
0.029
0.017
a = 0.122
(AQL) (LTPD)
Proportion defective (hundredths)
Probability of acceptance
b = 0.126
Figure I.3
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24. Operating Characteristic Curve
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25. 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
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Figure I.4
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26. 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 –
Producer’s Consumer’s
Risk Risk
n (p = AQL) (p = LTPD)
Probability of acceptance
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Figure I.4
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27. 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 –
Producer’s Consumer’s
Risk Risk
n (p = AQL) (p = LTPD)
Probability of acceptance
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Figure I.4
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28. 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 –
Producer’s Consumer’s
Risk Risk
n (p = AQL) (p = LTPD)
Probability of acceptance
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Figure I.4
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29. 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 –
Producer’s Consumer’s
Risk Risk
n (p = AQL) (p = LTPD)
Probability of acceptance
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Figure I.4
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30. 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 –
Producer’s Consumer’s
Risk Risk
n (p = AQL) (p = LTPD)
Probability of acceptance
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Figure I.4
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31. 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
Probability of acceptance
n = 100, c = 1
n = 120, c = 1
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Figure I.4
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32. Operating Characteristic Curve
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33. 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
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Figure I.5
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34. 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 –
Producer’s Consumer’s
Risk Risk
c (p = AQL) (p = LTPD)
Probability of acceptance
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Figure I.5
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35. 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 –
Producer’s Consumer’s
Risk Risk
c (p = AQL) (p = LTPD)
Probability of acceptance
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Figure I.5
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36. 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 –
Producer’s Consumer’s
Risk Risk
c (p = AQL) (p = LTPD)
Probability of acceptance
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Figure I.5
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37. 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 –
Producer’s Consumer’s
Risk Risk
c (p = AQL) (p = LTPD)
Probability of acceptance
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Figure I.5
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38. 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 –
Producer’s Consumer’s
Risk Risk
c (p = AQL) (p = LTPD)
Probability of acceptance
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Figure I.5
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39. 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
| | | | | | | | | |
(AQL) (LTPD)
Proportion defective (hundredths)
Figure I.5
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40. Acceptance Sampling Plan
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41. Acceptance Sampling Plan
AQL Based LTPD Based
Acceptance Expected Sample Expected Sample
Number Defectives Size Defectives Size
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42. Operating Characteristic Curve
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43. Operating Characteristic Curve
1.6 –
1.2 –
0.8 –
0.4 –
0 –
| | | | | | | |
Defectives in lot (percent)
Average outgoing quality (percent)
Example I.2
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44. Operating Characteristic Curve
1.6 –
1.2 –
0.8 –
0.4 –
0 –
| | | | | | | |
Defectives in lot (percent)
Average outgoing quality (percent)
Proportion Probability
Defective of Acceptance
(p) np (Pa)
Example I.2
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45. Operating Characteristic Curve
1.6 –
1.2 –
0.8 –
0.4 –
0 –
| | | | | | | |
Defectives in lot (percent)
Average outgoing quality (percent)
Proportion Probability
Defective of Acceptance
(p) np (Pa)
= ( )/2
= ( )/2
= ( )/2
Example I.2
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46. Operating Characteristic Curve
1.6 –
1.2 –
0.8 –
0.4 –
0 –
| | | | | | | |
Defectives in lot (percent)
Average outgoing quality (percent)
Proportion Probability
Defective of Acceptance
(p) np (Pa)
= ( )/2
= ( )/2
= ( )/2
For p = 0.01:
Example I.2
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47. Operating Characteristic Curve
1.6 –
1.2 –
0.8 –
0.4 –
0 –
| | | | | | | |
Defectives in lot (percent)
Average outgoing quality (percent)
Proportion Probability
Defective of Acceptance
(p) np (Pa)
= ( )/2
= ( )/2
= ( )/2
For p = 0.01: 0.01(0.974)(1000 – 110)/1000 =
Example I.2
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48. Operating Characteristic Curve
1.6 –
1.2 –
0.8 –
0.4 –
0 –
| | | | | | | |
Defectives in lot (percent)
Average outgoing quality (percent)
Proportion Probability
Defective of Acceptance
(p) np (Pa)
= ( )/2
= ( )/2
= ( )/2
For p = 0.01: 0.01(0.974)(1000 – 110)/1000 =
Example I.2
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49. Operating Characteristic Curve
1.6 –
1.2 –
0.8 –
0.4 –
0 –
| | | | | | | |
Defectives in lot (percent)
Average outgoing quality (percent)
Proportion Probability
Defective of Acceptance
(p) np (Pa)
= ( )/2
= ( )/2
= ( )/2
For p = 0.01: 0.01(0.974)(1000 – 110)/1000 =
For p = 0.02: 0.02(0.819)(1000 – 110)/1000 =
For p = 0.03: 0.03(0.581)(1000 – 110)/1000 =
For p = 0.04: 0.04(0.359)(1000 – 110)/1000 =
For p = 0.05: 0.05(0.202)(1000 – 110)/1000 =
For p = 0.06: 0.06(0.105)(1000 – 110)/1000 =
For p = 0.07: 0.07(0.052)(1000 – 110)/1000 =
For p = 0.08: 0.08(0.024)(1000 – 110)/1000 =
Example I.2
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50. Operating Characteristic Curve
1.6 –
1.2 –
0.8 –
0.4 –
0 –
| | | | | | | |
Defectives in lot (percent)
Average outgoing quality (percent)
Proportion Probability
Defective of Acceptance
(p) np (Pa)
= ( )/2
= ( )/2
= ( )/2
Example I.2
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51. Operating Characteristic Curve
1.6 –
1.2 –
0.8 –
0.4 –
0 –
Average outgoing quality (percent)
| | | | | | | |
Defectives in lot (percent)
Example I.2
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52. Operating Characteristic Curve
1.6 –
1.2 –
0.8 –
0.4 –
0 –
AOQL
Average outgoing quality (percent)
| | | | | | | |
Defectives in lot (percent)
Figure I.6
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53. Solved Problem Probability of acceptance (Pa) (AQL) (LTPD)
1.0 —
0.9 —
0.8 —
0.7 —
0.6 —
0.5 —
0.4 —
0.3 —
0.2 —
0.1 —
0 —
| | | | | | | | | |
Proportion defective (hundredths)(p)
Probability of acceptance (Pa)
(AQL) (LTPD)
1.000
0.996
0.951
0.810
0.587
0.363
0.194
0.092
0.039
0.015
 = 0.092
 = 0.049
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