Transcript OC Curve - Operating Characteristic Curve The OC curve

Recitation 8
• OC CURVES
• AOQ
Review of parameters
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N:Lot size
n1: Sample size on the first sample
c1: Acceptance # on the first sample
r1: Non-acceptance # on the first sample
n2: Sample size on the second sample
c2:Acceptance number for both samples
r2: Non-acceptance number for both
samples
• 100 Pa: Percent of Lots accepted.
• 100Po: Percent non-conforming
• Procedure: One value 100Po assumed
and the other calculated.
Difference between two types of curves:
TYPE A AND TYPE B
• TYPE B Curves: Lots come from a
continouos stream of product, therefore
the calculations are based on infinite lot
size. (Binomial for evaluating, but approx.
To poisson)
• TYPE A: Probability of accepting an
isolated lot. (Hypergeometric used to
calculate the acceptance probabilities)
OC Curve - Operating Characteristic Curve
The OC curve shows how the probability of acceptance (y-axis)
depends on the quality level (bottom axis).
Question 1
Percent of lots
accepted (100*Pa)
100
50
0
0
1
2
Percent Nonconforming
(100*Po)
3
4
Question 1
Percent of Lots
Accepted
100
50
0
0
1
2
3
Percent
Nonconforming
4
Producer’s Risk
• Producer’s risk : α= Probability of nonacceptance of a conforming lot.
• Refelected on the OC curve as Pa=1- α
• AQL(Acceptable Quality Level): Max.
Percent of nonconforming that can be
considered satisfactory for the purposes of
accepting sampling.
Consumer’s Risk
• β:
• Probability of accepting a non-conforming
lot. Usually given as Probability of
acceptance.
• Usually given as 0.10.
• Average Outgoing Quality: 100*po(Pa)
• Quality that leaves the inspection
operation.
• Without rectification: AOQ same as
incoming quality
• In rectification: Average outgoing quality is
always better than the incoming quality.
Question 2
Process QualitySample size n*Po
0,05
200
0,2
200
0,35
200
0,6
200
1
200
Probability of Acceptance (Pa)AOQ (100Po*Pa)
0,1
0,905
0,04525
0,4
0,67
0,134
0,7
0,549
0,19215
1,2
0,301
0,1806
2
0,135
0,135
Question 2
90
80
Percent of Lots
Accepted
70
60
50
40
30
20
10
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
Percent
Nonconforming
0,8
0,9
1,0
Question 2
0,20
AOQ
0,15
0,10
0,05
0,0
0,1
0,2
0,3
0,4
0,5
0,6
100PO
0,7
0,8
0,9
1,0
Question 3
Process Quality Sample size Probability of Acceptance (Pa) AOQ (100Po*Pa)
1
150
1
2
150
0,983
6
150
0,446
8
150
0,192
9
150
0,116
1
1,966
2,676
1,536
1,044
Question 3
1,0
0,9
Percent of Lots
Accepted
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
1
2
3
4
5
100po
6
7
8
9
Question 3
AOQ
2,5
2,0
1,5
1,0
0
1
2
3
4
5
100po
6
7
8
9