Control Charts for Attribute P-chart C-chart U-chart and the magnificent seven Notes | EduRev

: Control Charts for Attribute P-chart C-chart U-chart and the magnificent seven Notes | EduRev

 Page 1


Lecture 11: Attribute Charts
Spanos
EE290H F05
1
P-chart (fraction non-conforming) 
C-chart (number of defects)
U-chart (non-conformities per unit)
The rest of the “magnificent seven”
Control  Charts  for  Attributes
Page 2


Lecture 11: Attribute Charts
Spanos
EE290H F05
1
P-chart (fraction non-conforming) 
C-chart (number of defects)
U-chart (non-conformities per unit)
The rest of the “magnificent seven”
Control  Charts  for  Attributes
Lecture 11: Attribute Charts
Spanos
EE290H F05
2
Yield Control
30 20 10 0
0
20
40
60
80
100
Months of Production
30 20 10 0
0
20
40
60
80
100
Yield
Page 3


Lecture 11: Attribute Charts
Spanos
EE290H F05
1
P-chart (fraction non-conforming) 
C-chart (number of defects)
U-chart (non-conformities per unit)
The rest of the “magnificent seven”
Control  Charts  for  Attributes
Lecture 11: Attribute Charts
Spanos
EE290H F05
2
Yield Control
30 20 10 0
0
20
40
60
80
100
Months of Production
30 20 10 0
0
20
40
60
80
100
Yield
Lecture 11: Attribute Charts
Spanos
EE290H F05
3
The fraction non-conforming
The most inexpensive statistic is the yield of the production 
line.
Yield is related to the ratio of defective vs. non-defective, 
conforming vs. non-conforming or functional vs. non-
functional.
We often measure:
• Fraction non-conforming (P)
• Number of defects on product (C)
• Average number of non-conformities per unit area (U)
Page 4


Lecture 11: Attribute Charts
Spanos
EE290H F05
1
P-chart (fraction non-conforming) 
C-chart (number of defects)
U-chart (non-conformities per unit)
The rest of the “magnificent seven”
Control  Charts  for  Attributes
Lecture 11: Attribute Charts
Spanos
EE290H F05
2
Yield Control
30 20 10 0
0
20
40
60
80
100
Months of Production
30 20 10 0
0
20
40
60
80
100
Yield
Lecture 11: Attribute Charts
Spanos
EE290H F05
3
The fraction non-conforming
The most inexpensive statistic is the yield of the production 
line.
Yield is related to the ratio of defective vs. non-defective, 
conforming vs. non-conforming or functional vs. non-
functional.
We often measure:
• Fraction non-conforming (P)
• Number of defects on product (C)
• Average number of non-conformities per unit area (U)
Lecture 11: Attribute Charts
Spanos
EE290H F05
4
The P-Chart
P{D = X} =
n
x
p
x
(1-p)
n-x
x = 0,1,...,n
mean np
variance np(1-p)
thesamplefraction p=
D
n
mean p
variance
p(1-p)
n
The P chart is based on the binomial distribution:
Page 5


Lecture 11: Attribute Charts
Spanos
EE290H F05
1
P-chart (fraction non-conforming) 
C-chart (number of defects)
U-chart (non-conformities per unit)
The rest of the “magnificent seven”
Control  Charts  for  Attributes
Lecture 11: Attribute Charts
Spanos
EE290H F05
2
Yield Control
30 20 10 0
0
20
40
60
80
100
Months of Production
30 20 10 0
0
20
40
60
80
100
Yield
Lecture 11: Attribute Charts
Spanos
EE290H F05
3
The fraction non-conforming
The most inexpensive statistic is the yield of the production 
line.
Yield is related to the ratio of defective vs. non-defective, 
conforming vs. non-conforming or functional vs. non-
functional.
We often measure:
• Fraction non-conforming (P)
• Number of defects on product (C)
• Average number of non-conformities per unit area (U)
Lecture 11: Attribute Charts
Spanos
EE290H F05
4
The P-Chart
P{D = X} =
n
x
p
x
(1-p)
n-x
x = 0,1,...,n
mean np
variance np(1-p)
thesamplefraction p=
D
n
mean p
variance
p(1-p)
n
The P chart is based on the binomial distribution:
Lecture 11: Attribute Charts
Spanos
EE290H F05
5
The P-chart (cont.)
p=
m
S
i=1
p
i
m
mean p
variance
p(1-p)
nm
(in this and the following discussion, "n" is the number of 
samples in each group and "m" is the number of groups 
that we use in order to determine the control limits)
(in this and the following discussion, "n" is the number of 
samples in each group and "m" is the number of groups 
that we use in order to determine the control limits)
p must be estimated. Limits are set at +/- 3 sigma.
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