CONTROL CHARTS FOR
ATTRIBUTES
Name:S.Ramesh
Roll No:100712508122
M.SC(Applied Statistics)
IV semester
DEFINITION

The term Attribute refers to those quality
characteristics that conform to specifications or do not
conform to specifications.

Attribute are used:
1. Where measurements are not possible.
2. Where measurements can be made but are
not made because of time, cost, or need.
DEFECT:

Defect is appropriate for use when evaluation is in
terms of usage.

Nonconformity is appropriate for conformance to
specifications.

The term Nonconforming Unit is used to describe a
unit of product or service containing at least one
nonconformity.
DEFECTIVE

Defective is analogous to defect and is
appropriate for use when unit of product or service
is evaluated in terms of usage rather than
conformance to specifications.

Limitations of variable control charts: These charts
cannot be used for quality characteristics which
are attributes.
TYPES OF ATTRIBUTE CHARTS:
1.
Nonconforming Units (based on the
Binomial distribution): p chart, np chart.
2.
Nonconformities (based on the Poisson
distribution): c chart, u chart.
P CHART

The P Chart is used for data that consist of the
proportion of the number of occurrences of an
event to the total number of occurrences.

It is used in quality to report the fraction or
percent nonconforming in a product, quality
characteristic, or group of quality characteristics.
CALCULATE THE TRIAL CENTRAL LINE AND
CONTROL LIMITS
p (1 p )
UCL p 3
n
LCL
p
np
n
p (1 p )
p 3
n
= average of p for many subgroups
n = number inspected in a subgroup
EXAMPLE
p
np
n
138
0.018
7500
0.018(1 0.018)
UCL 0.018 3
300
0.041
0.018(1 0.018)
LCL 0.018 3
300
0.005 0.0
Subgroup
Number
Number
Inspected
n
np
p
1
300
12
0.040
2
300
3
0.010
3
300
9
0.030
4
300
4
0.013
5
300
0
0.0
6
300
6
0.020
7
300
6
0.020
8
300
1
0.003
19
300
16
0.053
25
300
2
0.007
7500
138
Total
P CHART
0.053
p
UCL
0.04
0.03
0.02
p-bar
0.01
LCL
0
5
10
15
20
Subgroup
25
NP
CHART
 The
np chart is almost the same as the p
chart.
Central line = npo
UCL npo 3 npo (1 po )
LCL npo 3 npo (1 po )
 If
po is unknown, it must be determined by
collecting data, calculating UCL, LCL.
EXAMPLE
Subgroup
n
np
UCL
np -bar
LCL
1
2
3
4
5
300
300
300
300
300
3
6
4
6
20
12.0
12.0
12.0
12.0
12.0
5.24
5.24
5.24
5.24
5.24
0.0
0.0
0.0
0.0
0.0
21
22
23
24
25
300
300
300
300
300
2
3
6
1
8
12.0
12.0
12.0
12.0
12.0
5.24
5.24
5.24
5.24
5.24
0.0
0.0
0.0
0.0
0.0
C
CHART
 The
procedures for c chart are the same as
those for the p chart.
 If count of nonconformities, is unknown, it
must be found by collecting data, calculating
UCL & LCL.
UCL c
c
3 c
LCL c 3 c
c
= average count of nonconformities
g
EXAMPLE
ID Number Subgroup
MY102
1
MY113
MY121
MY125
MY132
MY143
MY150
MY152
MY164
MY166
MY172
MY267
MY278
MY281
MY288
2
3
4
5
6
7
8
9
10
11
22
23
24
25
c
c
g
141
UCL 5.64 3 5.64
5.64
25
c
UCL
c -bar
LCL
7
6
6
3
20
8
6
1
0
5
14
4
14
4
5
12.76
12.76
12.76
12.76
12.76
12.76
12.76
12.76
12.76
12.76
12.76
12.76
12.76
12.76
12.76
5.64
5.64
5.64
5.64
5.64
5.64
5.64
5.64
5.64
5.64
5.64
5.64
5.64
5.64
5.64
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12 .76
LCL 5.64 3 5.64
1.48 0
c-Chart
25
20
Count of Nonconformities
c
UCL
c-bar
15
LCL
10
5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Subgroup Num ber
16
17
18
19
20
21
22
23
24
25
U
CHART
 The
u chart is mathematically equivalent to
the c chart.
c
u
n
u
c
n
u
UCL u 3
n
u
LCL u 3
n
EXAMPLE
ID Number Subgroup
30-Jan
1
31-Jan
1-Feb
2-Feb
3-Feb
4-Feb
28-Feb
1-Mar
2-Mar
3-Mar
4-Mar
u
c
n
3389
1.20
2823
n
c
u
UCL
u -Bar
LCL
2
3
4
5
6
110
82
96
115
108
56
120
94
89
162
150
82
1.091
1.146
0.927
1.409
1.389
1.464
1.51
1.56
1.54
1.51
1.52
1.64
1.20
1.20
1.20
1.20
1.20
1.20
0.89
0.84
0.87
0.89
0.88
0.76
26
27
28
29
30
101
122
105
98
48
105
143
132
100
60
1.040
1.172
1.257
1.020
1.250
1.53
1.50
1.52
1.53
1.67
1.20
1.20
1.20
1.20
1.20
0.87
0.90
0.88
0.87
0.73

For January 30:
c
u Jan 30
n
120
1.09
110
1.20
UCL Jan 30 1.20 3
110
1.51
1.20
110
0.89
LCL Jan 30 1.20 3
Advantages of attribute control
charts
 Allowing for quick summaries, that is, the
engineer may simply classify products as
acceptable or unacceptable, based on various
quality criteria.
 Thus, attribute charts sometimes bypass the
need for expensive, precise devices and timeconsuming measurement procedures.
 More easily understood by managers
unfamiliar with quality control procedures.
THANK YOU