1. CONTROL CHARTS FOR
ATTRIBUTES
Name:S.Ramesh
Roll No:100712508122
M.SC(Applied Statistics)
IV semester

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. CALCULATE THE TRIAL CENTRAL LINE AND
CONTROL LIMITS
n
pp
pUCL
)1(
3
n
pp
pLCL
)1(
3
n
np
p = average of p for many subgroups
n = number inspected in a subgroup

8. EXAMPLE
Sub-
group
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
Total 7500 138
018.0
7500
138
n
np
p
0.0005.0
300
)018.01(018.0
3018.0LCL
041.0
300
)018.01(018.0
3018.0UCL

9. P CHART
0.053
p-bar
LCL
UCL
Subgroup
p
5 10 15 20 25
0
0.01
0.02
0.03
0.04

10. NP CHART
 The np chart is almost the same as the p
chart.
Central line = npo
 If po is unknown, it must be determined by
collecting data, calculating UCL, LCL.
)1(3 ooo pnpnpUCL
)1(3 ooo pnpnpLCL

11. EXAMPLE
Subgroup n np UCL np -bar LCL
1 300 3 12.0 5.24 0.0
2 300 6 12.0 5.24 0.0
3 300 4 12.0 5.24 0.0
4 300 6 12.0 5.24 0.0
5 300 20 12.0 5.24 0.0
21 300 2 12.0 5.24 0.0
22 300 3 12.0 5.24 0.0
23 300 6 12.0 5.24 0.0
24 300 1 12.0 5.24 0.0
25 300 8 12.0 5.24 0.0

13. 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.
= average count of nonconformities
ccUCL 3 ccLCL 3
g
c
c

14. EXAMPLE
ID Number Subgroup c UCL c-bar LCL
MY102 1 7 12.76 5.64 0
MY113 2 6 12.76 5.64 0
MY121 3 6 12.76 5.64 0
MY125 4 3 12.76 5.64 0
MY132 5 20 12.76 5.64 0
MY143 6 8 12.76 5.64 0
MY150 7 6 12.76 5.64 0
MY152 8 1 12.76 5.64 0
MY164 9 0 12.76 5.64 0
MY166 10 5 12.76 5.64 0
MY172 11 14 12.76 5.64 0
MY267 22 4 12.76 5.64 0
MY278 23 14 12.76 5.64 0
MY281 24 4 12.76 5.64 0
MY288 25 5 12.76 5.64 0
64.5
25
141
g
c
c
76.1264.5364.5UCL
048.1
64.5364.5LCL

15. c-Chart
0
5
10
15
20
25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Subgroup Number
CountofNonconformities
c
UCL
c-bar
LCL

16. U CHART
 The u chart is mathematically equivalent to
the c chart.
n
c
u
n
c
u
n
u
uUCL 3 n
u
uLCL 3

17. EXAMPLE
ID Number Subgroup n c u UCL u -Bar LCL
30-Jan 1 110 120 1.091 1.51 1.20 0.89
31-Jan 2 82 94 1.146 1.56 1.20 0.84
1-Feb 3 96 89 0.927 1.54 1.20 0.87
2-Feb 4 115 162 1.409 1.51 1.20 0.89
3-Feb 5 108 150 1.389 1.52 1.20 0.88
4-Feb 6 56 82 1.464 1.64 1.20 0.76
28-Feb 26 101 105 1.040 1.53 1.20 0.87
1-Mar 27 122 143 1.172 1.50 1.20 0.90
2-Mar 28 105 132 1.257 1.52 1.20 0.88
3-Mar 29 98 100 1.020 1.53 1.20 0.87
4-Mar 30 48 60 1.250 1.67 1.20 0.73
20.1
2823
3389
n
c
u

18.  For January 30:
09.1
110
120
30
n
c
uJan
51.1
110
20.1
320.130JanUCL
89.0
110
20.1
320.130JanLCL

20. 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 time-
consuming measurement procedures.
 More easily understood by managers
unfamiliar with quality control procedures.

21. THANK YOU