The document discusses attribute control charts which are used to monitor quality characteristics that can only have discrete responses like pass/fail rather than continuous variable measurements. It provides information on the different types of attribute control charts including P, NP, C, and U charts. The key steps for constructing these charts are outlined which include collecting data, calculating control limits, and plotting sample points to check if the process is in control. Formulas for calculating control limits of each chart type are also presented along with examples of how to construct and interpret P, NP, C and U charts.

1. www.themegallery.com
UNIT 4 :UNIT 4 :
CONTROL CHART FOR
ATTRIBUTES
© Mechanical Engineering Department

2. LOGOOUTLINEOUTLINE
 Introduction
 Attribute vs Variable Control Chart
 Advantages & Disadvantages
 Defectives vs Defect
 P, np, C and U Charts

3. LOGOINTRODUCTIONINTRODUCTION
ATTRIBUTE
The term attribute, as used in quality, refers to those
quality characteristics that conform to specifications
or do not conform to specifications.
Where measurements are not possible - - for example,
visually inspected items such as color, missing parts,
scratches, and damage.
Where measurements can be made but are not
made because of time, cost, or need.
Attributes are used:

4. LOGOINTRODUCTIONINTRODUCTION
Two basic types of attribute control charts:
1. Classification Charts
2. Count Charts
Classification Charts
 deal with either the fraction of items or the number of
items in a series of subgroups that have a particular
characteristics
p Chart
 used to control the fraction of items with the
characteristics.
np Chart
 serves the same function as the p chart except that it
is used to control the number rather than the fraction
of items with the characteristics and is used only with
constant subgroup sizes.

5. LOGOINTRODUCTIONINTRODUCTION
Count Charts
 deal with the number of times a particular characteristic
appears in so me given area of opportunity.
c Chart
 used to control the number of times a particular
characteristic appears in a constant area of opportunity.
µ Chart
 serves the same basic function as a c chart, but is used
when the area of opportunity changes from subgroup to
subgroup.

6. LOGOATTRIBUTE VS VARIABLE
Attribute Variable
Used for product characteristics
that can be evaluated with a
discrete response (pass/fail,
yes/no, good/bad, number
defective)
Used when the quality
characteristic can be measured
and expressed in numbers
less costly when it comes to
collecting data
must be able to measure the
quality characteristics in numbers
can plot multiple characteristics on
one chart
may be impractical and
uneconomical
loss of information vs variable
chart

7. LOGOADVANTAGES & DISADVANTAGES
Advantages Disadvantages
Some quality characteristics can only
be viewed as a attribute
Attributes don’t measure the
degree to which specifications are
met or not met
Quality characteristic may be
measurable as a variable but an
attribute is used for time, cost or
convenience
Doesn’t provide much information
on cause
Combination of variables can be
measured as an attribute rather than
use a multivariate chart
Variable chart can indicate
potential changes which allow
preventive actions
loss of information vs variable
chart
Larger sample size required

8. LOGODEFECT VS DEFECTIVES
‘Defect’ – a single nonconforming
quality characteristic.
‘Defective’ – items having one or
more defects.

9. LOGO
p, np - Chart
p and np charts deal with nonconforming
 P is fraction nonconforming
 np is total nonconforming
Charts based on Binomial distribution.
Sample size must be large enough (example p=2%)
Definition of a nonconformity.
Probability the same from item to item.
DEFECT VS DEFECTIVES

10. LOGO
c, u - Charts
c and u charts deal with nonconformities.
 c Chart – total number of nonconformities
 u Chart – nonconformities per unit
Charts based on Poisson distribution.
Sample size, constant probabilities.
DEFECT VS DEFECTIVES

11. LOGOCONSTRUCTION PROCEDURE
The following procedure is used to construct all type of
attribute charts
Step 1
Preliminary samples are taken and inspected
Step 2
When the process achieves the control state, the required
quality characteristics is measured and recorded in the
prescribed data sheet
Step 3
Trial control limits are calculated using appropriate
formulae. Each chart is suitable for different applications

12. LOGOCONSTRUCTION PROCEDURE
Step 4
Draw the control chart
Step 5
Draw the control limits for computed values
Let X – axis Be the sample number
Let Y – axis Be the fraction defectives for the p–charts
Be the number of defectives for the np–charts
Be the number of non-conformities for the c–chart
Be the number of non-conformities per unit for the u – chart
UCL (Dotted line)
Centre Line, CL (Continuous line)
LCL (Dotted line)

13. LOGOCONSTRUCTION PROCEDURE
Step 6
Plot all the measured points (i.e.,past data) on the
appropriate charts. Connect successive points by straight
line segments.
Step 7
If all the points fall within the trial control limits, accept the
trial control limits for present and future references.
Step 8
If there is no systematic behaviour (i.e.,it implies random
pattern), it shown that the process was in control in the
past, therefore, the trial control limits are suitable for
controlling current and future production.

14. LOGOCONSTRUCTION PROCEDURE
Revised control limits:
Step 9
If one or more points fall outside the control limits, try to find
the causes and eliminate these points to the calculation of
the revised control limits.
Step 10
Draw the revised control limits on the previously draw chart
itself.

15. LOGOCONSTRUCTION PROCEDURE
Step 11
If the points other than the eliminated points fall within the
revised control limits, accept the revised control limits for
present and future use.
Step 12
If one or more points other than the removed points fall
outside the revised control limits, repeat the process as
before.

16. LOGOCONSTRUCTION PROCEDURE
TYPES OF ATTRIBUTE CHARTS ARE :
TYPE
p – chart chart for fraction rejected
np – chart chart for number of defective
c – chart chart for non-conformities
u - chart chart for non-conformities per unit

17. LOGOP CHART FORMULA
n
pp
pUCLp
)1(
3
−
+=
n
pp
pLCLp
)1(
3
−
−=
inspectednumberTotal
defectivesofnumberTotal
pCLLineCentre p ==,
The centre line and upper and lower control limits for the P
charts are :

18. LOGOP CHART EXAMPLE
Problem : (constant sample size)
The following table gives the result of inspection of 50 items per
day for 20 days. Construct the fraction defectives or percent
defectives chart and give inference about the process.
Day No. of defectives
1 4
2 0
3 3
4 2
5 3
6 5
7 1
8 2
9 2
10 0
Day No. of defectives
11 3
12 4
13 2
14 5
15 1
16 0
17 4
18 4
19 5
20 2

19. LOGOP CHART EXAMPLE
Solution : (constant sample size)
052.0
1000
52
, ====
inspectednumberTotal
defectivesofnumberTotal
ppCLLineCentre
50
)052.01(052.0
3052.0
)1(
3
−
+=
−
+=
n
pp
p
p
UCL
1462.00942.0052.0 =+=
50
)052.01(052.0
3052.0
)1(
3
−
−=
−
−=
n
pp
p
p
LCL
00422.00942.0052.0 ≈−=−=

20. LOGOP CHART EXAMPLE
Inference :
•All the sample points fall within the control limit and pattern of variation shows the
random pattern.
•The process is in control.
•This limits can be used for future references.

21. LOGOP CHART EXAMPLE
Problem : (variable sample size)
Construct the fraction defectives or percent defectives chart
and give inference about the process.
Day Sample
size
No. of
defectives
1 200 4
2 200 2
3 300 4
4 300 5
5 300 3
6 300 3
7 250 1
8 250 2
9 250 2
10 250 4
Day Sample
size
No. of
defectives
11 250 2
12 250 5
13 250 4
14 250 5
15 250 2
16 200 0
17 200 1
18 200 3
19 200 1
20 200 3

22. LOGOP CHART EXAMPLE
Samples n number of defective p UCL CL LCL
1 200 4 0.020 0.080 0.0115 -0.05644
2 200 2 0.010 0.080 0.0115 -0.05644
3 300 4 0.013 0.067 0.0115 -0.04397
4 300 5 0.017 0.067 0.0115 -0.04397
5 300 3 0.010 0.067 0.0115 -0.04397
6 300 3 0.010 0.067 0.0115 -0.04397
7 250 1 0.004 0.072 0.0115 -0.04926
8 250 2 0.008 0.072 0.0115 -0.04926
9 250 2 0.008 0.072 0.0115 -0.04926
10 250 4 0.016 0.072 0.0115 -0.04926
11 250 2 0.008 0.072 0.0115 -0.04926
12 250 5 0.020 0.072 0.0115 -0.04926
13 250 4 0.016 0.072 0.0115 -0.04926
14 250 5 0.020 0.072 0.0115 -0.04926
15 250 2 0.008 0.072 0.0115 -0.04926
16 200 0 0.000 0.080 0.0115 -0.05644
17 200 1 0.005 0.080 0.0115 -0.05644
18 200 3 0.015 0.080 0.0115 -0.05644
19 200 1 0.005 0.080 0.0115 -0.05644
20 200 3 0.015 0.080 0.0115 -0.05644
Total 4850 56 0.228
Solution : (variable sample size)

23. LOGOP CHART EXAMPLE
Inference :
•All the sample points fall within the control limit and pattern of variation shows the
random pattern.
•The process is in control.
•This limits can be used for future references.

24. LOGOnp CHART FORMULA
)1(3 ppnpnUCLnp −+=
)1(3 ppnpnLCLnp −−=
samplesofNumber
defectivesofnumberTotal
pnCLLineCentre np ==,
The centre line and upper and lower control limits for the np
charts are :

25. LOGOnp CHART EXAMPLE
Problem :
The following table
gives the result of
inspection of 100 items
per day for 25 days.
Construct the fraction
defectives or percent
defectives chart and
give inference about
the process.
Sample n Number of defective
1 100 2
2 100 0
3 100 3
4 100 0
5 100 0
6 100 0
7 100 1
8 100 1
9 100 1
10 100 0
11 100 0
12 100 2
13 100 1
14 100 3
15 100 1
16 100 1
17 100 2
18 100 1
19 100 1
20 100 0
21 100 3
22 100 0
23 100 1
24 100 0
25 100 1

26. LOGOnp CHART EXAMPLE
Solution :
0.1
25
25
.
, ====
samplesofNo
defectivesofnumberTotal
pnnpCLLineCentre
)01.01(0.130.1)1(3 −+=−+= ppnpn
np
UCL
985.3985.20.1 =+=
)01.01(0.130.1)1(3 −−=−−= ppnpn
np
LCL
0985.1985.20.1 ≈−=−=
01.0
2500
25
===
inspectednumberTotal
defectivesofnumberTotal
p

27. LOGOnp CHART EXAMPLE
Inference :
•All the sample points fall within the control limit and pattern of variation shows the
random pattern.
•The process is in control.
•This limits can be used for future references.

28. LOGOC CHART FORMULA
ccUCLc 3+=
ccLCLc 3−=
samplesofNumber
defectsofnumberTotal
cCLc ==
The centre line and upper and lower control limits for the c
charts are :

29. LOGOC CHART EXAMPLE
Problem :
In a copper foil laminations process
for every 500 feet of foil laminated,
one square foot of the laminated
copper foil is examned for visual
defect such as unever lamination,
scrath, etc. The data collected are
shown in the table below. Calculate
the control limit and plot the c-chart.
Time Number of Defect
100 5
200 3
300 2
400 6
500 6
600 7
700 3
800 3
900 6
1000 7
1100 7
1200 9
1300 7
1400 5
1500 3
1600 12
1700 6
1800 10
1900 7
2000 2
2100 6
2200 8
2300 0
2400 7
100 4
200 3

30. LOGOnp CHART EXAMPLE
Solution :
54.5
26
144
.
, ====
samplesofNo
defectsofnumberTotal
ccCLLineCentre
54.5354.53 +=+= cc
c
UCL
60.1206.754.5 =+=
052.106.754.5 ≈−=−=
54.5354.53 −=−= cc
c
LCL

31. LOGOC CHART EXAMPLE
Inference :
•All the sample points fall within the control limit and pattern of variation shows the
random pattern.
•The process is in control.
•This limits can be used for future references.

32. LOGOU CHART FORMULA
n
u
uUCLu 3+=
n
u
uLCLu 3−=
n
c
uCLLineCentre u ==,
The centre line and upper and lower control limits for the u
charts are :

33. LOGOU CHART EXAMPLE
Problem :
A radio manufacturer wishes to
use SQC charts for the detection
of non-conformities per unit on
the final assembly line. The
sample size is finalised as 10
radios. The data collected are
shown in the table. Calculate the
control limit and plot the u-chart.
Sample
number
Number of
non-conformities
1 18
2 20
3 10
4 11
5 15
6 10
7 14
8 13
9 18
10 12
11 19
12 20
13 18
14 14
15 17
16 20
17 22
18 10
19 14
20 12

34. LOGOU CHART EXAMPLE
Solution :
35.15
20
307
.
===
samplesofNo
defectsofnumberTotal
c
10
54.1
354.13 +=+=
n
u
u
u
UCL
72.218.154.1 =+=
36.018.154.1 =−=
53.1
10
35.15
, ====
n
c
uuCLLineCentre
10
54.1
354.13 −=−=
n
u
u
u
LCL

35. LOGOU CHART EXAMPLE
Sample
number
Sample
size
Number of
non-conformities (c)
Number of
non-conformities per unit (u)
1 10 18 1.8
2 10 20 2.0
3 10 10 1.0
4 10 11 1.1
5 10 15 1.5
6 10 10 1.0
7 10 14 1.4
8 10 13 1.3
9 10 18 1.8
10 10 12 1.2
11 10 19 1.9
12 10 20 2.0
13 10 18 1.8
14 10 14 1.4
15 10 17 1.7
16 10 20 2.0
17 10 22 2.2
18 10 10 1.0
19 10 14 1.4
20 10 12 1.2

36. LOGOU CHART EXAMPLE
Inference :
•All the sample points fall within the control limit and pattern of variation shows the
random pattern.
•The process is in control.
•This limits can be used for future references.

37. LOGOCONCLUSION
Control Chart Selection
Quality Characteristic
variable attribute
n>1?
n>=10 or
computer?
x and MR
no
yes
x and s
x and R
no
yes
defective defect
constant
sample
size?
p-chart with
variable sample
size
no
p
or
np
yes constant
sampling
unit?
c u
yes no

38. LOGO
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