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PIQC Institute of Quality
ATTRIBUTE CONTROL
CHARTS
Types of Data
ATTRIBUTE DATA give you counts representing the presence orabsence of a characteristic or defect.
ese counts are ase on t e occurrence o screte events, e.g.,
true/false statements
Accepted or rejected
Passed or fail
An attribute is not numerically measured; its either there or its not.
quality characteristic produced by the process, e.g.,
Diameter of a shaft
Temperature of Oven
Pressure of Steam, etc.
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Nonconforming Defect Defective
Types of Data
Attribute Control Charts
Data
Attribute
Data
Defectives/
UnitsDefects
n fixed n varies n fixed n varies
np Chart p Chart
c Chart u Chart
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Constructing p Chart
Attribute
Unit of measure
Defectives (defected units)
Sample Size
Varying (inconsistent)
Data Collection Frequencyhourly, daily, weekly, etc.
Constructing p Chart
Suppose you work in a plant that manufactures printed
circuit boards with various wave solder machine, which
passes the boards over a surface of liquid solder.
Soldered boards are then connected to test stations,
which test the circuits and classify the boards as either
conforming or nonconforming. Following table contains
records of the daily numbers of rejected circuit boards for
a 30 days period.
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Day Tested (ni) Rejects Proportion
1 286 14
2 281 22
Day Tested (ni) Rejects Proportion
16 297 15
17 283 14
18 321 13
Example 9.1 Step 1: Collect data
4 313 19
5 293 21
6 305 18
7 322 16
8 316 16
9 293 21
19 317 10
20 307 21
21 317 19
22 323 23
23 304 15
24 304 12
10 287 14
11 307 15
12 328 16
13 296 21
14 296 9
15 317 25
25 324 19
26 289 17
27 299 15
28 318 13
29 313 19
30 289 12
Day Tested (ni) Rejects Proportion
1 286 14 0.049
2 281 22 0.078
Day Tested (ni) Rejects Proportion
16 297 15 0.051
17 283 14 0.049
Example 9.1Step 2: Calculate the Fractions for each value
3 310 9 0.029
4 313 19 0.061
5 293 21 0.072
6 305 18 0.059
7 322 16 0.050
8 316 16 0.051
18 321 13 0.040
19 317 10 0.032
20 307 21 0.068
21 317 19 0.060
22 323 23 0.071
23 304 15 0.049
.
10 287 14 0.049
11 307 15 0.049
12 328 16 0.049
13 296 21 0.071
14 296 9 0.030
15 317 25 0.079
.
25 324 19 0.059
26 289 17 0.059
27 299 15 0.050
28 318 13 0.041
29 313 19 0.061
30 289 12 0.042
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Example 9.1
Step 3: Calculate the Central Limit
==
n
pp
Step 4: Calculate the control limits
Example 9.1
=
+=ni
pppUCL
)1(3
== pCL
=
=ni
pppLCL
)1(3
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Constructing the p Chart
Step 5: Plot the p Chart
0. 3
0. 2
roportion
P C hart for Rejects
P=0.1685
3.0SL=0.3324
20100
0. 1
0. 0
Sample Number
-3.0SL=0.004728
Constructing p Chart
printed circuit boards with various wave solder
machine, which passes the boards over a surface of
liquid solder. Soldered boards are then connected to
test stations, which test the circuits and classify the
boards as either conforming or nonconforming.
Following table contains records of the daily
numbers of rejected circuit boards for a 30 days
period.
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Constructing p Chart
Step 1
Choose Stat >
Control Charts >
Attributes Charts >
P.
Constructing p Chart
Ste 2
In Variables, enter
Rejects.
In Subgroup sizes,
enterSampled.
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Constructing p Chart
Step 3
Select tests for special
causes
Constructing p Chart
What is your analysis of
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Constructing np Chart
Attribute
Unit of measure
Defectives (defected units)
Sample Size
Constant
Data Collection Frequencyhourly, daily, weekly, etc.
Constructing np Chart
Suppose you work in a department, where items are
routed through successions of different processes. In
order to keep track of an items progress is to attach
paperwork, also known as travelers. To monitor the
quality of such paperwork; periodic samples of 100
travelers are examined for errors, where a
nonconforming document is defined to be one that
contains at least one error. Following table shows datafrom 25 daily samples of 100 drawn from completed
travelers prior to initiating production.
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PIQC Institute of Quality
Day Sample Size Nonconforming Doc
1 100 10
Example 9.2 Step 1: Collect data
Day Sample Size Nonconforming Doc
14 100 21
3 100 10
4 100 11
5 100 6
6 100 7
7 100 12
8 100 10
16 100 12
17 100 11
18 100 6
19 100 10
20 100 10
21 100 11
9 100 6
10 100 11
11 100 9
12 100 14
13 100 16
22 100 11
23 100 11
24 100 6
25 100 9
100
Constructing np Chart
Step 2: Calculate the Central Limit
==
kn
Xipn
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Constructing np Chart
Step 3: Calculate the control limits
)1(3 ppnpnUCL +=
)1(3 ppnpnLCL =
Constructing np Chart
Suppose you work in a department,
w ere ems are rou e roug
successions of different processes. In
order to keep track of an items
progress is to attach paperwork, also
known as travelers. To monitor the
quality of such paperwork; periodic
samples of 100 travelers are
examined for errors, where a
to be one that contains at least one
error. Following table shows data
from 25 daily samples of 100 drawn
from completed travelers prior to
initiating production.
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Constructing np Chart
Step 1
Choose Stat >
Control Charts >
Attributes Charts >
NP.
Constructing np Chart
Ste 2
In Variables, enter
Rejects.
In Subgroup sizes,
enterSampled.
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Constructing np Chart
Step 3
Select tests for special
causes
Constructing np Chart
Analyze the results.
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Exercise np Chart
The following tablecontains the number of
accidents on the work
site across 40 operating
Number of Accidents
Un
it
March-
June
July to
Oct
Nov to
Feb
1 2 1 2
Number of Accidents
Un
it
March-
June
July to
Oct
Nov to
Feb
21 3 4 1
divisions of a certain
company.3 2 4 0
4 1 2 4
5 1 3 1
6 1 1 1
7 4 8 8
8 0 0 0
9 2 1 2
10 1 0 2
11 3 2 0
23 1 4 1
24 3 1 2
25 1 4 4
26 1 0 0
27 1 0 0
28 1 0 0
29 0 0 0
30 0 0 0
31 0 0 12
12 2 6 3
13 0 3 1
14 0 0 0
15 1 0 1
16 2 2 4
17 0 3 2
18 0 0 3
19 2 0 4
20 2 6 7
32 1 0 1
33 2 3 2
34 0 0 0
35 0 2 3
36 0 0 0
37 0 0 0
38 0 0 0
39 0 1 0
40 1 1 1
ANSWER
=n
Any special cause variation?
______________________________________________
______________________________________________
______________________________________________
onc us on:
______________________________________________
______________________________________________
______________________________________________
______________________________________________
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Constructing c Chart
Attribute
Unit of measure
Defects (e.g., no. of defects in a unit)
Sample Size
Constant
Data Collection Frequencyhourly, daily, weekly, etc.
Constructing c Chart
One measure of software quality is the error rate per
1000 lines of code. With the abbreviation k for the word
thousand, a block of 1000 lines of computer code is
often abbreviated as KLOC (K lines of code). Following
table show the defects per KLOC obtained from daily
test logs in a software company. Plot a c chart for this
case.
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PIQC Institute of Quality
Constructing c Chart Step 1: Record the dataDay Number of Errors per C 1000
Lines of Code (KLOC), Ci
1 6
2 7
Day Number of Errors per C 1000
Lines of Code (KLOC), Ci
16 3
17 2
4 6
5 8
6 6
7 5
8 8
9 1
19 0
20 1
21 2
22 5
23 1
24 7
10 6
11 212 5
13 5
14 4
15 3
25 7
26 127 5
28 5
29 8
30 8
Constructing the c Chart
Step 2: Calculate the the average, UCL and LCL
csubgroupsofno.total
defectstotalCenterline
subgroupperdefectsofnumberc
==
=
cc
c
3LCL
3cUCL
=
+=
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Constructing the c Chartk
==
=
k
C
c ii
1
==
== cc 3LCL
Constructing the c Chart
Step 3: Plot the c Chart
15
10
leCount
C Chart for No. of Defects
1
=
1.0SL=7.966
2.0SL=10.33
3.0SL=12.70
109876543210
5
0
Sample Number
Sam
.
-1.0SL=3.234
-2.0SL=0.8671-3.0SL=0.000
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Constructing c ChartOne measure of software quality
s e error ra e per nes o
code. With the abbreviation k for
the word thousand, a block of
1000 lines of computer code is
often abbreviated as KLOC (K
lines of code). Following table
show the defects per KLOC
obtained from daily test logs in a
.
for this case.
Constructing c Chart
Step 1
Choose Stat >
Control Charts >
Attributes Charts >
c.
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Constructing c Chart
Step 2
In Variables, enter
Blemish.
Constructing c Chart
Step 3
Define the control limits
for standard deviations
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PIQC Institute of Quality 2
Constructing c ChartStep 4
Select tests for special
causes
Constructing c Chart
What is your analysis of
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Exercise c Chart
Off-color flaws in aspirins are caused by extremely small
amounts of iron that change color when wet aspirin
material comes into contact with the sides of drying
containers. At Dow Chemical plant, out of every batch of
aspirin, a 250-lb sample is taken and the number of off-
color flaws is counted. Following table shows the number
of flaws per 250-lb sample obtained over a 25-days
period.
Sample
Number
Number of Flaws
1 46
C Chart Step 1: Collect data
Sample
Number
Number of Flaws
14 49
3 56
4 57
5 37
6 51
7 47
8 34
16 59
17 53
18 61
19 63
20 42
21 45
9 30
10 44
11 47
12 51
13 46
22 43
23 42
24 39
25 38
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ANSWER
Any special cause variation?
______________________________________________
______________________________________________
______________________________________________
onc us on:
____________________________________________________________________________________________
______________________________________________
______________________________________________
Constructing u Chart
Attribute
Unit of measure
Defects (e.g., no. of defects in a unit)
Sample Size
Varying Data Collection Frequency
hourly, daily, weekly, etc.
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Constructing u Chart
The software error rate per 1000 lines of code (i.e., per
KLOC) were obtained from daily test logs for the purpose
of tracking error rates. Suppose that the programming
department decides to speed up the daily error counting
process by simply counting the numbers of errors in
finished software modules. Since the module may
consist of any number of lines of code, the reported error
rates must be converted to a per unit or per KLOC
basis before charting.
Constructing u Chart
ksubgroupsnformitieTotalNoncou
sin=
tsspect onunnum ero nota .
in
uuUCL 3+=
inuUCL 3=
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Constructing u Chart
Constructing u Chart
Step 1
Choose Stat >
Control Charts >
Attributes Charts >
u.
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Constructing u ChartSte 2
In Variables, enter
Defects.
In Subgroup sizes,
enterSample.
Constructing u Chart
Step 3
Select tests for special
causes
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Constructing u Chart
Analyze the results.
Exercise u Chart
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ANSWER
Any special cause variation?
______________________________________________
______________________________________________
______________________________________________
onc us on:
____________________________________________________________________________________________
______________________________________________
______________________________________________
ACCURACY & PRECISION
54
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ACCURACY & PRECISION
55PIQC Institute Of Quality
(A) Most of the da ta we re on ta rget,with very little variation from it.
(C) Even when most of the da ta w ereclose toge ther, they were located off
the target b y a significa nt am ount.
(B) Although some d ata were ontarget , ma ny ot hers were dispe rsed
awa y from the target.
(D) The da ta we re off targe t andwidely dispersed
Is Process within Specification Limits?
Capable
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Process capability is the natural variation in aprocess that results from common causes.
Chapter 08 Process Capability
Process capability
A process is in Statistical Control when
When special causes have been identified andeliminated.
stable.
Mostly the assumption for process capability isthat data is normally distributed.
Estimating Process Variation
Chapter 08 Process Capability
When subgroup are formed, Control chart data can.
For normally distributed data, R chart and s chartcan be used to calculate the standard deviation.
Where, R bar is the average of the ranges of all subgroups.
Assumption: Data is normally distributed
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Estimating Process Variation
Chapter 08 Process Capability
For normally distributed data, R chart and s chartcan e use o ca cu a e e s an ar ev a on.
Where, S bar is the average standard deviation of the std deviations of allsubgroups.
Assumption: Data is normally distributed
Example, you have 100 readings for a particular process.
Process Capability
Process capabil ityis the natural variation in a
Chapter 08 Process Capability
process that results from common causes.
Cp= (USL LSL)
6Where:
USL = upper spec. limitLSL = lower spec. limit
= standard deviation of the process
= An estimate of process standard deviation based on the samplestandard deviation, s)
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Chapter 08 Process Capability
Process Capability
USL LSL is the allowable process spread
6 is the actual process spread
6 is the estimated process spread
Cp < 1.0 not capable
Cp = 1.0 Marginally capableCp > 1.0 capable
Capability Indexes
Process capabil ityis the natural variation in aprocess that results from common causes.
Chapter 08 Process Capability
When Cp = 1, the natural variation is the sameas the design specification width
When Cp < 1, a significant percentage ofoutput will not conform to the specifications
Cp > 1, indicates good capability
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One-sided capability indices that consider off- centered processes
Cpu = (USL )/3
C = LSL /3
Chapter 08 Process Capability
Cpk = Min (Cpl, Cpu) orwhere
)(
|2
)(|
LSLUSL
uLSLUSL
k
+
=
ppk CkC )1( =
USL = upper spec. limit
LSL = lower spec. limit
= the mean performance of the process
= standard deviation of the process (or an estimate based on thesample standard deviation, s)
A controlled process shows an overall mean of 2.50 and
Chapter 08 Process Capability
Example
an average range o . . amp es o s ze were useto construct the control charts.
d2= 2.059
Part A: What are extreme values?
Part B:If specifications are 2.60 0.25, What is the process capability?
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Overall mean = 2.50
R bar = 0.42
Chapter 08 Process Capability
Sample size = 4
Part A:
d2= 2.059,
= R/d2= 0.42/2.059 = 0.20.
x reme va ues = ean
Thus, the observed extreme values are 2.50
3(.020), or 1.90to 3.10.
Part B:
Specifications are 2.60 0.25
Chapter 08 Process Capability
Example
LSL = 2.35
USL = 2.85
Target = 2.60
Apply the formula, Cp is less than 1 so not a capable process.
Example 8.3
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In an automobile company, a lot of 500 shafts has been received from a
vendor. The QC inspector at the receiving has taken a sample of 50pieces and measured the diameter of each of the 50 pieces. The
recorded readings of the 50 pieces are given below. The required
Exercise
Item: Sha ft Parameter Diameter
Lot size: 500 Sam ple size: 50
Standard: 145 +/ - 3
Dimensions (mm):
spec ca ons o e s a are mm w a + - mm o erance.
Calculate the Process Capability (Cp, Cpk) of the supplier.
148 145 143 142 140 149 150 143 148 150
148 145 147 148 141 147 144 142 149 146
145 144 145 148 143 141 145 143 147 145145 144 146 149 145 142 143 142 146 143
143 145 144 142 142 141 142 141 145 142
ANSWER
=
Cp =
Cpk =
Conclusion:
_____________________________________________
_____________________________________________
68PIQC Institute Of Quality
__________________________________________________________________________________________
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