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8/19/2019 Ch.4 - Control Charts for Attributes.ppt
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Topic 4.0
Control Chart forAttributes
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Introduction
Many quality characteristics cannot beconveniently represented numerically.
In such cases, each item inspected is
classied as either conforming ornonconforming to the specications onthat quality characteristic.
uality characteristics of this type are
called attributes. !"amples are nonfunctional semiconductor
chips, #arped connectin$ rods, etc,.
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When to use a control
chart? Controlling ongoing processes by finding and correcting
problems as they occur.
Determining whether a process is stable (in statistical
control).
Analyzing patterns of process variation from special
causes (non-routine events) or common causes (built intothe process).
Determining whether the quality improvement proect
should aim to prevent specific problems or to ma!e
fundamental changes to the process.
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"ariables control charts "ariable data are measured on a continuousscale.
#$ample% time& weight& distance or temperature canbe measured in fractions or decimals.
Attributes control charts Attribute data are counted and cannot havefractions or decimals. Attribute data arise when youare determining only the presence or absence ofsomething& such as%
o success or failureo accept or reecto correct or not correct.
#$ample& a report can have four errors or fiveerrors& but it cannot have four and a half errors.
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Advantages of attribute
control charts Allowing for quic! summaries& that is& the engineermay simply classify products as acceptable or
unacceptable& based on various quality criteria.
'hus& attribute charts sometimes bypass the needfor e$pensive& precise devices and time-consuming
measurement procedures.
ore easily understood by managers that unfamiliar
with quality control procedures.
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Defect vs. Defective
Defect* + a single nonconforming quality
characteristic.
Defective* + items having one or more
defects.
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Choice Between
Attributes
and Variables Control
Charts
#ach has its own advantages and disadvantages Attributes data is easy to collect and several
characteristics may be collected per unit.
"ariables data can be more informative sincespecific information about the process mean andvariance is obtained directly.
"ariables control charts provide an indication ofimpending trouble (corrective action may be ta!en
before any defectives are produced). Attributes control charts will not react unless the
process has already changed (more nonconformingitems may be produced.
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Advantages of attributecontrol charts Allowing for quic! summaries& that is& the engineer
may simply classify products as acceptable or
unacceptable& based on various quality criteria.
'hus& attribute charts sometimes bypass the needfor e$pensive& precise devices and time-consuming
measurement procedures.
ore easily understood by managers that unfamiliar
with quality control procedures.
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p charts: proportion of units nonconforming.
np charts: number of units nonconforming.
c charts: count of nonconformities.
u charts: count of nonconformities per unit.
Control Charts for Variables Data
X and R charts: for sample averages and ranges.
Md and R charts: for sample medians and ranges.
X and s charts: for sample means and standard deviations.
X charts: for individual measures; uses moving ranges.
Types of Control Charts
Control Charts for Attributes Data
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Type of Attribute Charts
p charts This chart sho#s the fraction of nonconformin$ or defective
product produced by a manufacturin$ process. It is also called the control chart for fraction nonconformin$.np charts
This chart sho#s the number of nonconformin$. Almost thesame as the p chart.c charts This sho#s the number of defects or nonconformities
produced by a manufacturin$ process.u charts This chart sho#s the nonconformities per unit produced by a
manufacturin$ process.
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p charts
• ,n this chart& we plot the percent of
defectives (per batch& per day& per machine&
etc.).
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p-Chart construction forconstant subgroup size %elect the quality characteristics. &etermine the sub$roup si'e and method Collect the data. Calculate the trial central line and control
limits. !stablish the revised central line and
control limits. Achieve the ob(ective.
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Forula
raction nonconforming%
p (np)/n
0here&
p proportion or fraction nc in the sample
or subgroup&
n number in the sample or subgroup& np number nc in the sample or subgroup.
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Calculate the trial central line andcontrol limits
'he formula%
average of p for many subgroups
Where, n number inspected in a subgroup
n
p p pUCL
)1(3
−+=
n
p p p LCL
)1(3
−−=
∑∑=
nnp p
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%ub)$roup
*umber
*umberInspected
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
018.07500
138===
∑∑
n
np p
0.0005.0
300
)018.01(018.03018.0
=−=
−−= LCL
041.0
300
)018.01(018.03018.0
=
−+=UCL
*e$ative value of +C+ is possible in a theoriticalresult, but not in practical proportion of nc never
ne$ative-.
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p Chart
p-bar
1C1
2C1
3ubgroup
p
4 56 54 76 74
6
6.65
6.67
6.68
6.69
6.648
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!stablish the revised central lineand control limits
Determine the standard or reference value for
the proportion nc& po.
#here npd number nc in the discarded
sub$roups nd number inspected in the discarded
sub$roups
∑∑
−−=
d
d
newnnnpnp p
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!"!#CI$!%
3hows data for the result inspection
operation bottel from au a!mur
Company 3dn :hd. ;aving 76 subgroup
each another 566 bottel. Define%i) Average zero defect
ii) 1ine for limit control upper ang loer
iii)
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SUBGROUP NONCONFORMING (np) SUBGROUP NONCONFORMING (np)
1 14 11 8
2 10 12 12
3 12 13 9
4 13 14 10
5 9 15 11
6 11 16 10
7 10 17 8
8 12 18 12
9 13 19 10
10 10 20 16
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np Chart
'he np chart is almost the same as the p chart.
Central line npo
,f po is un!nown& it must be determined bycollecting data& calculating 2C1& 1C1.
)1(3 ooo pnpnpUCL −+=
)1(3 ooo pnpnp LCL −−=
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!&aple
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$epintas lalu'$epintas lalu'
;ati > itu !adang!ala perlu ua di!etu! ia dgn
uian& agar ia terdidi! ut! tida! sentiasa
selesa pada ?!esu!aan? tapi uga selesa dgn
?!esa!itan?... @adi senyumlahB wahai saudara!u& walau
su!a walau du!a !erana yg su!a itu
anugerah dan yg duka itu tarbiyyah dari,1A;, buat hambanya yg di!asihi.
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!nd (f $ession
'han! ou and
%!*/M
http://../Documents/Raihan%20-%20Senyum.flvhttp://../Documents/Raihan%20-%20Senyum.flv
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c Chart
'he procedures for c chart are the same a sthose for the p chart.
,f count of nonconformities& co& is un!nown& it
must be found by collecting data& calculating2C1 E 1C1.
average count of nonconformities
ccUCL 3+= cc LCL 3−=
g
cc =
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!&aple 64.525
141===
g
cc
76.1264.5364.5 =+=UCL
048.1
64.5364.5
=−=
−= LCL
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c-Chart
6
4
56
54
76
74
5 7 8 9 4 F G H I 56 55 57 58 59 54 5F 5G 5H 5I 76 75 77 78 79 74
ubgroup !umber
C o u n t o f ! o n c o n f o r m i t i e s
c
2C1
c-bar
1C1
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#evised
Jut-of-control% sample no. 4& 55& 78.
23.4
325
141420141=
−
−−−=
−
−=
d
d new
g g
ccc
40.1023.4323.43 =+=+= oo ccUCL
094.123.4323.43 =−=−=−= oo cc LCL
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u Chart
The u chart is mathematically equivalentto the c chart.
ncu =
∑∑=
ncu
n
uuUCL 3+=
n
uu LCL 3−=
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!&aple20.1
2823
3389===
∑
∑n
cu
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or @anuary 86%
09.111012030 ===
ncu Jan
51.1
110
20.1320.130 =+= JanUCL
89.0110
20.1320.130 =−= Jan LCL
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)onconfority Classi*cation
Critical nonconformities ,ndicate hazardous or unsafe conditions.
aor nonconformities ailure
inor nonconformities
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Control Charts for +ariables vs. Charts for Attributes
3ometimes& the quality control engineer has
a choice between variable control charts and
attribute control charts.