????? ?????? ????? ?????? ?????? Control Charts for Attributes

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????? ??????????? ?????? ??????Control Charts
for Attributes

• ?. ???? ?????????
• m_aichouni_at_yahoo.co.uk
• http//aichouni.tripod.com

????? ????? ??? ??????? ??????????? - 2004
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????? ?? ????? ?????? ??????

• ????? ?????? ?????? ?? ???? ????? ????? ????????
  ????? ????????? ???? ??? ?????? ???? ???? ??????
  ??????? ??????? ?? ????????? ???????? ?? ????.
• ???? ?????? ?????? ?????? ??? ??? ????? ?????
  ???????? conforming ?? ??? ???????? (???? ????)
  non conforming.
• ??? ??????? ??? ?????
• ????? ???? ?????? p chart
• ????? ??? ?????? c chart

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????? ???? ?????? p chart

• ???? ??? ??????? ??? ????? ???? ?????? ? ?????
  ?????? ? ??? ?????? ?????? ??????? ????? ??????
  ????????? (?? ???????).
• ????
• ??? ??????? ??????? ?? ?????? 5
• ????? ???????? ??????? ???????? (???????? ??
  ??????) 50
• ???? ??????? ??????? 5/ 50 100 10
• ?????? ???????? ?????? ?? ??? ??????

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????? ???? ?????? p chart

• ???? ????? ?? ?? ??????? ??? ????? ?????? ? ????
  ??? ???? ?????? ????? ??? ??????? ???????
  (nonconforming items) ? ?? ?? ? ??? ????? ?????
  ???? ?????? ???? ??? ???
• ???? ???? ?????? ?? ?? ????
• ???? ???? ????? ??????
• ??? ????? ???? ?????? ?? ???? ?????
• ????? ????? ?? ???????? ?? ???????.

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p Chart Control Limits ???? ???? ?????
???? ?????? ????? Upper Control Limit ????
?????? ????? Lower Control Limit ????????
???????? ????? ?????? ?p
????? ???? ?????? ?? ??????? p

• ???? z ????? ??? ??????? ???????
• z 2 for 95.5 limits
• z 3 for 99.7 limits

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???? ???? ?????? ???? ?????? p chart

• ???? ?????? ???? ??? ????????? ??????? ??????.
  ???? 10 ????? ?? ?? ???????, ????? ?? ????? ???
  100 ???? ? ?? ??????? ???? ??? ??????? ????? ?
  ???? ????? ????? ??????? ??? ?????? ??????
• ?? ???? ??????? ????? ??????? ?? ?? ?

?????? 1 2 3 4 5 6 7 8 9 10
??? ????? ??????? 5 2 3 8 4 1 2 6 3 4
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???? ???? 2 p chart

• ??? ??????? m 10
• ??? ????? ?? ?? ???? n 100

?????? 1 2 3 4 5 6 7 8 9 10
??? ?????? 5 2 3 8 4 1 2 6 3 4
???? ?????? 0.05 0.02 0.03 0.08 0.04 0.01 0.02 0.06 0.03 0.04
????? ???? ?????? ?? ?? ???????
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???? ???? 3 p chart

• ???? ???? ?????

z 3
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p chart ??? ????? ???? ?????? 4
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????? ??? ?????? ?? ?????? c chart

• ????? ??? ?????? ?? ???? ??? ????? ?????? (???
  ??????) ??????
• ????? ?? ????? ?????? (?? ???? ?????? ???????
  ???????) .
• ???? ??? ??????? ??? ?????? (nonconformities
  (defects)) ?? ?? ???? ?? ??????
• ?????? ?? ???? ???? ????, ????? ??? ?? ????? ...
• ??? ?????? ???? ????.
• ???? ???? ??? ?????? (????, ?????? ??? ?????
  ???..) ?? ?? ???? ?? ???? ????? ??? 100 ????
• .

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c Chart Control Limits ???? ???? ?????

??? ?????? ?? ?? ???? ci

• ???? z ????? ??? ??????? ?????? ?????? ??????
  ???????
• z 2 for 95.5 limits
• z 3 for 99.7 limit

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???? ???? ?????? ??? ?????? c chart

• ???? ??????? ???? ??? ?????? ???????. ?? ???
  ????? ??????? ??? ???? ?????? ??? ?????? ????????
  ?? ???? ????? ?????? ?????? ?????? ?????? ??? 5
  ???? ?? ????? ?????? ? ??? ??????? ????????
  ?????.
• ??????? ?? ???? ????? ?????? ???? ?????? ????
  ??????? ??????? ????????? ?????? (?? ???? ???????
  ????? ??????? ?? ?? ?) (????
  ? z 2)

????? 1 2 3 4 5
??? ?????? 16 21 17 22 24
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c Chart Control Limits ???? ???? ?????

????? ??? ?????? ?? ?? ??????? c
(1621172224) / 5 20
???? ?????? ????? Upper Control Limit
???? ?????? ????? Lower Control Limit
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c chart ??? ????? ??? ??????
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????? 1 ???? ?????? ?? ???
Construction of p chart Example 1
Sample Wrong Number Account Number 1 15
2 12 3 19 4 2 5 19 6 4 7 24
8 7 9 10 10 17 11 15 12 3
The operations manager of the booking services
department of Hometown Bank is concerned about
the number of wrong customer account numbers
recorded by Hometown personnel. Each week a
random sample of 2,500 deposits is taken, and the
number of incorrect account numbers is recorded.
The records for the past 12 weeks are shown in
the following table. Is the process out of
control? (Use 3-sigma control limits.)
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????? 2
Construction of c chart Example 2
Surface defects have been counted on 25
rectangular steel plates, and the data are shown
in the table. Construct a c control chart for
nonconformities using this data to study if the
process is under control
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????? ???? ???? ??? ??? ???????? ?? ?? ????? ?
2000
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???? ????????? ????? 4 ????? ?????? ??????

• ?. ???? ?????????
• m_aichouni_at_yahoo.co.uk

????? ????? ??? ??????? ??????????? - 2004
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Ex 1 - Hometown Bank
Sample Wrong Number Account Number 1 15
2 12 3 19 4 2 5 19 6 4 7 24
8 7 9 10 10 17 11 15 12 3
Total 147
The operations manager of the booking services
department of Hometown Bank is concerned about
the number of wrong customer account numbers
recorded by Hometown personnel. Each week a
random sample of 2,500 deposits is taken, and the
number of incorrect account numbers is recorded.
The records for the past 12 weeks are shown in
the following table. Is the process out of
control? Use 3-sigma control limits.
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Control Charts for Attributes p-chart
Sample Wrong Number Account Number 1 15
2 12 3 19 4 2 5 19 6 4 7 24
8 7 9 10 10 17 11 15 12 3
Total 147
n 2500
Total defectives Total observations
p
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Control Charts for Attributes p-chart
Sample Wrong Proportion Number Account
Number Defective 1 15 0.006 2 12 0.0048
3 19 0.0076 4 2 0.0008 5 19 0.0076 6
4 0.0016 7 24 0.0096 8 7 0.0028 9 10
0.004 10 17 0.0068 11 15 0.006 12
3 0.0012 Total
147
n 2500
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Control Charts for Attributes p-chart
Hometown Bank
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p Chart Wrong Account Numbers
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Plate No. of No.
Nonconformities 1 1 2
0 3 4 4 3 5 1 6 2
7 5 8 0 9 2 10 1 11
1 12 0 13 8 14 0 15
2 16 1 17 3 18 5 19
4 20 6 21 3 22 1 23
0 24 2 25 4
Construction of c Control charts Example 2
Surface defects have been counted on 25
rectangular steel plates, and the data are shown
below. The control chart for nonconformities is
set up using this data
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c Chart Control Limits ???? ???? ?????

????? ??? ?????? ?? ?? ??????? ???????? c
(104.)/25 2.36
???? ?????? ????? Upper Control Limit
???? ?????? ????? Lower Control Limit
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Example 2
The c chart