Chapter 5 Control Charts for Variables - PowerPoint PPT Presentation

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Chapter 5 Control Charts for Variables

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Chapter 5 Control Charts for Variables – PowerPoint PPT presentation

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Title: Chapter 5 Control Charts for Variables


1
??????
  • Chapter 5 Control Charts for
    Variables

  • ???????
  • ????? ???
  • ???
    ???
  • ???

2
????
  • 5.1 ??
  • 5.2 ? R ????????
  • 5.3 ? S ????????
  • 5.4 ????????????
  • 5.5 ??????
  • 5.6 ????????

3
5.1??
  • ???????????????????,?????? ( variable
    ),??????????
  • ? R????????????????????????

4
5-2.2????????
  • ?????
  • ?? ?????,???? ,????
  • ???? (1 - a )?????

  • ???


5
5-2.2????????
  • ??? m ???,??? n ????,? ???
  • ?????,????? ??????
  • ?? ,? ? m ??????
  • ,??????
  • ?????,???????????????,???
  • ???

6
???
  • ????????

7
R ???
  • R ????????

8
5-2.2 ?R?????????
  • ??????????????????????,?????? ?R???????????25??,?
    ????5????,???

9
  • ?? ?R????,????R?????,??
    ????????????????,???????????,????????,?R????????
  • ???n5,?D30,D42.114,??????????

10
R???
11
  • ??R???????????,???????? ???,?????
  • ???n5,?A20.577,??????????

12
???
  • ?? ?R????????,?????????????????????????????????

13
???????
  • ? ?????????????????1.5056??,???????
  • ?????????1.50 0.50??,??????????????????,?????????
    ??????

14
(Cont.)
  • ??????????????????Cp,??????????????,????
  • Cp????,?P?????????????,
  • ????????84??????

15
Cp????????
16
???????????
  • ????????????,??????????????,????? ?????????
    ?R??????????

????????????????
  • ????????? ?R????????????????????????????????
  • ??????????????(?????????),???????????????,????????
    ???3s?????????????????
  • ????????????

17
????????
  • ??? ?R???,???????????????????????
  • ????????????????????,?n4,5,6???????????????????
    ???,??????????15?25?
  • R??????????,??????????????????????????,???n??10?12
    ?,????S????S2?????R????

18
(Cont.)
  • ?R????OC????????????,???????????,???????,????????
    ??
  • ?????????????????????????????????????????????????
    ,????????????

19
???????? ?R???
  • ??????,???????????????????????????????????????,???
    ?????????,???????????????
  • ????????????
  • ????????????
  • nold ?????
  • nnew ?????
  • d2(old) ?????????
  • d2(new) ?????????

20
(Cont.)
  • ??????

21
(Cont.)
  • ??????,???????5 ,????????3,?????
  • nold 5
    0.325321
  • d2(old) 2.326 d2(new) 1.693

22
?R???
23
5-2.3???????????
  • ?????????????????????,?????????????,???????
    ?R???
  • A????n,???????
  • d2???????????
  • d3???????????
  • D1d2 -3d3
  • D2d23d3

24
5-2.4 ?R??????
  • ???????????????,???????????????,???????,??????????
    ?,?????????????????????????????????,??????????????
    ???
  • ??(cyclic)
  • ??(mixture)
  • ???????(shift in process level)
  • ??(trend)
  • ??(stratification)

25
5-2.5????? ?R??????
  • R???????????? ????????
  • ?
  • 6 7 5 6 7 8 7 4 6 ??5.6 ??4
  • 6 7 5 6 7 8 20 4 6 ??6.9 ??16
  • ?????,?????????,??,??????????

26
5-2.6??????
  • ?R????????????????????????
  • ?s???????,?? ????OC??,?????
  • ?? ??? ?,????????????(ß??)
    ??????
  • OC???

27
  • ????,????????n4,5,6?, ????????????????(??1.5s??
    ),?,???1s, n5,??????ß0.75,?????????????????0.25,
    ??,???????????????ß(1- ß)0.75(0.25)0.19,????????
    ?????? ,??,??r????????????

28
  • ????,???????,?????????????????(average run
    length, ARL)
  • R??????????,?????????WR/s???????????????s0,?s0???
    s1gts0?,??????????????????,??????????, ?
    s1/s0(???????)????????
  • ??????,R?????????????????????R????????????????????
    ??,???20?25????????????????????

29
5-2.7 ??????????
  • ??????????
  • ??????

30
  • ??????????ARL?????,????????,??ARL?????????????????
  • ????ARL???????????????????????????
  • ?????????????????,?s??10,????ARL??517,?????370,?
    ???????,??10,???268,??370,???????392,????ARL????

31
  • ??????(average time to signal, ATS)
  • ATS??????????????????,??????h???????,?ATS?,ATSARL
    h
  • ????ARL??,??????????????(I),????????????????,?????
    ?n,?I?ARL????,InARL,??????

32
BACK
33
R??????????
BACK
34
  • ??????1.5s???,??n16?????????16???,??n3,???????9?
    ?????

BACK
35
Cyclic
  • ?????????????,????????????????????????????????

BACK
36
Mixture
  • ????????????,??????????
  • ?????????????????????,????????????????????

BACK
37
Shift in process level
  • ???????????????????????????

BACK
38
Trend
  • ?????????
  • ???????????????????????

BACK
39
Stratification
  • ???????????
  • ??????,?????????????????????,??????,??????????????
    ?

BACK
40
5-3.1 ? S ?????????
  • ?2 ??????S2
  • ?????S ?? ??????
  • ?????S??? c4 ??c4 ???
  • S ??????

41
5-3.1 ? S ?????????
  • ? ???????? S ?????????
  • B5, B6, c4 ??????????

42
5-3.1 ? S ?????????
  • ?? ? ??????????????????
  • S??????

43
5-3.1 ? S ?????????
  • ???? ?? ????? ????
  • ????
  • A3???????

44
5-3.1 ? S ?????????
  • ?? ? ??????????????????

45
5-3.2?????? ?S???
  • ??????????????? ?S ?????
  • ? ?
  • m ???
  • ni ? I ?????

46
5-3.2 ?????? ?S???
  • ???????? ???
  • ???????? ???

47
5-3.3 S2 ???
  • S2 ????????
  • ? ?????(n-1)?
  • ????? ??????

48
5-4????????????
  • ?????????n1(??????????)
  • ??????????????????(?????????,?8???????????????????
    ??)
  • CASE
  • ???????????,???????????
  • ???????????ngt1????
  • ???????????????????????????
  • ????????????
  • ??????????
  • ??2????????????????,???
  • MRi xi - xi-1

49
5-4????????????(?)
?5-6
??5-5 ??????????????,???????????????,??????????,?
?????,?????????,?????
50
5-4????????????(?)
  • ??5-5
  • ???????,?n2?,D30,D43.267,
  • LCL0
  • UCLD4
  • (3.267)0.5726
  • 1.871

51
5-4????????????(?)
  • ???????????

??5-6??? (n2,d2 1.128) UCL35.61 ????34.088 L
CL32.57
52
5-4????????????(?)
  • ?5-19

53
5-4????????????(?)
  • ?5-20
  • ???

54
5-4??????
  • ??????????????? ?????,???????????????(?????????
    ????)??,???????????????????
  • ?5-7???5-5?????,??????21?35,????????????????,??5-2
    1

55
5-4??????(?)
  • ?5-21

56
5-4??????(?)
  • ??????????????????,???????????????????
  • ???,??????????????????,?????????????????,?????????
    ?

57
5-4??????(ARL)
  • Crowder(1987)??????????????????????ARL,????????ARL
    ,??????????,??????????????(3s?,ARL?370),????,?????
    ?????3s????,???ARL??????????????????????
  • ?????????????????
  • (D???4?5?????)

58
5-4??????(ARL)(?)
??? ß ARL1
1s 0.9772 43.96
2s 0.8413 6.30
3s 0.5000 2.00
  • ?????????5-15????????5-17ARL??????????????????????
    ,?????????
  • ???????????????????ARL,???????????

59
5-4???
  • Borror?Montgomery?Runger(1997)?????????,??????????
    ????
  • ??????????????t??????????,????????,???????
  • ???3s????????,????????,ARL370,??????ARL??4597??(
    ???????)?t????,ARL??76?283??????4???50(??????????
    ??)
  • ??????????????!

60
5-4???(?)
  • ???????????,???????????,??????????????(?5-22)?
  • ??????????????????????,???????????????????,???????
    ?!

61
5-4???(?)
  • ?5-8??25???????????????,?????????????
  • (??????????Minitab???????)

62
???(?)
  • ?5-23 ?5-24

????????????
?????????
63
5-4???(?)
  • ?5-25

64
5-4????s???
  • ???,???????????????????s
  • MRi xi - xi-1 ,i2,3,.,m(???2?????)
  • ?????s????

65
5-4????s???(?)
  • s???????
  • (0.8865?d2?n2??)
  • ??????????,Cryer?Ryan(1990)???????????????????????
    ??,?

66
5-4????s???(?)
  • ???m??????????????,?2????????????,???????????,???
    ??????
  • ?m????X1 , X2 ,Xt , Xt1 , . Xm,?t?????????(µ0,s
    0),??t1?????????????????µds?

67
5-4????s???(?)
  • Woodall?Montgomery(2001)???
  • Cruthis?Rigdon(1992-93)??,?2????????,?????????????
    ????

68
5-5?????
  • ?5-9

µ?s??
s??
69
5-6????????
  • 1.?????????????
  • 2.??SPC???????
  • 3.SPC????????????
  • 4.?????????? ? R ????
  • 5.????????????

70
5-6????????
  • ????????????

71
5-6????????
  • ????????????

72
  • ????
  • ????
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