Ch5 Control Charts for Variables - PowerPoint PPT Presentation

About This Presentation
Title:

Ch5 Control Charts for Variables

Description:

Ch5 Control Charts for Variables Variable numerical measurement A single measurable quality characteristic, such as a dimension, weight, or volume, is called a ... – PowerPoint PPT presentation

Number of Views:175
Avg rating:3.0/5.0
Slides: 61
Provided by: edut1279
Category:

less

Transcript and Presenter's Notes

Title: Ch5 Control Charts for Variables


1
Ch5 Control Charts for Variables
  • Variablenumerical measurement
  • A single measurable quality
    characteristic, such as a
  • dimension, weight, or volume, is called a
    variable.

2
  • Process mean?Process variability????control.
  • (a) Mean and standard deviation at nomial levels.

3
(No Transcript)
4
Statistical Basis of the Charts
?X ??Normal,?n ???,???C.L.?????
5
relative range.
App. VI)
6
?n?????
??exhibit in control.
7
C.C. for process mean
C.C. for process mean
8
R chart???
App. VI)
9
Example 1
25?samples,??n5(???)
(???)
(???)
10
Estimating Process Capability
?????????Capability(??)
  • ??????specification limits?74 0.05mm,
  • ??????????????????
  • PCR(process capability ratio)?????capability???

11
????????natural tolerance limits????? USL?LSL???
12
  • PCR gt 1

13
(No Transcript)
14
Revision of Control Limits and Center Lines
(?????C.L.?Center Lines)
?????????25?50?100????
  1. ?R chart??in control?process mean?????variable??,?
    ??center line??target value,??process
    mean??????variables???,?????????
  2. ?R chart??out of control,?eliminate????????center
    line?control limit?

15
  • ???????
  • ?????tolerance chart(??tier diagram)?
  • ?n?7 or 8?,????Box plot.

16
  • CL ?SL?NTL CL ?SL??????????????
  • CL??process?natural variability(?NTL)????
  • SP???management?engineer?customers??
  • (??????????)?
  • Control chart??CL?
  • Tolerance chart??specification limits?

17
2. ?R chart?? ? ??process variability within
sample
??variability within samples???chance ?random
causes
18

??C.C.???
  • CC?????
  • ?????cost of sampling, costs of investigating
  • and possibly correcting the process in
    response to out
  • of control signals, costs associated with
    producing a
  • product that does not meet specifications.

19
  • small n ???shift?????sample???

20
  • ????small, frequent or larger samples less
    frequently,
  • ?????????small, frequent?????
  • ??????rate of production???

21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
Example 2??????
??process exhibits good control
(???)
(???)
25
(?????Type I level????control limitUK?????)
26
(No Transcript)
27
  • ??????,???out of control???!

28
Case 1 Cycles
29
Case 2 Mixture pattern
???? ?????overlapping ??????????
??,overlap??,? ????????????overcontrol????
Case 3 Shift in process level
???? ?????????? ??????????
???????,?? skill????????motivations?
30
Case 4 Trend
???? tool?????,operator
fatigue?presence of supervisor(????
critical process component)?????????????
??????????(??????)?
Case 5 Stratification (?????????? ???,lack of
natural variability!)
31
  • ???????underlying????????????
  • ????,???????probability limit,????
  • CC,????????,underlying???????,
  • ??????CC?normality???robustness???

32
(No Transcript)
33
The Operating-Characteristic Function
(???)
(??k?sample(after the shift)?detect?shift???)
(???????????)
34
R chart?O.C. curve
(???)
??O.C. curve????????,?????2025 subgroups???C.C. ?
35
(???)
Average Time to Signal ATSARL.k
Expected number of individual units
sampled InARL (???)
36
?
2. The sample size n is variable.
37
(No Transcript)
38
(No Transcript)
39
(No Transcript)
40
Example 3
???????(???)
41
(No Transcript)
42
(No Transcript)
43
Example 4
??????n3n5(???)
44
????sample,n5?C.L.
(??????)
45
(No Transcript)
46
(recommended by some practitioners)
47
Control Limits Base on a Small Number of
Samples (Short Production Runs)
48
Control Charts for Individual Measurements
  • ?n1???
  • 1. ??????????
  • 2. ??????,???ngt1?
  • 3. ?????????????????????,
  • (e.g. ????),???????????
  • 4. ????????????,???????,
  • ?????????,????std. dev.?????

49
  • ??detect?shift???,????Ch 7?cumulative
  • sum?exponential weighted moving-average
    C.C. ?

50
Example 5
  • ????????
  • ????????
  • ????????
  • ??batch???,
  • ????????
  • ???batch?

51
Control chart for the moving range
In control
Control chart for individual observations
52
  • ???,???????1630 batches?

??Moving range C.C.????moving ranges???,
??,???Moving range C.C.??pattern?,?
???????????moving range chart,?
???????center line??,?????out of
control,???x chart?,??????? out of
control !
53
  • ???individual?moving range C.C.?3-sigma limit
  • ???narrow???detect small process shift???,
  • ?????????cumulative sum C.C.?
  • exponentially weighted moving-average C.C. ?

54
  • ?individual C.C.??,?????normality???,?
  • 1. ??percentiles of underlying
    distribution???control
  • limits?
  • 2. ?transfer variable??????Normal???,??
  • ?C.C.?

55
Applications of Variable Control Charts
Example 7
Supplier A
Center??,?variability??(??SPC??)?
Supplier B
Center??,?variability??(????,?? ????NC?????center?
?????)?
56
Example 8
  • Job-shop???????????short production runs?
  • ???? process characteristic.
  • ?????????part?,?????????,
  • ???????????,????????????
  • ???????correct diameter,????????
  • deviation of the actual hole diameter from
    the nominal
  • diameter, ??????????????

57
Example 9
  • ??????,??????specification limits,?
  • process capability?????!

58
Example 10
  • ????????????????,???????
  • ????????????(???)?
  • ??????

1. ??????????5?????(vane), ??????(i.e. n5)?
4. ??????,????part??5????,? ??????rational
subgroup?
59
  • ?????five vanes???????individual
  • measurement,??moving-range chart?monitor
  • between sample?variability?
  • ??S chart Moving range chart tolerance
    chart
  • ????????

60
  • ???quality characteristic?casting??opening
    diameter?
  • ?????????,???opening???24?(??
  • ??????)(i.e. n24)
  • S chart??????????part?roundness,??out
  • of control????,??????????(???) ?

61
Back
62
Back
63
Back
64
Back
65
Inside diameter measurements(mm) on forged piston
rings
Back
66
R chart for Example 1
Back
67
Back
68
Back
69
Continuation of the R chart for Example 1
Back
70
Tolerance chart for Example 1
Back
71
Recalculated control limits for the piston- ring
data to reflect changing the sample size form
n5 to n3.
Back
72
Back
73
O.C. curve for the R chart with 3-sigma limits
Back
74
Back
75
Back
76
Computation of control limits for Example 4
Back
77
Back
78
Control chart for individual observations
Control chart for the moving range
Back
79
Actions taken to improve a process
Is the process capable?
Yes
No
Yes
Is the process in control?
No
Back
80
Control chart for S and tolerance chart for vane
height data, Example 10
?S chart???within part ?variation??????
?
Back
81
S chart for diameter, Example 10. This is
essentially a control chart for roundness
??wax pattern??,????wooden cooling
fixture???pattern?????
Back
82
An aerospace casting
Back
Write a Comment
User Comments (0)
About PowerShow.com