six sigma를위한...
TRANSCRIPT
-
SIX SIGMA
-
. ?
1. SIX-SIGMA ?
6 ( : Process) .
6
Tool.
(Ideal Process)
Improvement
Avenue(6)
Q P
Q P
Q P
-
2. SIXMA (PPM)
6 .
(Sigma) % CpkPPM
2
3
4
5
6
95.45%
99.73%
99.994%
99.99994%
99.9999998%
45,000PPM
2,700PPM
63PPM
0.6PPM
2PPB
Cpk = 0.67
Cpk = 1.00
Cpk = 1.33
Cpk = 1.67
Cpk = 2.00
*PPB : Parts Per Billion( )*6 : 6-Sigma (2PPB = 0.002PPM)
*DPU : Defects Per Unit ( = /)
*DPMO : Defects Per Million Opportunities
(100 = /TOP)
*TOP : Total Opportunities = Units op/Unit
( = )
(+1.5 SHIFT )
(K = 0 )
-
3. PPM
PPM
() TV
PPM .
, TV PPM ?
TV 1 = 500EA
(AQL) = 10PPM
TV (, TV = 0% )
, TV
= 100 1 .
10
1,000,000( ) 500 = 1/200
World Class Car = 1,000 DPTV/Year Warranty (35PPM)
1 = 15,000, AQL = 10 DPTV
,
World Class Car Level 1,000 DPTV ,
Maker = (70PPM/2) = 35PPM
, Cpk = 1.33 .
10
1,000P=( ) 15,000 = 150/
10DPTV
150( ) = 0.067DPTV 70PPM
-
4. () (m- )
6 ,
, ,
,
.
A-Type B-Type C-Type
?
B-Type ?
C-Type ?
Spec : m A-Type B-Type C-Type
(m-X bar)
-
5. (Statistical) ?
, ( = Sample)
( = Population) .
(Statistics) .
6 .
.
, .
UCL
CL
LCL
,
,
(X bar) (R) ,
, (=Plot) .
UCL(Upper Control Limit = )
CL(Center Line = )
LCL(Lower Control Limit = )
(Su, SL or USL, LSL)
-
6. (Process) ? (6 Process .)
(Output=, ) ,
(Input=4M) .
.
< >
*
()*
*/4M=Man+Machine+Material+Method
Process = ( = ) =
(, ) ,
Process .
, ( = = .)
*Six Sigma Process !
-
7. (Control) ?
4 .
< >
(Change)
/
(Observe and
or Measure)
(Investigate)
(Decide)
(Compare)
.
.* ., . * .
-
8. Six Sigma (MAIC-CYCLE)
ControlMeasure
(*Define )
Improve Analyze
MAIC
(Deming-cycle)
SPC // /
Improve Quality Increase Productivity Reduce Cost
Lower Price More Competitive Capture More Market
Share Create More Jobs
-
9. (QE) Six sigma
(, Taguchi )
, (Loss)
Quality Engineering
OFF-Line-QC ON-Line-QC
(Robust-Design Of
Experiments)
(SPC)
SIX SIGMA TOOL
-
. Data ( )
1.
* N=(//)* (/)
* n
DATA
*
Action
Tool :
* : , * : X bar, s,* : Cp, Cpk, Z, DPO, DPMO, etc
* : Histogram* : Control-Chart* : Six Sigma
* N = n =
* RS = Random Sampling ( )
* M = Measurement () T = Testing ()
RS M
T
-
2. (MSA) .
SPC , (Gage)
(Measurement Method) , 6
.
(Measurement System analysis)
(, Bias) , .
, . . , .
, , .
, .
1.
(Accuracy)
2.
(Repeatability or
Precision)
3.
(Stability)
4.
(Reproducibility)
* R&R .
* Six Sigma Measure .
-
3. .
(Random Sampling)
*, .
*()=
( = = Stratified Sampling)
* , .
( = = Cluster Sampling)
*.* .
,, ., ,
.
-
4. Pareto()
Vital - Few ( = )Trivial - Many ( = )
Vital-Few
Trivial-Many
* Paretos Diagram J.M.Juran .
* QC 7 Tools .
* , ABC
-
5. ( )
Sample
< Population Parameters > < Sample Statistics >
* Inferences(or Estimation)
S or
1) () =
* N= * n=
= NX
X bar = n
X
-
2) () =
(Sum Of Squares) = = ()
S = (Xi - X bar) 2 = Xi 2 - ( Xi) 2 / n
= s2 = () = 2
* Sample Mean Of Squares
s2 = nS
* Unbiased Variance
2 = = n-1S
= s
* Sample Standard Deviation
s =
* True Standard Deviation
= S2
(Unbiased Estimator) =
(Degrees Of Freedom) = = (n-1)* : (Xi - X bar) = 0 *
= () = 25
-
6.
DATA : 25, 40, 35, 10, 17, 15 ( )
Xi Xi2
25625
401600
351225
10100
17289
15225
xi = 142Xi2 = 4064
(X bar)
X bar = 6
142= 23.67()
(S)
S = 4,064 -1422
= 703.336
(s)
s = 703.336
= 10.83 ()
()
= 703.335
= 11.86 ()
* 6
*
* 6
4
-
. Histogram
1.
.
* (Spray or Dispersion)
.
*(Distribution)
.
* (Spray or Dispersion)
* .
* (Normality-Study) .
* N-Study ( Six Sigma measure )
Location Spread Shape
-
2. Histogram
(Freqency Distribution)
KS A 3001 ,
,
(, Class) ,
.
Histogram,
() .
Histogram
.
.
() () .
* (Normality-Study)
() () .
* = X bar =
(6) .
* Cp, Cpk, Cpu, Cpl, PP%, Ppk .. .
Six Sigma Z-value .
-
< >
1
2
3
4
5
6
7
8
9
No (Class) (Xi) Check fi
20.5~25.5
25.5~30.5
30.5~35.5
35.5~40.5
40.5~45.5
45.5~50.5
50.5~55.5
55.5~60.5
60.5~65.5
25
28
33
38
43
48
53
58
63
4
8
15
18
24
17
10
3
1
100
< Histogram >
0
5
10
15
20
25
20.5 25.5 30.5 35.5 40.5 45.5 50.5 55.5 60.5 65.5
sL = 25.0 m = 37.5 Su = 50.0
-
< Histogram >
* *
*
*
* , *
* , 2
*
*
* 50 , 100 , .
* A ?
-
. (Normal-Distribution)
1.
.
(Parttern)
.
,
, .
, ?
(pdf =Probability Density Function)
f(X) = 2
122 ~ N (, 2)
-e(- )2
-
100, 5 ?
f(X) = 5 2
1 (X-100)2
~ N (100, 52)
=0.5
,
,
=1.0
=1.5
=-2 = 0 = 2
= X bar(Mean)=X median = X mode
-e50
-
2. (Standard Normal Distribution)
U = p.d.f.,
X-
f(U) = 2
12U2
~ N (0, 12)
3 0.27%. (1 = )
-3 -2 -1 +1 +2 +3
68.26%
95.44%
99.73%
,
68.26% 1
95.44% 2
99.73% 3
. Minitab u Z
-e
-
X-Z = U = , OK!
N(1,4), Pr(1X7) ?
() Pr(1X7)= 0.5 - Pr(X7)= 0.5 - Pr(U )= 0.5 - Pr(U3)= 0.5 - 0.0013 = 0.4987
27-1
Pr ?
0.0013
1 7
, Pr(-3X7) ?
() Pr(1X7)= 1 - - = 1 - - Pr(X-3)= 1 - - Pr(U )= 1 - - 0.0228= 1- 0.0013 - 0.0228 = 0.9759
Pr ?
=0.0013
1 7
2-3-1
0.0228=
-3
, SL = 3, Su = 7,
() = + = 0.0013 + 0.0228
(, )
(Normality - Study)
-
3. (U Pr )
Pr ?
O U
N(0,1) Pr = 2
1U e 2
U 2 du
U
0.0*0.1*0.2*0.3*0.4*0.5*
0.6*0.7*0.8*0.9*1.0*
1.1*1.2*1.3*1.4*1.5*
1.6*1.7*1.8*1.9*2.0*
2.1*2.2*2.3*2.4*2.5*
2.6*2.7*2.8*2.9*3.0*
.5000
.4602
.4207
.3821
.3446
.3085
.2743
.2420
.2119
.1841
.1587
.1357
.1151
.0968
.0808
.0668
.0548
.0446
.0359
.0287
.0228
.0179
.0139
.0107
.0082
.0062
.0047
.0035
.0026
.0019
.0013
.4960
.4562
.4168
.3783
.3409
.3050
.2707
.2389
.2090
.1814
.1562
.1335
.1131
.0951
.0793
.0655
.0537
.0436
.0351
.0281
.0222
.0174
.0136
.0104
.0080
.0060
.0045
.0034
.0025
.0018
.0013
.4930
.4522
.4129
.3745
.3372
.3015
.2676
.2358
.2061
.1788
.1539
.1314
.1112
.0934
.0778
.0643
.0526
.0427
.0344
.0274
.0217
.0170
.0132
.0102
.0078
.0059
.0044
.0033
.0024
.0018
.0013
.4880
.4483
.4090
.3707
.3336
.2981
.2643
.2327
.2033
.1762
.1515
.1292
.1093
.0918
.0764
.0630
.0516
.0418
.0336
.0268
.0212
.0166
.0129
.0099
.0075
.0057
.0043
.0032
.0023
.0017
.0012
.4840
.4443
.4052
.3669
.3300
.2946
.2611
.2296
.2005
.1736
.1492
.1271
.1075
.0901
.0749
.0618
.0505
.0409
.0329
.0262
.0207
.0162
.0125
.0096
.0073
.0055
.0041
.0031
.0023
.0016
.0012
.4801
.4404
.4013
.3632
.3264
.2912
.2578
.2266
.1977
.1711
.1469
.1251
.1056
.0885
.0735
.0606
.0495
.0401
.0322
.0256
.0202
.0158
.0122
.0094
.0071
.0054
.0040
.0030
.0022
.0016
.0011
.4761
.4364
.3974
.3594
.3228
.2877
.2546
.2236
.1949
.1685
.1446
.1230
.1038
.0869
.0721
.0594
.0485
.0392
.0314
.0250
.0197
.0154
.0119
.0091
.0069
.0052
.0039
.0029
.0021
.0015
.0011
.4721
.4325
.3936
.3557
.3192
.2843
.2514
.2206
.1922
.1660
.1423
.1210
.1020
.0853
.0708
.0582
.0475
.0384
.0307
.0244
.0192
.0150
.0116
.0089
.0068
.0051
.0038
.0028
.0021
.0015
.0011
.4681
.4286
.3897
.3520
.3156
.2810
.2483
.2177
.1891
.1635
.1401
.1190
.1003
.0838
.0694
.0571
.0465
.0375
.0301
.0239
.0188
.0146
.0113
.0087
.0066
.0049
.0037
.0027
.0020
.0014
.0010
.4641
.4247
.3859
.3483
.3121
.2776
.2451
.2148
.1867
.1611
.1379
.1170
.0985
.0823
.0681
.0559
.0455
.0367
.0294
.0233
.0183
.0143
.0110
.0084
.0064
.0048
.0036
.0026
.0019
.0114
.0010
*=0 1 2 3 4 5 6 7 8 9
-
-
4.
Color-TV A =50(), =8()
. SL=45, SU=62() ,
?
()Pr(X62) + Pr(X45)= + = Pr(U + Pr(U )
= Pr(U1.50)+Pr(U-0.63)= 0.0668+0.2643 = 0.3311
( 33.11%)O U
Wafer =3.10(), =0.02()
, 3.10 0.0392() ,
?
()
862-50
845-50
Pr(XSU) + Pr(XSL) = Pr(U )
= Pr(U1.96) 2 = 0.025 2 = 0.05 = 5%
3.1392-3.100.02
2
-
. (6) Cp, Cpk
1. (Process Capability = 6 SIGMA
6 SIGMA.
J.M.Juran ,
,
,
(Natural Tolerance)
.
,
= 6 Sigma.
()
()
*4M
-
2. (Process Capability Index)
= Cp, Cpk, Cpu, CpL
1) (m) = ( ) m=X bar ( ) = Cp
6
SL m SU
6
6
Cp 1.00
Cp =1.00
Cp 1.00
T
Cp =6T
(, T=SU - SL = = R bar/d2 )
-
mX bar ( ) = Cpk
(T/2)
(m-Xbar)
SL m X bar Su
() = Bias = K | m-X bar | / ( ) Cpk
Cpk = (1-K) Cp = (1-K)
2T
6T
--- Cpk
Cp = ... K
m X bar(m=X bar) Cpk.
-
2)
Su = ()
X bar Su
(Su-Xbar) Cpu = (Su-X bar)/3
SL = ()
X barSL
(Xbar-SL) CpL = (X bar-SL)/3
3
3
--- Cpk
* Capability Ratio = CR = Cp =
* Performance Percent = PP % = Cp = %
(75% Rule !)
-
3. (Cp, Cpk, PP%) ()
Cp or Cpk PP% /
Cp 1.67 59.9%
* .. , .
11.67 Cp1.33
75.2%* ..
21.33 Cp1.00
100%
* .
.Cp 1 ,
.
31.00 Cp0.67
149.3%
* .. , , .
4 0.67 Cp149.3%
* . . , ,
. .
* +1.5 Shift
-
4.
* User,
*
4M
/
Action/
() () ,
Action
()
,
,
()
()
,
/,
Action
-
5. Cpk (*PPM )
(Cp PPM 2)
0.30
.31
.32
.33
.34
.35
.36
.37
.38
.39
.40
.41
.42
.43
.44
.45
.46
.47
.48
.49
.50
.51
.52
.53
.54
.55
.56
.57
.58
.59
.60
.61
.62
.63
.64
184060
176186
168528
161087
153864
146859
140071
133499
127143
121000
115070
109348
103835
98532
93417
88508
83793
79270
74934
70781
66807
63008
59380
55917
52616
49471
46479
43633
40930
38364
35930
33625
31443
29378
27429
0.65
.66
.67
.68
.69
.70
.71
.72
.73
.74
.75
.76
.77
.78
.79
.80
.81
.82
.83
.84
.85
.86
.87
.88
.89
.90
.91
.92
.93
.94
.95
.96
.97
.98
.99
25588
23852
22216
20675
19226
17865
16586
15386
14262
13209
12225
11304
10444
9642
8894
8198
7549
6947
6387
5868
5386
4940
4527
4145
3792
3467
3167
2890
2635
2401
2186
1988
1807
1641
1489
1.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
.10
.11
.12
.13
.14
.15
.16
.17
.18
.19
.20
.21
.22
.23
.24
.25
.26
.27
.28
.29
.30
.31
.32
.33
.34
1350
1223
1107
1001
904
816
736
664
598
538
483
434
390
350
313
280
251
240
200
179
159
142
126
112
100
89
79
70
62
55
48
43
38
33
29
1.35
.36
.37
.38
.39
.40
.41
.42
.43
.44
.45
.46
.47
.48
.49
.50
.51
.52
.53
.54
.55
.56
.57
.58
.59
.60
.61
.62
.63
.64
.65
.66
.67
.68
.69
26
23
20
17
15
13
12
10
9
8
6
6
5
5
4
3
3
3
2
2
2
1
1
1
1
1
1
1
1
0
0
-
-
-
-
Cpk PPMCpk PPMCpk PPMCpk PPM
*PPM(Parts Per Million) = DPM(Defects Per Million)
-
6. Cp, Cpk
() Cp, Cpk , ?
(, 500 10)
bar = 500 (=2.4) bar = 495 (=2.4)
()
Cp =6T =
62.420 = 1.39
Cp = 1.39 ,
( m=500) X bar=495
() K .
2T
220* K = | m-X bar | / ( ) = | 500-495 | / ( ) = 0.5
* Cpk = (1-K) Cp = (1-0.5) 1.39 = 0.695 0.7
SL=490 m=500 =X bar SU=510 SL=490 X bar=495 m=500 SU=510
()
( x bar m )
-
7. Cp, Cpk ( )
X bar m
SL m SLSU m SU SL m SU
Cpk = 0.5 Cpk = 1.0 Cpk = 1.5
SL m SU SL m SU SL m SU
Cp = 0.5 Cp = 1.0 Cp = 1.5
, .
(m-x bar)
-
8. 6 SIGMA
, 6 2 6
. ,
.
1.5
* = 2PPB
*Parts Per Million
x bar
-6 -5-4 -3 -2 -1 1 2 3 4 5 6
SL Su
* 1.5 * = 3.4PPM
x bar
-6 -5-4 -3 -2 -1 1 2 3 4 5 6
SL Su
-1.5 +1.5
0
-
9. 4
6 ( ), 8
.
1.5 , 6210PPM
.
34
* = 63 PPM * = 6,210 PPM
x bar
-4-3 3 4
SL SU-4 -3 3 4
SL SU
-1.5 +1.5
6 12
. * Cp=2.00
Customer , , .
-
10. ()
() X A n=100
. . , A
1510().
No
1
2
3
4
5
6
7
8
9
10.5 ~ 12.5
12.5 ~ 14.5
14.5 ~ 16.5
16.5 ~ 18.5
18.5 ~ 20.5
20.5 ~ 22.5
22.5 ~ 24.5
24.5 ~ 26.5
26.5 ~ 28.5
11.5
13.5
15.5
17.5
19.5
21.5
23.5
25.5
27.5
2
8
14
20
23
15
10
6
2
?
?
%
? ( )
Cp Cpk , ?
-
( )
.
No
1
2
3
4
5
6
7
8
9
10.5 ~ 12.5
12.5 ~ 14.5
14.5 ~ 16.5
16.5 ~ 18.5
18.5 ~ 20.5
20.5 ~ 22.5
22.5 ~ 24.5
24.5 ~ 26.5
26.5 ~ 28.5
11.5
13.5
15.5
17.5
19.5
21.5
23.5
25.5
27.5
2
8
14
20
23
15
10
6
2
Xi fi Ui fiUi fiUi2
-4
-3
-2
-1
0
1
2
3
4
-8
-24
-28
-20
0
15
20
18
8
32
72
56
20
0
15
40
54
32
100 -19 321()
= X bar = 19.5 + 2 = 19.12()
= = 2 = 3.58 ()
100(-19)
9999
321 (-19)100
Histogram (SL & SU ) :
SL=5 M=15 SU=25
27.511.5
X bar =19.12
2
-
,
, ( )
Su=25 , 5.05% .
Cp Cpk
* 0.67 Cp 1.00 ,
.
* m=15 X bar=19.12 ,
Cpk .
* K = | m-X bar| / ( ) = 15-19.12 | / ( ) = 0.412
* Cpk = (1-K) Cp = (1-0.412) 0.931 0.55
* , , .
X bar Su ,
SN(Near) ,
Cpk =
*
* K ,
. -D.J.Lee
U =
X- = 3.58
25-19.12 1.64 Pr = 0.0505
Cp = 6SU-SL =
63.5825-5
0.931
2T
220
3SN- =
33.5825-19.12
0.55
-
1945 ,
.
,
.
*
(Taguchi Genichi),
** Taguchi, (NTT) (ECL)
1950~1960 ,
.
*** 1962 Deming .
Robust ?
()(), ,Strong
. Taguchi()
1. Deming() Taguchi
-
, !
!
* = = =
!
* = + + +
() ( )
( )
+ +
+
+
=
2. Taguchi
-
1979 Sony-USA Sony-JAPAN TV
. (* .)
TV
.
* , ?
2) 1979 4 17 Asahi (TV )
1)
3) ,
4)
Sony-JAPANSony-USA
m-5 m m+5
Sony-JAPAN = m, = 5/3 0.3% > > >
Sony-USA m 5 0.0%
3. !
-
m- m+ m- m+
* * 2
2)
1) Old New
3) L(y) = k { 2 + ( m - x bar )2 }
(Norminal-the-best Type Characteristics)
: , m
(Smaller-the-better Type Characteristics)
: , , Su
(Larger-the-better Type Characteristics)
: , , SL
, L(y)
- Old- - New-
L(y) L(y)
4. Taguchi (Quality Loss Function)
m m
-
FMC W.H.Moor Weather-Strip
Weather-Strip () : Y = 20 4(mm)
Weather-Strip Maker 3 :
Front Door Weather-Strip Door Weather-Strip ()
1) Cpk
20 4(mm)
Maker X bar (mm) (mm) Cpk
20.0 1.333 1.00251.00
18.0 0.667 0.99951.00
17.2 0.400 0.99991.00
Weather-Strip Maker 3 Cp, Cpk
16.0 20.0 24. 0m- m m+
( )CpkCpkbarXmk
Cpm
=
=
=
1
62
5. Cpk ? (Ford-Motor )
-
2) FMC 250,000 (/Year) , ($50/).
(1)
Maker = 250,000 0.00270 50$ = 33,750 $ Maker = 250,000 0.00135 50$ = 16,875 $ * Maker = 250,000 0.00135 50$ = 16,875 $ *
(2) L(Y) = K { 2 + ( X bar - m )2 }
Maker = L1 = 2.0 { 1.3332 + (20-20.0)2 } = 3.55$/ *Maker = L2 = 2.0 { 0.6672 + (20-18.0)2 } = 8.89$/Maker = L3= 2.0 { 0.4002 + (20-17.2)2 } = 16.00$/
(3)
Maker X bar Cpk Taguchi
20.0 1.333 1.00 0.270% 33,750$ 887,500$ *
18.0 0.667 1.00 0.135% 16,875$ 2,222,500$ *
17.2 0.400 1.00 0.135% 16,875$ 4,000,000$ *
L(y) 250,000
* , K=2
* ?