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( MEASUREMENT )
. , .
.
( MEASUREMENT ), , ( INSPECTION )
, , LOT ,
.
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(Measurement System
: :
(Measurement system)
, , , , , , ,
.
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ProductProcess
Inputs Outputs
Products
Process
Process Product Process OutputMeasurement Process .
MeasurementProcess
Outputs
Process
Inputs Data
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( MEASUREMENT DATA )
. , ( MASTER VALUE ) ,
.
( DECISION ) . .
.
. .
(MEASUREMENT VALUE)
=
(TRUE VALUE)+
(MEASUREMENT ERROR)
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)
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Data Product , Data Product.
Data
= 5
=80
Products
= 5
=80
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Data Product.
Data
= 5
=80
Products
= 5
=100
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Data Product.
( )
Data
= 5
=80
Products
= 4
=80
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Data Product.
( )
Data
= 0
=80
Products
= 2
=80
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(: ) , ( ).
Data
= 5
=80
Products
= 5
=100
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:
:
:
(: ) , ( ). Process
.
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. .
.
( SPEC LIMIT ) .
, . , 1/10
.
, , .
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(Standards)
( CALIBRATION ) . , ,
( TRACEABILITY ) .
PRIMARY
STANDARDS
SECONDARY
STANDARDS
WORKING
STANDARDS
= NATIONAL STANDARD> :
) NIST( National Institute of Standards andTechnology )
NBS( National Bureau of Standards ))
= COMPANY STANDARD> SRM( STANDARD REFERENCE MATERIAL )
= PRODUCTION STANDARD > . VRM( VERIFICATION REFERENCE MATERIAL )
,
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SPEC ( CALIBRATION ) “( TRACEABILITY )
, ” . , ( VERIFICATION ) “
” .
. VRM)
..
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( ), , ,
, . , (
, )
( Measurement Uncertainty )
( Accuracy ) ( Precision )
(Bias) (Stability)( Repeatability ) ( Reproducibility )(Linearity)
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( BIAS )
( MASTER VALUE REFERENCE VALUE ).
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( ACCURACY )
( BIAS ) (ACCURACY) ., ( CALIBRATION )
.
(ACCURATE ) (NOT ACCURATE )
( BIAS )
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( PRECISION )
( REPEATABILITY ) ( REPRODUCIBILITY ).
R&R .
) R&R = 5.15 , ( STANDARD DEVIATION OF MEASUREMENT )5.15 ( 99% )
( WIDTH ) ,.
m m
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(REPEATABILITY) (EV:EQIUPMENT VARIATION)
>
( ONEMEASUREMENT INSTRUMENT )
( EV : EQUIPMENT VARIATION )
.
EV = 5.15 , ( STANDARD DEVIATION OF EQUIPMENT )e e
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(REPEATABILITY) (EV:EQIUPMENT VARIATION)
>
, ( WITHIN VARIATION )SYSTEM
.
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(REPRODUCIBILITY) (AV:APPRAISER VARIATION)
>
( AV : APPRAISER VARIATION ) .
) AV = 5.15 , ( STANDARD DEVIATION OF OPERATOR )o o
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(REPRODUCIBILITY) (AV:APPRAISER VARIATION)
>
, ( BETWEENVARIATION )
B
C
A
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( STABILITY )
( CONTROL CHART )
.
2
1
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( LINEARITY )
( BIAS )SRM
.
) )
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( LINEARITY )
( REFERENCE VALUE )
( Same BIAS )
( Different BIAS)
( OBSERVED
AVERAGE VALUE )
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( MEASUREMENT SYSTEM DISCRIMINATION )
,
10 .
( DISCRIMINATION,
RESOLUTION
.
, ,
.
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(MEASUREMENT SYSTEM DISCRIMINATION)
( FLAT )
( INSENSITIVE )
.
1 Data
2~4
5
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( RESULTS )
( SOURCES ) .
.
( DISTRIBUTION ) .
( LOCATION )
( BIAS )( LINEARITY )
( WIDTH or SPREAD )
( REPEATABILITY )( REPRODUCIBILITY )
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( BIAS )
. .
, .
.
( IMPROPERLY )
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34
.
.
( GAGE R&R )
( COMPONENTS OF VARIATION )
²Total Variation
²Product Variation ²R&R
²Repeatability ²Reproducibility
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35
.
( .
) TV = 5.15
( TV:TOTAL VARIATION )
t
TV
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( R&R
) PV = 5.15
) ( PV:PRODUCT VARIATION )
p
TV
PV
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. (Repeatability)(Reproducibility) .
) RR = 5.15
(RR:Gage Repeatability&Reproducibility)
TV
PV
RR RR
EV
AV
TV2 = PV2 + RR2 RR2 = EV2 + AV2
m
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38
, R( CONSISTENCY ) .
, R
.
.
( ) .
. )
.
Page . )
(EV:Equipment Variation)
R / d2*
R
EV e R d515 515 2. . ( / *)
d2*
m
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Tabled2*
(m)
2 3 4 5 6 7 8 9 10 11 12
1 1.41 1.91 2.24 2.48 2.67 2.83 2.96 3.08 3.18 3.27 3.35
2 1.28 1.81 2.15 2.40 2.60 2.77 2.91 3.02 3.13 3.22 3.30
3 1.23 1.77 2.12 2.38 2.58 2.75 2.89 3.01 3.11 3.21 3.29
4 1.21 1.75 2.11 2.37 2.57 2.74 2.88 3.00 3.10 3.20 3.28
5 1.19 1.74 2.10 2.36 2.56 2.73 2.87 2.99 3.10 3.19 3.28
6 1.18 1.73 2.09 2.35 2.56 2.73 2.87 2.99 3.10 3.19 3.27
7 1.17 1.73 2.09 2.35 2.55 2.72 2.87 2.99 3.10 3.19 3.27
8 1.17 1.72 2.08 2.34 2.55 2.72 2.87 2.98 3.09 3.19 3.27
9 1.16 1.72 2.08 2.34 2.55 2.72 2.86 2.98 3.09 3.18 3.27
(g) 10 1.16 1.72 2.08 2.34 2.55 2.72 2.86 2.98 3.09 3.18 3.27
11 1.16 1.71 2.08 2.34 2.55 2.72 2.86 2.98 3.09 3.18 3.27
12 1.15 1.71 2.07 2.34 2.55 2.72 2.85 2.98 3.09 3.18 3.27
13 1.15 1.71 2.07 2.34 2.55 2.71 2.85 2.98 3.09 3.18 3.27
14 1.15 1.71 2.07 2.34 2.54 2.71 2.85 2.98 3.08 3.18 3.27
15 1.15 1.71 2.07 2.34 2.54 2.71 2.85 2.98 3.08 3.18 3.26
>15 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078 3.173 3.258
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40
.( REPEATABILITY ) .
SHEET
A B
1
2
3
4
5
217
220
217
214
216
216
216
216
212
219
216
218
216
212
220
216.3
218.0
216.3
212.7
218.3
1.0
4.0
1.0
2.0
4.0
216
216
216
216
220
219
216
215
212
220
220
220
216
212
220
218.3
217.3
215.7
213.3
220.0
4.0
4.0
1.0
4.0
0.0
217.3
217.7
216.0
213.0
219.2
XA = 216.3, RA = 2.4 XB = 216.9, RB = 2.6 217.3
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41
SHEET ..
> R
= 25 / 10 = 2.5, = 0, = 2.574
= = 2.5 × 2.574 = 6.44
= = 0
X
R D3 D4
UCLR
LCLR
D R4
D R3
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42
.
> R
R
0
2
4
6
8
UCL
R
.
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43
= 2.5 / 1.72 = 1.45 .
40 PAGE ( m = 3 ) ,
( g = 5 × 2 = 10 ) . )
= 5.15 × 1.45 = 7.47 .
**
= 2.5 ×3.04 = 7.60
e R d/ *2
d2*
EV e R d515 515 2. . ( / *)
EV R K1
(r) 2 3
K1 4.57 3.04
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44
5.15 99% .
%R&R
.
Cp
Cp =
= ( SU - SL ) / 6 .
,
99.73% .
99%
99% 5.15
5.15 .
5.15
99%
5.15
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45
.
( ) .
( ) .
.
**
(AV:Appraiser Variation)
AV X Kdiff( )22
2 3
K2 3.65 2.70
AV X do diff515 515 2. . ( / )*
X ddiff / *2o
Xdiff
X
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46
( Reproducibility, AV ) .
A B
1
2
3
4
5
217
220
217
214
216
216
216
216
212
219
216
218
216
212
220
216.3
218.0
216.3
212.7
218.3
1.0
4.0
1.0
2.0
4.0
216
216
216
216
220
219
216
215
212
220
220
220
216
212
220
218.3
217.3
215.7
213.3
220.0
4.0
4.0
1.0
4.0
0.0
217.3
217.7
216.0
213.0
219.2
XA = 216.3 XB = 216.9 X=
216.6R = 2.5
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47
SHEET ..
X
X
X
X
(UCL) = X= RA2
(LCL) = X= RA2
(CL) = X=
= 216.6 + 1.023 * 2.5 = 219.2
= 216.6 – 1.023 * 2.5 = 214.1
= 216.6
R
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48
.
213214215216217218219220
Xbar Chart
UCL=219.2
LCL=214.1
A B
.
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49
> ,
=
= ( 216.9 - 216.3 ) / 1.41 = 0.6 / 1.41 = 0.43
m = 2 ( , g =1(
)
= 5.15 × = 2.21
( EV )
.
Xdiff
o diffX d/ *2
d2*
o
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, AV )
or
n = 5 ( ,
r = 3 ( .
AVX
d nrdiff e[ . ] [ (5. ) ]*515 15
2
22
( ) ( )X K EVnrdiff 2
22
( . ) ( . )
.
2 2 7 55 3
109
22
( . ) ( . )
.
2 2 7 65 3
109
22
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(PV:Product Variation)
( R&R STUDY (Rp)
.
.
A B
1
2
3
4
5
217
220
217
214
216
216
216
216
212
219
216
218
216
212
220
216.3
218.0
216.3
212.7
218.3
1.0
4.0
1.0
2.0
4.0
216
216
216
216
220
219
216
215
212
220
220
220
216
212
220
218.3
217.3
215.7
213.3
220.0
4.0
4.0
1.0
4.0
0.0
217.3
217.7
216.0
213.0
219.2
XA = 216.3, RA = 2.4 XB = 216.9, RB = 2.6 217.3
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.
= ( 219.2 - 213.0 ) / 2.48 = 6.2 / 2.48 = 2.50
m = 5 ( , g = 1(
)
PV = 5.15 × p = 5.15 × 2.50 = 12.88
**
PV = 6.2 × 2.08 = 12.90
P PR d/ *2
d 2*
PV R KP 3
(n) 2 3 4 5 6 7 8 9 10
K3 3.65 2.70 2.30 2.08 1.93 1.82 1.74 1.67 1.62
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(RR) (TV)
.
EV
AVX
d n r
PV
RR EV AV
TV RR PV
e
odiff e
p
m
t
515 7 47
515 15 15 1 09
515 12 88
515 7 55
515 14 93
2
22
2 2
2 2
. .
. (5. ) (5. ) .
. .
. ( ) .
. ( ) .
*
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1
2
3
4
5
6
7
8
9
10
No
Gage R&R Data Sheet( )Clic
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1 52.70 52.65 52.70 52.80 52.70 52.80 52.75 52.70 52.70
2 52.20 52.25 52.30 52.45 52.40 52.40 52.35 52.35 52.30
3 51.05 51.05 51.05 51.05 51.05 51.10 51.00 52.05 51.00
4 51.90 52.05 52.00 51.90 51.95 51.95 52.10 52.00 52.05
5 51.55 51.60 51.50 51.60 51.50 51.60 51.60 51.60 51.50
6 52.20 51.25 51.25 51.25 51.25 51.20 51.20 51.20 51.30
7 51.50 51.40 51.40 51.50 51.45 51.50 51.45 51.50 51.50
8 52.20 52.25 52.25 52.20 52.10 52.15 52.20 52.30 52.30
9 51.15 51.20 51.15 51.30 51.25 51.25 51.40 51.40 51.40
10 51.00 51.05 51.10 51.05 51.10 51.10 51.10 51.20 51.20
No
Gage R&R (1)Clic
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Column
No
Gage R&R (2)Clic
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> > > Gage R&R
Gage R&R (3)Clic
k to buy N
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.
.
1.
Gage R&R (4)Clic
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Gage R&R (4_1)
>
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60
,,
R-Chart
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Gage R&R (5)
Gage R&R
% ()
Gage R&R 0.005567 1.700.001979 0.600.003588 1.09
operator 0.001184 0.36operator*part no 0.002404 0.73
- - 0.322727 98.300.328294 100.00
(SD) (6 * SD) % (%SV)Gage R&R 0.074613 0.44768 13.02
0.044488 0.26693 7.760.059900 0.35940 10.45
operator 0.034407 0.20644 6.01operator*part no 0.049032 0.29419 8.56
- - 0.568090 3.40854 99.150.572969 3.43781 100.00
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R&R
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Gage R&R
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# # 95% CI
1 12 10 83.33 (51.59, 97.91)
2 12 5 41.67 (15.17, 72.33)
3 12 8 66.67 (34.89, 90.08)
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# # 95% CI1 12 9 75.00 (42.81, 94.51)2 12 4 33.33 ( 9.92, 65.11)3 12 8 66.67 (34.89, 90.08)
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# / # / #
1 1 16.67 0 0.00 2 16.67
2 1 16.67 0 0.00 7 58.33
3 0 0.00 0 0.00 4 33.33
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# # 95% CI
12 3 25.00 (5.49, 57.19)
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# # 95% CI
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