Key comparison APMP.L-K3
12-sided polygon
MEASURAND : Deviation from nominal angle between two faces of the polygon
result of measurement carried out by laboratory i
combined standard uncertainty of x i
xi :
ui :
Face
1-2
2-3
3-4
4-5
5-6
6-7
7-8
8-9
9-10
10-11
11-12
12-1
Year of
measurement
1.434
1.56
1.581
1.52
0.90
1.60
1.48
1.42
1.46
0.97
1.53
1.20
-0.546
-0.481
-0.63
-0.655
-0.63
-0.30
-0.53
-0.62
-0.59
-0.43
-0.39
-0.61
-0.50
0.422
0.58
0.597
0.53
0.20
0.46
0.62
0.44
0.23
0.27
0.56
0.40
2005 to 2007
2005
2005
2005
2006
2006
2006
2006
2007
2007
2007
2007
9-10
10-11
11-12
12-1
0.080
0.10
0.064
0.07
0.30
0.17
0.06
0.08
0.39
0.26
0.06
0.83
0.080
0.10
0.064
0.07
0.30
0.17
0.06
0.08
0.39
0.26
0.04
0.39
0.080
0.10
0.064
0.07
0.30
0.17
0.06
0.08
0.39
0.26
0.04
0.19
0.080
0.10
0.064
0.07
0.30
0.17
0.06
0.08
0.39
0.26
0.04
0.15
x i / arc seconds
NMISA
NMIA
KRISS
NMIJ/AIST
NMC/A*STAR
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
Face
NMISA
NMIA
KRISS
NMIJ/AIST
NMC/A*STAR
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
0.444
0.42
0.428
0.43
0.20
0.36
0.39
0.48
0.41
0.24
0.45
0.40
-0.192
-0.532
-0.202
0.048
-0.664
0.04
0.050
0.08
0.20
0.00
0.03
0.10
0.00
-0.03
0.05
0.00
0.095
0.17
0.185
0.17
0.10
0.07
0.17
0.17
0.11
0.21
0.18
0.10
-0.08
-0.101
-0.11
0.00
-0.16
-0.08
-0.13
0.09
-0.04
-0.11
-0.20
-0.53
-0.511
-0.50
-0.40
-0.47
-0.47
-0.50
-0.53
-0.34
-0.53
-0.40
-0.30
-0.271
-0.28
-0.30
-0.16
-0.30
-0.26
-0.28
-0.13
-0.30
-0.20
0.02
0.033
0.07
0.00
0.14
0.03
0.05
-0.06
0.05
0.04
0.10
-0.88
-0.890
-0.81
-0.40
-0.73
-0.90
-0.73
-0.65
-0.54
-0.84
-0.50
1-2
2-3
3-4
4-5
5-6
0.080
0.10
0.064
0.07
0.30
0.17
0.06
0.08
0.39
0.26
0.04
0.18
0.080
0.10
0.064
0.07
0.30
0.17
0.06
0.08
0.39
0.26
0.04
0.28
0.080
0.10
0.064
0.07
0.30
0.17
0.06
0.08
0.39
0.26
0.04
0.20
0.080
0.10
0.064
0.07
0.30
0.17
0.06
0.08
0.39
0.26
0.04
0.18
0.096
The BIPM key comparison database, September 2016
6-7
7-8
8-9
u i / arc seconds
0.080
0.080
0.080
0.080
0.10
0.10
0.10
0.10
0.064
0.064
0.064
0.064
0.07
0.07
0.07
0.07
0.30
0.30
0.30
0.30
0.17
0.17
0.17
0.17
0.06
0.06
0.06
0.06
0.08
0.08
0.08
0.08
0.39
0.39
0.39
0.39
0.26
0.26
0.26
0.26
0.04
0.04
0.04
0.06
0.30
0.19
0.16
0.18
-0.38
-0.446
-0.46
-0.30
-0.56
-0.35
-0.45
-0.49
-0.25
-0.44
-0.40
1/22
Key comparison APMP.L-K3
12-sided polygon
MEASURAND : Deviation from nominal angle between two faces of the polygon
For each face-to-face reading, the key comparison reference value, x R, is calculated as the weighted mean of all participants' results. Its
standard uncertainty, u R, is calculated as the standard deviation of the weighted mean.
xR
1-2
0.056
2-3
0.166
3-4
0.429
uR
4-5
-0.111
5-6
-0.505
6-7
7-8
-0.276
0.043
0.023
8-9
-0.082
9-10
1.498
10-11
-0.608
11-12
0.541
12-1
-0.427
x R and u R are expressed in arc seconds.
For each face-to-face reading, the degree of equivalence of laboratory i with respect to the key comparison reference value is given by a pair
of terms, both expressed in arc seconds:
D i = (x i - x R) and its expanded uncertainty U i = 2(u i 2 - u R2)1/2.
The BIPM key comparison database, September 2008
2/22
Key comparison APMP.L-K3
12-sided polygon
MEASURAND : Deviation from nominal angle between two faces of the polygon
Face
NMISA
NMIA
KRISS
NMIJ/AIST
NMC/A*STAR
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
Face
NMISA
NMIA
KRISS
NMIJ/AIST
NMC/A*STAR
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
1-2
2-3
3-4
4-5
5-6
0.040
-0.016
-0.006
0.024
0.144
-0.056
-0.026
0.044
-0.056
-0.086
-0.006
-0.056
-0.071
0.004
0.019
0.004
-0.066
-0.096
0.004
0.004
-0.056
0.044
0.014
-0.066
0.015
-0.009
-0.001
0.001
-0.229
-0.069
-0.039
0.051
-0.019
-0.189
0.021
-0.029
-0.081
0.031
0.010
0.001
0.111
-0.049
0.031
-0.019
0.201
0.071
0.001
-0.089
-0.027
-0.025
-0.006
0.005
0.105
0.035
0.035
0.005
-0.025
0.165
-0.025
0.105
1-2
2-3
3-4
4-5
5-6
0.153
0.197
0.119
0.126
0.598
0.337
0.100
0.153
0.779
0.518
0.072
0.357
0.153
0.197
0.119
0.126
0.598
0.337
0.100
0.153
0.779
0.518
0.072
0.558
0.153
0.197
0.119
0.126
0.598
0.337
0.100
0.153
0.779
0.518
0.072
0.397
0.153
0.197
0.119
0.126
0.598
0.337
0.100
0.153
0.779
0.518
0.072
0.357
0.153
0.197
0.119
0.126
0.598
0.337
0.100
0.153
0.779
0.518
0.072
0.317
The BIPM key comparison database, September 2008
6-7
7-8
D i / arc seconds
0.074
-0.024
0.005
-0.004
-0.024
0.116
-0.024
0.016
-0.004
0.146
-0.024
0.076
0.005
-0.023
-0.010
0.027
-0.043
0.097
-0.013
0.007
-0.103
0.007
-0.003
0.057
6-7
7-8
U i / arc seconds
0.153
0.153
0.197
0.197
0.119
0.119
0.126
0.126
0.598
0.598
0.337
0.337
0.100
0.100
0.153
0.153
0.779
0.779
0.518
0.518
0.072
0.072
0.357
0.598
8-9
9-10
10-11
11-12
12-1
0.151
-0.065
-0.075
0.005
0.415
0.085
-0.085
0.085
0.165
0.275
-0.025
0.315
-0.064
0.062
0.083
0.022
-0.598
0.102
-0.018
-0.078
-0.038
-0.528
0.032
-0.298
0.062
-0.022
-0.047
-0.022
0.308
0.078
-0.012
0.018
0.178
0.218
-0.002
0.108
-0.119
0.039
0.056
-0.011
-0.341
-0.081
0.079
-0.101
-0.311
-0.271
0.019
-0.141
-0.054
0.047
-0.019
-0.033
0.127
-0.133
0.077
-0.023
-0.063
0.177
-0.013
0.027
8-9
9-10
10-11
11-12
12-1
0.152
0.196
0.118
0.124
0.598
0.336
0.098
0.152
0.778
0.518
0.115
0.377
0.152
0.195
0.117
0.124
0.598
0.336
0.097
0.152
0.778
0.517
0.115
1.659
0.153
0.196
0.119
0.126
0.598
0.337
0.100
0.153
0.779
0.518
0.072
0.779
0.153
0.197
0.119
0.126
0.598
0.337
0.100
0.153
0.779
0.518
0.072
0.377
0.153
0.197
0.119
0.126
0.598
0.337
0.100
0.153
0.779
0.518
0.072
0.296
3/22
APMP.L-K3, Polygon, Deviation from nominal angle between faces 1 and 2
Degrees of equivalence Diand expanded uncertainty (k = 2) Ui, expressed in arc seconds
NMISA
NMIA
KRISS
NMIJ/AIS
1.00
0.80
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
Di = [(xi - xR)] / millisecond
0.60
0.40
0.20
0.00
-0.20
-0.40
-0.60
-0.80
-1.00
The BIPM key comparison database, September 2008
4/22
APMP.L-K3, Polygon, Deviation from nominal angle between faces 2 and 3
Degrees of equivalence Diand expanded uncertainty (k = 2) Ui, expressed in arc seconds
NMISA
NMIA
KRISS
NMIJ/AIS
1.00
0.80
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
Di = [(xi - xR)] / millisecond
0.60
0.40
0.20
0.00
-0.20
-0.40
-0.60
-0.80
-1.00
The BIPM key comparison database, September 2008
5/22
APMP.L-K3, Polygon, Deviation from nominal angle between faces 3 and 4
Degrees of equivalence Diand expanded uncertainty (k = 2) Ui, expressed in arc seconds
NMISA
NMIA
KRISS
NMIJ/AIS
Di = [(xi - xR)] / millisecond
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
The BIPM key comparison database, September 2008
6/22
APMP.L-K3, Polygon, Deviation from nominal angle between faces 4 and 5
Degrees of equivalence Diand expanded uncertainty (k = 2) Ui, expressed in arc seconds
NMISA
NMIA
KRISS
NMIJ/AIS
Di = [(xi - xR)] / millisecond
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
The BIPM key comparison database, September 2008
7/22
APMP.L-K3, Polygon, Deviation from nominal angle between faces 5 and 6
Degrees of equivalence Diand expanded uncertainty (k = 2) Ui, expressed in arc seconds
NMISA
NMIA
KRISS
NMIJ/AIS
1.00
0.80
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
Di = [(xi - xR)] / millisecond
0.60
0.40
0.20
0.00
-0.20
-0.40
-0.60
-0.80
-1.00
The BIPM key comparison database, September 2008
8/22
APMP.L-K3, Polygon, Deviation from nominal angle between faces 6 and 7
Degrees of equivalence Diand expanded uncertainty (k = 2) Ui, expressed in arc seconds
1.00
NMISA
NMIA
KRISS
NMIJ/AIS
0.80
Di = [(xi - xR)] / millisecond
0.60
0.40
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
0.20
0.00
-0.20
-0.40
-0.60
-0.80
-1.00
The BIPM key comparison database, September 2016
9/22
APMP.L-K3, Polygon, Deviation from nominal angle between faces 7 and 8
Degrees of equivalence Diand expanded uncertainty (k = 2) Ui, expressed in arc seconds
1.00
NMISA
NMIA
KRISS
NMIJ/AIS
0.80
Di = [(xi - xR)] / millisecond
0.60
0.40
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
0.20
0.00
-0.20
-0.40
-0.60
-0.80
-1.00
The BIPM key comparison database, September 2016
10/22
APMP.L-K3, Polygon, Deviation from nominal angle between faces 8 and 9
Degrees of equivalence Diand expanded uncertainty (k = 2) Ui, expressed in arc seconds
1.00
0.80
Di = [(xi - xR)] / millisecond
0.60
0.40
NMISA
NMIA
KRISS
NMIJ/AIS
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
0.20
0.00
-0.20
-0.40
-0.60
-0.80
-1.00
The BIPM key comparison database, September 2016
11/22
APMP.L-K3, Polygon, Deviation from nominal angle between faces 9 and 10
Degrees of equivalence Diand expanded uncertainty (k = 2) Ui, expressed in arc seconds
1.00
0.80
Di = [(xi - xR)] / millisecond
0.60
0.40
NMISA
NMIA
KRISS
NMIJ/AIS
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
0.20
0.00
-0.20
-0.40
-0.60
-0.80
-1.00
The BIPM key comparison database, September 2016
12/22
APMP.L-K3, Polygon, Deviation from nominal angle between faces 10 and 11
Degrees of equivalence Diand expanded uncertainty (k = 2) Ui, expressed in arc seconds
1.00
NMISA
NMIA
KRISS
NMIJ/AIS
0.80
Di = [(xi - xR)] / millisecond
0.60
0.40
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
0.20
0.00
-0.20
-0.40
-0.60
-0.80
-1.00
The BIPM key comparison database, September 2016
13/22
APMP.L-K3, Polygon, Deviation from nominal angle between faces 11 and 12
Degrees of equivalence Diand expanded uncertainty (k = 2) Ui, expressed in arc seconds
1.00
0.80
Di = [(xi - xR)] / millisecond
0.60
0.40
NMISA
NMIA
KRISS
NMIJ/AIS
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
0.20
0.00
-0.20
-0.40
-0.60
-0.80
-1.00
The BIPM key comparison database, September 2016
14/22
APMP.L, Polygon, Deviation from nominal angle between faces 12 and 1
Degrees of equivalence Diand expanded uncertainty (k = 2) Ui, expressed in arc seconds
1.00
NMISA
NMIA
KRISS
NMIJ/AIS
0.80
Di = [(xi - xR)] / millisecond
0.60
0.40
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
0.20
0.00
-0.20
-0.40
-0.60
-0.80
-1.00
The BIPM key comparison database, September 2016
15/22
Key comparison APMP.L-K3
Angle blocks
MEASURAND : Deviation from nominal angles 5", 5', 30', and 5°
xi :
ui :
result of measurement carried out by laboratory i
combined standard uncertainty of x i
5'
5"
Lab i
NMISA
NMIA
KRISS
NMIJ/AIST
NMC/A*STAR
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
xi
xi
ui
/ arc seconds
1.00
0.71
0.882
0.82
0.6
0.79
0.58
0.74
0.80
1.32
0.800
0.70
0.10
0.13
0.082
0.07
0.4
0.27
0.10
0.09
0.21
0.32
0.059
0.42
30'
ui
/ arc seconds
-0.64
-0.39
-0.455
-0.44
1.8
-0.45
-0.38
-0.51
-0.75
-0.69
-0.390
-0.50
The BIPM key comparison database, September 2016
0.15
0.16
0.082
0.08
0.4
0.27
0.14
0.09
0.21
0.32
0.073
0.20
xi
5°
ui
/ arc seconds
-0.88
-0.98
-0.857
-0.87
-0.9
-0.79
-0.98
-0.92
0.69
-0.31
-0.900
1.00
0.10
0.12
0.082
0.08
0.4
0.27
0.13
0.09
0.21
0.32
0.059
0.18
xi
ui
/ arc seconds
0.40
0.35
0.370
0.45
0.5
-0.51
0.31
0.50
-0.95
0.56
0.440
-0.20
0.10
0.12
0.082
0.07
0.4
0.27
0.13
0.09
0.21
0.32
0.059
0.23
Year of
measurement
2005 to 2007
2005
2005
2005
2006
2006
2006
2006
2007
2007
2007
2007
16/22
Key comparison APMP.L-K3
Angle blocks
MEASURAND : Deviation from nominal angles 5", 5', 30', and 5°
For each angle block, the key comparison reference value, x R, is calculated as the weighted mean of all participants' results but
excluding outliers. Its standard uncertainty, u R, is calculated as the standard deviation of the weighted mean.
xR
5"
0.805
xR
uR
uR
0.030
x R and u R are expressed in arc seconds
5'
-0.460
0.035
xR
30'
-0.892
xR
5°
0.412
uR
0.032
uR
0.031
For each angle block, the degree of equivalence of laboratory i with respect to the key comparison reference value is given by a pair of
terms, both expressed in arc seconds:
D i = (x i - x R) and its expanded uncertainty U i = 2(u i 2 - u R2)1/2.
The BIPM key comparison database, September 2016
17/22
Key comparison APMP.L-K3
Nominal angle 5"
Lab i
NMISA
NMIA
KRISS
NMIJ/AIST
NMC/A*STAR
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
Angle blocks
Nominal angle 5'
Di
Ui
/ arc seconds
0.195
-0.095
0.077
0.015
-0.205
-0.015
-0.225
-0.065
-0.005
0.515
-0.005
-0.105
0.191
0.253
0.152
0.120
0.778
0.537
0.193
0.170
0.416
0.637
0.101
0.838
Lab i
NMISA
NMIA
KRISS
NMIJ/AIST
NMC/A*STAR
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
The BIPM key comparison database, September 2016
Nominal angle 5°
Nominal angle 30'
Di
Ui
/ arc seconds
-0.180
0.070
0.005
0.020
2.260
0.010
0.080
-0.050
-0.290
-0.230
0.070
-0.040
0.292
0.314
0.148
0.149
0.783
0.535
0.273
0.166
0.414
0.636
0.128
0.394
Lab i
NMISA
NMIA
KRISS
NMIJ/AIST
NMC/A*STAR
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
Di
Ui
/ arc seconds
0.012
-0.088
0.035
0.022
-0.008
0.102
-0.088
-0.028
1.582
0.582
-0.008
1.892
0.189
0.229
0.151
0.152
0.777
0.536
0.254
0.168
0.425
0.637
0.099
0.366
Lab i
NMISA
NMIA
KRISS
NMIJ/AIST
NMC/A*STAR
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
Di
Ui
/ arc seconds
-0.012
-0.062
-0.042
0.038
0.088
-0.922
-0.102
0.088
-1.362
0.148
0.028
-0.612
0.190
0.222
0.152
0.119
0.778
0.544
0.255
0.169
0.425
0.637
0.101
0.456
18/22
APMP.L-K3, Angle block, Deviation from nominal angle 5"
1.50
Degrees of equivalence Diand expanded uncertainty (k = 2) Ui, expressed in arc seconds
Di = [(xi - xR)] / millisecond
1.00
0.50
NMISA
NMIA
KRISS
NMIJ/AIST
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
0.00
-0.50
-1.00
-1.50
The BIPM key comparison database, September 2016
19/22
APMP.L-K3, Angle block, Deviation from nominal angle 5'
3.50
Degrees of equivalence Diand expanded uncertainty (k = 2) Ui, expressed in arc seconds
NMISA
NMIA
KRISS
NMIJ/AIST
3.00
Di = [(xi - xR)] / millisecond
2.50
2.00
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
1.50
1.00
0.50
0.00
-0.50
-1.00
-1.50
The BIPM key comparison database, September 2016
20/22
APMP.L-K3, Angle block, Deviation from nominal angle 30'
2.50
Degrees of equivalence Diand expanded uncertainty (k = 2) Ui, expressed in arc seconds
Di = [(xi - xR)] / millisecond
2.00
1.50
NMISA
NMIA
KRISS
NMIJ/AIST
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
1.00
0.50
0.00
-0.50
-1.00
The BIPM key comparison database, September 2016
21/22
APMP.L-K3, Angle block, Deviation from nominal angle 5°
1.00
Degrees of equivalence Diand expanded uncertainty (k = 2) Ui, expressed in arc seconds
Di = [(xi - xR)] / millisecond
0.50
0.00
NMISA
NMIA
KRISS
NMIJ/AIST
NIMT
SCL
CMS/ITRI
NPLI
RCM-LIPI
NIM
NSCL
-0.50
-1.00
-1.50
-2.00
The BIPM key comparison database, September 2016
22/22