Index
En , 314–316, 328, 363, 367
H0 , 38, 41, 364
L1 -norm, 171
L2 -norm, 149
χ2 , 21, 83, 308
δ-Dirac, 47
t-Student, 41, 69, 80, 86, 97
z –score, 21
http://www.amctm.org, VI
http://www.imeko-tc21.org, VI
http://www.imeko.org, VI
htto://www.npl.co.uk/ssfm, 169
http.//www.npl.co.uk/SSfM, 467
http://adn.tm.agilent.com/index.
cgi?CONTENT\_ID=771, 449
http://cholm.home.cern.
ch/cholm/misc/gslmm/
random\_2generator-test\
_8cc-example.html, 368
http://e00051.berlin.ptb.de/
portal/page?_pageid=42,1&_
dad=portal&_, 468
http://ieeexplore.ieee.org/iel4/
6051/16227/00751254.pdf?
arnumber=751254, 448
http://ieeexplore.ieee.org/iel5/
7542/20537/00949422.pdf, 449
http://inms-ienm.nrc-cnrc.gc.ca/
qde/montecarlo/, 369
http://iridia.ulb.ac.be/, 255
http://java.sun.com/applets/, 448
http://java.sun.com/docs/books/
tutorial/java/concepts/, 448
http://java.sun.com/, 448
http://javascript.internet.com, 466
http://kcdb.bipm.org, 464
http://support.microsoft.com/kb/
833855, 369
http://tf.nist.gov/service/its.
htm, 468
http://volt.ni.com/niwc/products/
ieee1394.jsp, 447
http://www.R-project.org, 117
http://www.aonaware.com/, 255
http://www.apache.org, 466
http://www.bipm.org/en/bipm/
nmij-bipm_workshop/, 468
http://www.bipm.org/en/scientific/
tai/time_server.html, 467
http://www.bipm.org/utils/en/pdf/
news\_jcgm-wg1.pdf, 115
http://www.bipm.org, 24
http://www.cg.tuwien.ac.at/
~theussl/DA/thesis.html, 253
http://www.compactflash.org/, 448
http://www.cs.hku.hk/~diehard, 369
http://www.cs.utep.edu/
interval-comp, 146
http://www.csie.ntu.edu.
tw/cjlin/papers/nusvmtutorial.pdf,
255
http://www.data-fusion.org/, 252
http://www.eng.tau.ac.il/~bengal/
BN.pdf, 256
http://www.evitherm.org/, 465
472
Index
http://www.geocities.com/adotsaha/
NN/SOMinExcel.html, 237
http://www.interscience.wiley.com,
255
http://www.irmm.jrc.be/html/
homepage.htm, 467
http://www.iro.umontreal.ca/
~simardr/testu01/tu01.html,
369
http://www.itep.ws/, 275, 330
http://www.itl.nist.gov/div898/
pubs/author/guthrie/
guthrie-2002-01.pdf, 116
http://www.iupac.org/reports/
provisional/abstract07/
fajgelj\290208.html, 275
http://www.ivifoundation.org/
About\%20IVI/Architecture.
htm, 449
http://www.keithley.com/products/
dataacqmodules, 447
http://www.keithley.com/products/
software/testpointdevpackage/
?mn=testpoint, 449
http://www.linux.org, 466
http://www.lxistandard.org/home,
448
http://www.mathworks.com/products/
matlab/?BB=1, 448
http://www.mathworks.com, 179, 242
http://www.mirs.gov.si/en/, 468
http://www.mrc-bsu.cam.ac.uk/bugs/
welcome.shtml, 115
http://www.mysql.com, 466
http://www.nag.co.uk/, 179
http://www.ni.com/compactrio/
whatis.htm, 448
http://www.ni.com/
dataacquisition/, 447
http://www.ni.com/labview/, 449
http://www.nist.gov/stat.handbook,
28
http://www.nist.gov/, 468
http://www.npl.co.uk/ssfm, 24
http://www.npl.co.uk, 24
http://www.nrc-cnrc.gc.ca/, 468
http://www.oiml.org/, 468
http://www.patentstorm.us/patents/
6108609.html, 253
http://www.php.net, 466
http://www.phy.duke.edu/~rgb/
General/dieharder.php, 368
http://www.pxisa.org/overview.htm,
448
http://www.ramas.com/intstats.pdf,
147
http://www.sei.cmu.edu/cmmi/cmmi.
html, 410
http://www.selma-project.de/, 468
http://www.sm.luth.se/grip/
Research/Publications/
Wavelets/SoftwareComparison/
Gri04S_Wavelet_Software_
Comparison_Table.pdf, 222
http://www.stat.colostate.edu/
research/2002\_10.pdf, 116
http://www.stat.colostate.edu/
research/2006\_3.pdf, 116
http://www.stat.ucla.edu/history/
essay.pdf, 116
http://www.sun.com/download/
products.xml?id=43208d3d, 448
http://www.usno.navy.mil/, 468
http://www.virm.net/, 464
http://www.wavelet.org, 222
http://www.welmec.org/, 411, 467
http://www.zigbee.org/en/index.
asp, 467
http://zone.ni.com/devzone/cda/
tut/p/id/3358, 448
http://zone.ni.com/devzone/cda/
tut/p/id/3889, 448
http://zone.ni.com/devzone/cda/
tut/p/id/4381, 448
http://zone.ni.com/devzone/cda/
tut/p/id/5423, 448
https://bi.offis.de/viem/
tiki-index.php, 465
A2LA Guide, 7, 8, 11
absolute value minimisation, 171
accuracy, 2–4, 6, 10, 16, 80, 128, 142,
160, 161, 209, 212, 329, 345, 353,
415
bound, 141
computation, 135, 137
fractional, 345, 353, 358
lack of, 119
Index
of approximation, 157
of method, 360
of protocol, 457
relative, 128, 353
state estimate, 223
ADC, 184, 417
bandwidth, 188
input range, 184
multiplexed-single, 417
parallel-multiple, 417
resolution, 184
sampling rate, 184
Nyquist, 186
aliasing, 186, 215
Allan variance, 74
AMCTM, VI
analogue-to-digital converter, 184
ANN, 227
feed-forward, 228
Kohonen, 228
multilayer perceptron, 228
radial-basis, 228
recurrent, 228
Elman, 229
scalability, 230
ANOVA, 42, 306, 307
one-factorial, 307
random effects
between-groups, 307
within-group, 307
approach
χ2 test, 308
A, 16, 20
B, 18, 21
Bayesian, 13, 32, 39, 44, 46, 75, 77,
89, 106, 112, 159, 277
Birge, 309
cause-effect modelling, 279
engineering, 123, 124
fiducial, 12, 75, 77, 95, 109, 333
frequentist, 75, 76, 79, 104, 112
Gauss, 31
Laplace, 34
Maximum Entropy, 123, 277
other, 18
sequential quadratic program, 166
statistical, 76
systematic
to measurement modelling, 290
473
artificial neural networks, 204, 210, 227
training, 205, 228
assumptions, 2, 14
distributional, 78
back-propagation, 205
Bayes, 44, 238
risk, 251
theorem, 89, 107, 113, 327
Bayesian inference, 238
bias, 5, 7, 11, 14, 15, 17, 228, 302, 305,
306
between-groups, 306
between-laboratories, 322
additive, 321
consistent, 7
correction, 310
lack of, 152
significant, 306
term not included, 18
un–biased, 153
uncorrected, 9
unknown, 5, 304
Birge factor, 310
bootstrap, 77, 81, 83, 87–89, 104, 112
nested, 85
non-parametric, 84
parametric, 84
second level, 85
box, 122, 128, 134
p–, 144
Box-Muller method, 347
BS 7925, 379
calibration, 15, 48, 63, 109, 168, 270,
457
error, 37
calibrator, 266, 270
Campbell, 57
CEM, 382
central limit theorem, 35, 80, 124
ceptrum, 216
Chirplet Transform, 201, 203, 204
chirplet: mother, 201
Cholesky factorisation, 153, 158, 160,
164, 318
CITAC Guide, 312, 327
classification, 229, 234
clustering, 231, 235
474
Index
algorithms, 231
analysis, 315
density-based, 231
grid-based, 231
hierarchical, 233
model-based, 231
partitioning, 231
combination, 5
of measurement results, 267, 302
combination arithmetic, 5
comparability (metrological), 262, 264
comparison, 3, 15, 258, 261
inter -laboratory, 3, 15, 16, 264
intra-laboratory, 3
key, 4, 9, 15, 19, 362
calibration measurement capabilities (CMC), 21
key comparison reference value, 21,
362
significant unresolved deviation, 21
of measurement results
many, 267, 306
two, 258, 302
outcomes, 19, 22
protocol, 20
compatibility, 20, 21, 260, 272, 304
lack of, 304
complex coefficient, 183
computer hardware
CompactFlash, 421
Ethernet
LAN, 422
FireWire (IEEE 1394), 420
GPIB, 422
LXI, 423
MIOB chacteristics, 418
USB, 419
computer interfacing
CompactRIO, 425
FieldPoint, 424
PXI, 424
computer platforms, 416
bus compatibility, 416
IBM compatible, 416
Macintosh, 416
PXI, 416
UNIX, 416
VME, 416
VXI, 416
confidence
interval, 19, 22, 77, 79, 80, 83, 86, 320
level, 22, 128, 364
conformity, 2, 453
consensus, 14, 272
consistency, 1, 21, 62, 309
degree of, 1, 303, 307, 308
lack of, 304, 308, 309
test of, 22
correction, 11, 43, 46, 310
correlation
-type algorithm, 213
effect, 161, 303, 305, 316
cost-benefit analysis, 245
BRAND, 246
decision-tree, 248
grid, 247
pair-compared, 247
Pareto, 246
SWOT, 246
Cov, 83, 144
covariance, 43, 82, 91, 144, 223, 224,
309, 315, 317, 338–340
coverage
lack of, 309
level of, 52, 304, 306, 363
CRM, 266
data
ambiguity, 208
coordinate transformation, 210
experimental, 22, 150, 337, 338
fusion, 207
architecture, 209
decision stage, 210
implementation, 241
raw, 209
space and time coverage, 208
terminology, 208
vector stage, 210
heteroscedastic, 320
homoscedastic, 3, 33, 34
mining, 229
modelling, 3, 278
multivariate, 80, 154, 159, 225, 278,
315, 338
non-numerical, 2
normalised, 325
numerical, 2
Index
of different accuracy, 209
pooled, 306
pooling, 267, 303
processing, 121
reference set, 463, 464
robustness, 208
security, 395
univariate, 278, 302
decision, 2, 5, 139, 237, 270
making, 209, 244
techniques, 245
tree, 248
degree of equivalence, 4, 21, 22
degrees of freedom, 41, 80, 81, 83, 97,
103, 104, 110, 171, 334, 365
deviation
additive, 291
multiplicative, 291
DFT, 184, 189
algorithm, 185
inverse, 214, 216
difference, 3, 258
extended coverage, 304
minimum coverage, 304
pair, 308
dimensionality reduction, 225
DIN 1319, 6, 8
DIN 66270, 382
Dirac-delta operator, 47
Dirichlet condition, 183
discriminant analysis, 315, 325
dispersion
of measured values, 2, 260, 322
distance
Chebishev, 212
Minkowski, 211
distribution
χ2 , 98
t-Student, 41, 83, 104, 110, 171, 278,
334, 348
F -Fisher, 38
arcsine, 110, 336
binomial, 326
bootstrap, 84
bounded, 127
Cauchy, 127
conditional, 51, 66, 86, 89
cumulative function, 80, 96, 140, 350
double exponential, 171
475
empirical, 83, 122
fiducial, 77, 95
function
cumulative, 140
general, 336
skewed, 337
tabular form, 337
generating a specific one, 346
heavy tail, 173
joint, 47, 90
marginal, 47
multinormal, 159
multivariate, 338
normal, 15, 19, 33, 34, 53, 80, 83, 96,
124, 261, 267, 268, 272, 311, 323,
334, 347, 355
multivariate, 155
objective prior, 39
parameter-free, 80
Pearson, 75
Poisson, 326
posterior, 89, 106, 154, 158
prior, 92, 107
rectangular, 277, 304, 335
simulated, 99
truncated, 101
U-shaped, 335, 349
uniform, 39, 45, 86, 87, 95, 100, 104,
123, 277, 335, 349
limitations, 124
DoE
bilateral, 21
unilateral, 21
domain
frequency, 295, 297
Laplace, 295
DVD Contents, 53, 66, 147, 368, 371,
409
dynamic system, 286
EA Guide, 7, 8, 11
edge, 240
Eisenberg principle, 216
ELMEC-Guide 7.2, 390
enclosure, 132, 135
for the values range, 129
equation
algebraic, 282
linear system of, 151
476
Index
non linear, 309
normal, 151
observation, 286
ordinary differential, 286
structural, 97, 114
equivalence
degree of, 272
metrological, 261
error
approach, 6, 11
bound, 121
guaranteed, 129
upper, 121
calibration, 37
component
lab specific, 11, 14, 18
shared, 11, 18
dynamic, 295
quick-changing response, 297
mean squared, 83
dynamic, 297
normalised En , 21
normalised En , 314, 363
of linearity, 295
propagation, 43, 81, 102, 284, 303
random, 5, 11, 12, 14, 33
systematic, 5, 7, 10, 12, 13, 33, 141
as random variable, 5, 15
constant, 5, 19, 46, 142
correction of, 11
known, 6
neglected, 33, 37
not-probabilistic, 19
randomising, 9, 14
unknown, 6, 19
upper bound, 141
theories, 11
classical, 33, 76
total, 11, 18
unforeseen, 12
estimate, 5
‘best’, 280
robust, 23, 81, 95, 145, 150, 171, 175,
306, 311
subjective, 81
unbiased, 152, 153
worst case, 5
Euclidean
metric, 212
vector, 151
EUROLAB, 312
evidence theory, 32
examples, 37, 40, 49, 58, 64, 66, 78,
86–88, 91, 94, 95, 98–101, 104,
106, 109, 111, 121, 132, 134,
136–138, 141, 161, 168, 169, 188,
200, 205, 221, 224, 227, 234, 235,
237, 242, 243, 261, 279, 282, 287,
293, 296, 298, 312, 317, 340, 354,
363, 366, 454, 455, 462
expectation, 5, 6, 11, 14, 17, 23, 40, 43,
67, 106, 139, 141, 152, 278, 280,
308
client, 12
constant, 291
differences, 15
non-zero, 5, 13, 17, 22
of utility, 139
zero, 5, 8, 9, 11, 13–15, 17, 18, 40, 46,
307
expected utility, 139
expected value, 91
experiment design, 37
experimental unit, 9, 13
expert judgment, 10, 14, 19, 77, 89, 145
feature extraction, 226
FFT, 185–188
inverse, 194, 215
figure of merit, 212
filter
bandpass, 196
high-pass, 200, 220
Kalman, 222
algorithm, 223
extended, 224
gain, 224
Kalman-Bucy, 224
Fisher, 36, 39, 77
footpoint
parameters, 166
problem, 166
Fourier
analysis, 183
Discrete Transform (DFT), 184, 214
Fast Transform, 185–187
Fast Transform (FFT), 185, 213
series, 183
Index
Short Term Transform, 216
Short Time Transform, 201
Transform, 289
frequency
angular, 183, 214
domain, 181, 186, 191, 203, 213
fundamental, 183, 200
harmonic, 183
Nyquist, 186, 215
sampling, 185, 215
function
activation, 227
hard-limit, 227
linear, 227
sigmoidal, 227
auto-correlation, 289
basis (LS), 150
cost, 228
likelihood, 40
linear, 83
membership, 240
neighborhood, 236
range, 122
similarity, 212
transfer, 281, 282, 287
functional
relationships, 318
functional relationship
2D averaging, 320
grid projection, 319
kernel estimation, 320
fuzzy, 5, 32, 323, 327
inference, 240
Sugeno-Takagi type, 240
Zadeh-Mamdani type, 240
logic, 240
logic vs Boolean logic, 240
gate
elliptical, 213
rectangular, 213
gating, 213
Gauss problem, 31
Gauss-Markov problem, 153, 155
non linear (NGM), 158, 163
structured generalised, 170
Gauss-Newton algorithm, 156
Gaussian probability distribution, 334
geometrical interpretation, 151
477
GPS, 459
gradient, 156
GUM, 6, 8–11, 13, 17, 19, 32, 42, 47,
73, 81, 83, 101, 106, 110, 260, 266,
273, 274, 280, 284, 290, 303, 306,
312, 316, 323, 334, 349, 362
Supplement 1, 75, 332, 335
harmonic total distorsion (THD), 188
Helmholtz, 56
hierarchy, 22, 266
higher, 14
lack of, 8
histogram, 111, 141, 338, 345, 351,
355–361, 363, 368
‘reflection’, 338
simulated samples, 332
I/O hardware, 416
identification
in chemistry, 324, 325
qualitative, 324
quantitative, 324
IEC 61508, 380
IEC 62056-46, 452
IEC 62056-61, 452
IEEE 1008, 379
IEEE 1284, 431
IEEE 1394, 420
IEEE 1588, 448
IEEE 488, 422
IEEE 802.15.4, 452
IEEE 829, 379
IMEKO TC21, VI
INC-1, 8, 42
inference, 41, 45, 238
Bayesian, 54
deductive, 46, 53
inductive, 46, 54
probabilistic, 53
statistical, 75
influence factors, 4, 8–10, 54, 150, 291
variability, 3, 6, 10, 11, 14
Internet
–supported
metrological service, 457
-supported
calibrations, 457
entirely remote calibrations, 459
478
Index
with local standards, 461
with signal transmission, 460
with travelling standards, 461
Time Service, 457
interoperability, 12
interval, 5, 86
website, 130
addition, 137
affined Taylor techniques, 137
alternative definition, 132
arithmetic, 130
addition, 131
algorithm, 130
division, 130
multiplication, 131
operation function range, 131
reciprocal, 132
subtraction, 131, 137
bisection, 134
bound
guarantee, 129
on moments, 144
bounded, 19
centered form, 133
closed, 130
computation, 122, 129
excess width, 133
history, 130
refined, 132
straightforward, 132
confidence, 77, 79, 80, 324
bootstrap, 84
credible, 95
Eisenhart, 86, 88
error confining, 5, 19
fiducial, 99
general Taylor techniques, 136
half-width, 80, 82, 133
midpoint, 128, 133, 307
monotonicity, 135
multiplication, 138
of expectation, 142
general case, 143
knowing moments, 142
of integration, 216
open problems, 144
probabilistic partial information, 139
range, 123
uncertainty, 122
inverse problem, 44, 119, 150, 179, 210,
242, 278
inverse transform, 213
ISO 12119, 381
ISO 12207, 378
ISO 14471, 379
ISO 14598, 381
ISO 14764, 379
ISO 15408, 382, 395
ISO 15504, 380
ISO 15910, 379
ISO 17025, 73, 342, 383, 400
ISO 17050, 383
ISO 18019, 379
ISO 21748, 26
ISO 21749, 5
ISO 25000 Series, 380
ISO 25051, 381
ISO 2859, 327
ISO 3534, 3, 5, 7, 26
ISO 5725, 3–7, 17, 312
ISO 6592, 382
ISO 9000, 378
ISO 9001, 378
ISO 9126, 390
ISO 9127, 382
ISO 9241, 394
ISO TR15846, 379
ISO TR9294, 379
ITSEC, 382
ITSEM, 382
Jacobian matrix, 156
KCRV, 16, 18, 21, 22, 362
Kinderman-Monahan-Ramage method,
348
knowledge, 2
between-laboratories, 17
between-laboratories, 14
within-laboratory, 14, 15
imperfect, 2, 285, 291
prior, 15, 33, 89, 155
qualitative, 321
quantitative, 258, 302
subjective, 113
Lagrange multiplier, 123, 166
learning
Index
paradigm, 228
supervised, 234
unsupervised, 231
Least Squares Method, 35, 77, 149
generalised, 320
generalised distance regression
(GDR), 163
generalised Gauss-Markov regression
(GGM), 169
linear, 150, 160
non linear, 156, 157, 163
orthogonal distance (ODR), 169
parameters estimation, 149
robust (RLS), 171
algorithms, 175
empirical implementation, 173
Huber M-estimator, 175
one-sided, 175
variable separation, 165, 169
likelihood function, 40, 77, 89, 171
maximum, 127, 154, 158
linear transmission element, 291
linearisation, 125, 157, 284
no need for, 333
Lipschitz exponent, 196
loss, 250
lti system, 282, 285, 286
MANOVA, 315
Markov formula, 278
matrix, 151
block-angular, 164
covariance, 226
diagonal, 160
eigenvalues, 226
full rank, 151, 160, 166
Hessian, 156
identity, 164
invertible, 151
Jacobian, 156, 157, 164
lower triangular, 153
non diagonal, 317
of uncertainties, 153
approximate, 157
non diagonal, 169
structure, 160
positive definite, 153, 163
positive semi-definite, 318
structured, 164
479
transposed, 227
uncertainty, 161
approximate, 158
upper triangular, 151, 154, 165
MCMC, 93, 113
mean
common, 303
hypothesis test, 364
grand, 306, 308
weighted, 303, 305, 309, 354, 360, 365
departure from, 362
from Monte Carlo simulation, 360
zero, 46
mean value, 5, 16, 124, 270, 303, 307
arithmetic, 5, 34
from Monte Carlo simulation, 358
posterior, 90, 93–95
measurand, 4, 6, 12, 13, 17, 20, 43, 48,
76, 102, 112–114, 258, 278, 280,
303
multiple, 316
measure of belief, 77
measurement, 12
capability, 15
distributed system, 453
error, 2, 32, 121
underestimated, 125
formal theory, 63
non-repeated, 18
pair, 264, 318
probabilistic theory, 32, 56, 64
procedure, 4
different, 4, 264
same, 3
process, 2, 11, 32, 55, 66
repeated, 34
replicated, 9
representational theory, 60
results, 259
combining, 261, 267, 302
discrepant, 302–304
pooling, 267, 303, 306, 307
small number, 261
scale, 57, 58, 60, 65
invariance, 58
uncertainty, 32, 46, 121, 259, 266, 302
enflated, 272
evaluation, 266, 277, 302
model, 280, 304
480
Index
Measurement Instrument Directive
(EU), 327
measurements
–pseudo, 332
inter -laboratory, 14
intra-laboratory, 13
autocorrelated, 74
cutting-edge, 122
direct, 43
in chemistry, 258
independent, 303
indirect, 43
modelling of, 277
non-repeated, 2, 13, 14
procedure, 14
repeated, 1, 3, 5, 9, 13, 14, 37, 46,
142, 278
replicated, 1, 4, 13, 306, 338
shop-floor, 122
measuring system, 63, 281
disregarding non-linearity, 294
functional elements, 281
linearity, 282, 284
linearity time-invariance, 282
non linearity, 285
time variant, 286
median, 67, 270, 311, 362
from Monte Carlo simulation, 360
metric
Euclidean, 212
Manhattan, 212
of association, 211
metrology, 2, 13
Internet, 451
remote access, 455
legal, 376, 377, 390, 399, 453
databases, 465
web-hosted databases, 464
MID, 390
minimisation, 36, 323
MINPACK program, 163
model, 2, 13, 37, 278, 319
basic categories of, 278
graphical type, 279
mathematical type, 279
verbal type, 279
cause-effect approach, 279, 284, 290
graph, 291
common random effect, 160, 163
data, 13, 15, 16, 157
data fusion, 209
Omnibus, 209
Dempster-Shafer, 239
deterministic, 50
equation, 280
fitting, 90, 150
piecewise, 320
imperfection, 294
input-output, 48, 81
inverse, 210, 280, 286
mixture, 23
nonexistent laboratory effect, 13
of bias, 321
of Kalman filter, 222
of randomness, 332
parameters, 150, 280, 291, 319
polynomial, 285, 320
probabilistic, 48
measurement error, 33
random effect, 163
random laboratory-effect, 5, 15
statistical, 76
structure, 290
systematic laboratory-effect, 5, 17
modelling
concept, 290
of measurement process
for uncertainty evaluation, 279
systematic approach, 290
procedure steps, 292
standard components, 290
tasks, 277
Monte Carlo method, 90, 99, 104, 126,
141, 331, 363
arbitrary pdf, 357
features, 333
finite number of re-samples, 353
Gaussian pdf, 354
hypothesis test
common mean, 364
common mean (χ2 ), 365
Markov Chain, 93
non-Gaussian pdf, 357
number of simulated samples, 353
scalar quantities, 333
MRA, 4, 9, 19, 21, 22
neuron
Index
layers, 228
hidden, 229
scalar with bias, 227
NIST e-Handbook, 5, 7
NMI, 74
nomenclature, 3, 8
non-quantitative, 1
non-repeated, 14, 17, 18, 21
NORDTEST, 312, 383
normal equations, 151
not-repeated, 10, 13
NP-hard problem, 133, 144
NPL Best Practice Guide N.1, 385
null hypothesis (H0 ), 38, 364
observations, 1, 48
combination of, 1
vector, 32, 151, 160
OECD, 384
offset, 161
OIML Guide, 455
operating-point vector, 280, 284
optimisation problem, 123, 161
ordering, 80
orthogonal factorisation, 151
outlier, 22, 150, 171, 173, 175, 261, 267,
306
p-box, 141
paragraph, 469
parameter, 76
of a model, 150, 319
random variables, 89
unknown constant, 80
Parceval theorem, 193
partial derivative, 82, 91, 126, 151, 156
pdf, 16, 23, 171, 277, 278, 280, 334
Gaussian, 278
graphed, 337
non-normal, 23
Pearson
coefficient, 315
correlation matrix, 315
percentile, 34, 80, 84, 104
bootstrap, 84
perceptron, 204, 228
Popper, 55
population, 22, 23, 268
same, 270
481
samples, 15
precision, 4
intermediate, 4, 9
Principal Components Analysis, 225,
315, 325
algorithm, 226
Factor Analysis, 225
Principal Co-ordinates, 225
prior knowledge, 89
probabilistic relation, 65
probabilistic theory of measurement, 32
probability, 122
density function, 16, 23
distribution, 13, 34, 66, 77, 139, 150
t-Student, 41, 80
moments, 16, 23, 90, 139, 141, 336
non symmetric, 332
normal, 33, 35, 267, 268, 334
objective prior, 39
of the measurand, 332
of the measurements, 332
partial information, 140
prior, 33, 45, 89
symmetric, 34, 35
uniform, 39, 123
unknown, 122
in metrology, 32
measure of belief, 77
of a relation, 64
of causes, 45
of detection, 327
process, 2
discrete-time, 224
non-stationary, 74
prediction-updating, 223
pseudo-random number generator, 332,
341
compact algorithm, 342
distribution generation
for tabulated distribution, 351
for U-shaped distribution, 350
dynamic range, 345
generic, 342
RANLUX, 342
testing, 343
user testing, 344
PTB-IT-14, 410
QR factorisation, 151, 154, 157
482
Index
QUAM, 4, 6, 7
quantile, 88, 99, 104, 110, 323
quantitative, 1
quantity, 1, 6, 56, 76
input, 277, 278, 280, 291
vector, 291
output, 278, 280
pivotal, 80, 82
fiducial, 110
generalised, 96
unit, 273
R program, 88, 110
random effect, 5, 150
random number generator, 128
random variable, 5, 9, 11, 13, 17, 21, 37,
43, 52, 66, 76–78, 124, 152, 307,
334, 339, 343, 366
Bernoulli, 322
range enclosure, 129
Rayleigh quotient, 318
redundancy of information, 225, 251
regression, 176, 319
generalised, 320
generalised distance (GDR), 163, 164,
169
generalised Gauss-Markov (GGM),
169
non linear, 315, 319
orthogonal distance (ODR), 164
weighted, 320
both variables, 320, 324
remote operation, 422, 428, 443
measuring instrument, 455
repeatability, 2–4, 6, 8–10, 15, 266, 312,
313, 322
conditions, 2, 13, 14, 18
repeated, 1–3, 5, 7–10, 13–16, 18, 21,
33, 34, 37, 39, 46, 47, 53, 141, 142,
301, 319, 337, 338, 363
replication, 1, 13
reproducibility, 2–4, 6, 9, 10, 14, 15, 17,
266, 312, 320, 322, 327
reproducility, 322
requirements, 376, 377
response, 150
characteristic, 49
approximation, 210
normalisation, 210
forward characteristic, 286
function, 46
impulse, 198
inverse characteristic, 286
of a measuring system, 286
restitution, 49
risk
analysis, 250, 327
level, 22
management, 251
contingency plans, 251
insurance, 251
metrological software, 371
robust rank-based procedure, 81
sample
bootstrap, 84
discrete, 80
finite number of, 184, 215
size, 81
standard deviation, 85
second-order
approximation, 284
Self-Organising Maps Networks, 235
SELMA, 455
sensitivity, 2
analysis, 91, 107, 113
coefficients, 43, 82, 83, 104, 284
sensor network, 209
signal, 281
amplitude, 184
analogue, 184
coherence, 289
digital, 184
discrete-time, 184
multidimensional, 216
periodic
continuous, 183, 188
stationary, 185
stochastic, 288
time variant, 286, 295
transients, 190
oscillatory, 201
signal-to-noise ratio (SNR), 188
significance
level, 304
significance level, 41, 55
similarity function, 211
simulation
Index
bootstrap, 83
Monte Carlo, 332
SNR, 190
software, 221, 224, 227, 230, 234, 235,
237, 241, 242, 371
NORDTEST validation method, 386
ageing, 373
audits, 388, 398
cause-effect applicability, 374
corruption, 371
definition of, 372
development, 378
for metrology, 376
guidelines, 376
standards, 383
for virtual instruments, 425
installation, 406
functional tests, 408
measurability, 375
negative synergy effects, 374
peculiarities, 373
process
assessment, 388
product testing, 388
quality
assurance, 371, 387
standards, 377
quality management, 378
relations to space and time, 374
requirements, 380, 383, 389, 391, 397,
401
process, 384
products, 385
safety-related systems, 380
security, 371, 395
test, 391
test execution, 397
tested components, 392
ergonomic characteristics, 395
functionality, 393
programming techniques, 394
security, 395
tolerances, 375
usability, 395
validation, 371
archiving, 404, 407
confidentiality, 403
data security, 405
documentation, 403
483
for metrology, 400, 462
functional scopes, 402
integrity, 403
management, 404
method for, 407
of mathematical functions, 463
of metrological functions, 463
overall, 406
plausibility checks, 402
requirements systematisation, 401
towards a GUM-like, 408
SOM
incremental-learning, 235
iterative algorithm, 236
spectral
composition, 183
leakage, 186, 188
noise power, 200
power density, 290, 297
representation, 183
resolution, 185, 186
standard
classes or types, 16, 19, 23
local, 15
measurement, 3, 57
same, 3
several, 3
single, 13, 14
written, 3, 4, 14
standard deviation, 13, 16, 34, 74, 78,
80, 81, 83, 84, 90, 150, 212, 278,
304, 334, 347, 355, 358
of the mean, 307, 308, 310, 311, 313,
353
posterior, 90, 93–95
standard method, 14, 17
statistic
ortodox, 36
robust, 311
sufficient, 86
summary, 15
steady state behaviour, 284
Stevens, 58
subband, 191, 197, 198, 200
multiresolution
decomposition, 200
reconstruction, 200
subjective evaluation, 81
subsampling, 186
484
Index
SUD, 21
Support Vector Machines (SVM), 234
systematic
approach
to measurement modelling, 290
difference, 3
effect, 4, 17, 46, 55, 113, 161
constant, 46
correction of, 9, 17, 43
of method, 313
recognised, 8, 9
Taylor series expansion, 84, 91, 105,
108, 125, 133, 284, 294
higher terms, 134
test, 3
false positive/negative, 324
of hypothesis, 42
Monte Carlo method, 363
of significance, 38, 55
proficiency, 3, 19, 261
statistical, 40, 80
true positive/negative, 324
testing, 2, 7, 13
non destructive, 327
non-quantitative, 321
qualitative, 321
inspection, 326
involving measurements, 322
tools, 322
uncertainty estimate, 327
THD, 189
time, 4
–frequency analysis, 181
–frequency representation, 192
as influence factor, 10
domain, 186, 191
invariance, 282
series, 229
short period, 4, 6
to frequency conversion, 181, 215
traceability, 2, 12, 22, 262–264, 266, 271
traking system, 213
transformation
functional, 127
inverse, 290
Laplace, 287
true value, 4, 7, 14, 261, 272, 280
of the measurand, 4
trueness, 7
unknowable, 7
Type A uncertainty component, 8–10,
43, 74, 75, 78, 81, 83, 260, 301,
316, 332
Type B uncertainty component, 8–10,
43, 74, 75, 78, 81, 88, 89, 94, 95,
260, 328, 332
uncertainty, 2
approach, 6, 11
assessment, 74
budget, 16, 260, 266, 303, 335
due to dynamic components, 295
excess, 304, 309
expanded, 52, 80, 82, 306, 363
expressions, 334
interval, 77, 79, 121
inverse evaluation, 160
lower bounded, 216
matrix, 153, 154
propagation, 43, 81, 102, 113, 154,
284, 303
standard, 76, 162, 302
combined, 303
Taylor series expansion, 81
Type A component, 8, 43, 74, 81, 83,
106, 338
Type B component, 8, 43, 74, 81, 83,
89, 94, 103, 106, 113, 273, 339
UTC, 459
utility function, 139
non-smooth, 140
smooth, 139
UTP, 188
value
“best”, 267
consensus, 272, 273
reference, 7, 18, 261, 267, 268
representative, 15
Var, 36, 52, 153
variability, 4, 43
within-group, 308
of influence factors, 11
variable
correlated, 225
internal state, 286
pseudo-random, 339, 340
Index
random, 5, 9, 13, 43, 76
variance, 15, 18, 19, 21, 22, 35–38, 46,
48, 90, 95, 304, 317
inverse of, 305
minimum, 36, 152
verifiability, 55
of ANN, 230
VIM, 3, 4, 6, 10, 18, 20, 21, 75, 258,
259, 261, 266
Virtual Institutes, 464
virtual instrument, 413
comparison with traditional, 414
drawbacks, 416
hardware for, 416
operation, 442
virtual laboratory, 443
single
multifunction I/O (MIOB), 417
software, 425
C, 426
graphical programming, 432
IVI, 441
Java, 431
LabView, 432
LabWindows/CVI, 426
MATLAB, 427
object oriented programming, 430
TestPoint, 437
textual languages, 425
VEE Pro, 435
VISA, 439
virtual instruments
multi-unit
distributed, 422
distributed with RTS, 424
networking capabilities, 421
485
visualisation, 235
voting, 237
waveform, 186
distorted, 200
synthetised, 186
Wavelet
Networks, 204
Transform, 190, 192, 217
banks of filters, 197
Continuous, 191, 192
Discrete Time, 191, 197
Fast, 220
implementation, 193
inverse, 218
modulus maxima properties, 196
properties of Discrete Time, 200
wavelet, 191, 217
discrete, 218
father, 219
mother, 192, 198, 217, 221
complex conjugate, 192, 218
Daubechies filter, 200
discrete, 198
features, 194
nodes, 204
variance, 74
weighting function, 173, 175, 228, 305,
324, 354, 360, 363, 366
Welch-Satterthwaite formula, 82, 83,
335
WELMEC Guide, 455
Wiener-Chinchine theorem, 290
WinBUGS, 94, 107
windowing, 187
rectangular, 188
triangular and other types, 188