Accred. Qual. Assur. 2015 Springer Verlag Berlin Heidelberg
Electronic Supplementary Material
Procedure validation and laboratory performance monitoring for the measurement of moisture,
ash and volatile matter mass fractions in solid biofuels
Maria Trancosoa, Ana Rita Sousaa, Sandra Calistoa
a
Laboratório Nacional de Energia e Geologia, LNEG, Unidade de Bionergia, Estrada do Paço do Lumiar,
Ed. E, 1649-038 Lisboa, Portugal; email – maria.trancoso@lneg.pt
Table S1 Uncertainty budget for moisture mass fraction
Input quantities
f rep
wM ad 
m3
m1
m2
(g)
(g)
(g)
xi
25.0231
26.0233 26.0125 1.0000
u xi  0.00065
0.00029 0.00065 0.00071
0.011
ci
0.01080
0.98900 -0.99980 1.0000
ri
0.00005
0.08152 0.41324 0.50520
xi
25.1231
26.0831 25.9125 1.0000
u xi  0.00065
0.00029 0.00065 0.00071
0.178
ci
0.18511
0.85655 -1.04167 1.0000
ri
0.01377
0.05942 0.43590 0.49092
wM ad  moisture mass fraction as analysed (Eq. 1), x i input
uc wM ad  U wM ad 
0.0010
0.002
0.0010
0.002
quantities, u xi  standard
measurement uncertainty associated to an input quantity x i , ci sensitivity coefficients [10], m1
mass of the empty dish plus lid, m2 mass of dish plus lid containing sample before the drying
step, m3 mass of dish plus lid containing sample after drying, f rep precision component under
repeatability conditions, ri relative variance of each input quantity [10], uc wM ad  combined
standard measurement uncertainty of wM ad  (Eq. 4), U wM ad  expanded measurement
uncertainty of wM ad  (k = 2, α = 0.05) [10] k coverage factor,  significance level.
Table S2 Uncertainty budget for ash mass fraction on dry basis
Input quantities
m4
m5
m6
(g)
(g)
(g)
f rep
wM ad 
wA d 
uc wA d 
utg wA d 
U wA d 
xi
29.2524
u xi  0.00029
ci
-1.02596
ri
0.11263
30.2200 29.2800 1.0000
0.0214
0.00029 0.00041 0.00071 0.0010
0.029 0.00089 0.0011
0.002
-0.030124 1.05609 1.00000 0.0298
0.00010 0.23750 0.64864 0.00113
xi
29.1539 30.2055 29.3490 1.0000
0.0501
u xi  0.00029 0.00029 0.00041 0.00140 0.0010
0.195 0.0015
0.0021
0.003
ci
-0.81536 -0.18573 1.00109 1.00000 0.2056
ri
0.02526 0.00131 0.07578 0.87857 0.01908
xi - input quantities, u xi  - standard measurement uncertainty associated to an input quantity xi ,
ci  ∂y ∂xi - sensitivity coefficients [10], wA d  - ash content, on dry basis (Eq. 2), m4 - mass of the
empty dish, m5 - mass of dish containing sample before ignition, m6 - mass of dish containing
sample after ignition, f rep - precision component under repeatability conditions, ri - relative variance
of each input quantity [10], uc wA d  - combined standard measurement uncertainty of wA d  (Eq.
5), utg wAad  - target measurement uncertainty for w Ad  , U wA d  - expanded measurement
uncertainty of w Ad  (k = 2, α = 0,05) [10], k - coverage factor,  -significance level.
Table S3 Uncertainty budget for volatile matter mass fraction on dry basis
Input quantities
m7
m8
m9
(g)
(g)
(g)
f rep
wM ad  wVd  uc wVd 
utg wVd  U wVd 
xi
u xi 
ci
ri
14.0458 15.0513 14.6563 1.0000 0.0380
0.00029 0.00029 0.00029 0.00263 0.0010
0.369 0.0027
0.0052
0.006
0.40612 0.62769 -1.03382 1.00000 -0.65607
0.00185 0.00442 0.01198 0.92443 0.05732
xi
13.5607 14.5671 13.8576 1.00000 0.0280
u xi  0.00029 0.00029 0.00029 0.00497 0.0010
0.697 0.0050
0.0010
0.010
ci
0.72068 0.30158 -1.02226 1.00000 -0.31225
ri
0.00175 0.00031 0.00352 0.99052 0.00390
xi - input quantities, u xi  - standard measurement uncertainty associated to an input quantity
xi , ci  ∂y ∂xi - sensitivity coefficients [10]; wM ad  - moisture mass fraction as analysed (Eq.
1), wVd  - ash content on dry basis (Eq. 3), m7 - mass of the empty dish with lid, m8 - mass of
dish with lid containing sample before heating, m9 - mass of dish with lid containing sample
after heating, f rep - precision component under repeatability conditions, ri - relative variance
of each input quantity [10], uc wVd  - combined standard measurement uncertainty of wVd 
(Eq. 6), utg wVd  - target measurement uncertainty for wVd  , U wVd  - expanded
measurement uncertainty of wVd  (k = 2, α = 0,05) [10], k - coverage factor,  - significance
level.