[Header]
Format=SMU
ver=3
appl=GUMWB32
MR=0
FUEB=0

[Title]
Title='Determination of Cadmium Release from Ceramic Ware by Atomic Absorption Spectrometry'
Description=12
Description[0]='This is the example A5 of the EURACHEM / CITAC Guide "Quantifying Uncertainty'
Description[1]='in Analytical Measurement", Second Edition.'
Description[2]=''
Description[3]='The amount of released cadmium from ceramic ware is determined using atomic'
Description[4]='absorption spectrometry. The procedure employed is the empirical method BS'
Description[5]='6748.'
Description[6]=''
Description[7]='The item to be tested is filled with a 4 % v/v acetid acid solution for a given'
Description[8]='lenght of time, the amount of cadmium released from the item is then calculated'
Description[9]='from the measured cadmium concentration in the leach solution and the volume of'
Description[10]='the leach solution. Parameters such as leaching time, temperature, acid'
Description[11]='concentration etc. are specified in the empirical method.'

[Model]
Model=11
Model[0]='{calculation of the uncertainty of volume V_L}'
Model[1]=''
Model[2]='V_L = V_L\sp\nominal * f_VL\minus\filling * f_VL\minus\temperature * f_VL\minus\reading * f_VL\minus\calibration;'
Model[3]=''
Model[4]='{calculation of the uncertainty of the surfache area}'
Model[5]=''
Model[6]='a_V = a_V\sp\nominal * f_aV\minus\length1 *f_aV\minus\lenght2 * f_aV\minus\area;'
Model[7]=''
Model[8]='{calculation of the mass of cadmium leached}'
Model[9]=''
Model[10]='r = c_0 * V_L / a_V * d * f_acid * f_time * f_temperature;'

[Components]
CompOrder=3
Comp=17
Comp[0]=V_L_
Comp[1]=V_L\sp\nominal_
Comp[2]=f_VL\minus\filling_
Comp[3]=f_VL\minus\temperature_
Comp[4]=f_VL\minus\reading_
Comp[5]=f_VL\minus\calibration_
Comp[6]=a_V_
Comp[7]=a_V\sp\nominal_
Comp[8]=f_aV\minus\length1_
Comp[9]=f_aV\minus\lenght2_
Comp[10]=f_aV\minus\area_
Comp[11]=r
Comp[12]=c_0_
Comp[13]=d
Comp[14]=f_acid_
Comp[15]=f_time_
Comp[16]=f_temperature_

[COMP 0]
Type=Temp
Definition='Volume of the leachate'
Unit='L'
Description=0
Fcov=2
NomUnit=
UncUnit=
CovID=1
UncID=0
Vnom=0.33034
Ustd=0.00182090668528546
Neff=10000
HB=0
HC=0
HR=0
IO=0

[COMP 1]
Type=Const
Definition='Nominal volume of the leachate'
Unit='L'
Description=5
Description[0]='The nominal volume is not associated with any uncertainties. Four different'
Description[1]='factors contribute to the uncertainty of the real volume, filling, temperature,'
Description[2]='reading and calibration. These are introduced in the uncertainy budget through'
Description[3]='the factors f_VL\minus\filling, f_VL\minus\temperature, f_VL\minus\reading and'
Description[4]='f_VL\minus\calibration.'
Vnom=0,332

[COMP 2]
Type=TypBTriangl
Definition='Uncertainty contribution of V_L due to filling of the vessel'
Unit=''
Description=3
Description[0]='The method requires the vessel to be filled ''to within 1mm from the brim''. For'
Description[1]='a typical drinking or kitchen utensil, this represents about 1% of the total'
Description[2]='height. The vessel will therefore be 99.5% ± 0.5% filled.'
Vnom=0.995
Hlim=0.005

[COMP 3]
Type=TypBRectang
Definition='Uncertainty contribution of V_L due to temperature variation'
Unit=''
Description=10
Description[0]='The temperature of the acetic acid has to be 22 ±2°C, according to the method.'
Description[1]='This range leads to an uncertainty in the measured volume, due to a'
Description[2]='considerably larger volume expansion of the liquid compared to the vessel. The'
Description[3]='coefficient of volume expansion for water is 2.1\cdot\10^-4^°C^-1^. This leads'
Description[4]='to a possible volume variation of ±(332 \cdot\ 2 \cdot\ 2.1\cdot\10^-4^) mL. A'
Description[5]='rectangular distribution is assumed for the temperature variation of the'
Description[6]='volume. Since f_VL\minus\temperature is a multiplicative factor to the nominal'
Description[7]='volume, which is only used to introduce the temperature uncertainty, it has the'
Description[8]='value 1. Its uncertainty is calculated as the possible volume variation divided'
Description[9]='by the volume.'
Vnom=1
Hlim==2.1e-4*2

[COMP 4]
Type=TypBTriangl
Definition='Uncertainty contribution of V_L due to reading of the measuring cylinder'
Unit=''
Description=0
Vnom=1
Hlim=0.01

[COMP 5]
Type=TypBTriangl
Definition='Uncertainty contribution of V_L due to calibration of the measuring cylinder'
Unit=''
Description=8
Description[0]='The volume is calibrated within ±2.5 mL for a 500 mL measuring cylinder. No'
Description[1]='further statement is made about the level of confidence or the underlying'
Description[2]='distribution. An assumption is necessary to work with this uncertainty'
Description[3]='statement. In this case a triangular distribution is assumed. Since'
Description[4]='f_VL\minus\calibration is a multiplicative factor to the nominal volume, which'
Description[5]='is only used to introduce the calibration uncertainty, it has the value 1. The'
Description[6]='halfwidth of limits corresponds to the relative uncertainty as stated by the'
Description[7]='manufacturer (i.e. 2.5 mL / 332 mL).'
Vnom=1
Hlim==2.5/332

[COMP 6]
Type=Temp
Definition='Surface area of the vessel'
Unit='dm^2'
Description=0
Fcov=2
NomUnit=
UncUnit=
CovID=1
UncID=0
Vnom=2.37
Ustd=0.0642752209228003
Neff=63
HB=0
HC=0
HR=0
IO=0

[COMP 7]
Type=Const
Definition='Nominal surface area of the vessel'
Unit='dm^2'
Description=4
Description[0]='The nominal surface are is not associated with any uncertainties. Three'
Description[1]='different factors contribute to the uncertainty of the real surface area, that'
Description[2]='are the two length measurements required to calculate the surface area, and an'
Description[3]='area-factor, covering the imperfect geometry of any real vessel.'
Vnom=2.37

[COMP 8]
Type=TypBNormal
Definition='Uncertainty contribution to a_V of first length measurement (i.e. height)'
Unit=''
Description=5
Description[0]='Typically, two length measurements are required to calculate the surface area'
Description[1]='of a vessel. In this case, the item was approximated by a cylindrical geometry.'
Description[2]='Typical dimensions are between 1.0 and 2.0 dm, leading to an estimated'
Description[3]='uncertainty of 1 mm. The two length measurements required for this vessel were'
Description[4]='1.45 and 1.64 dm.'
Vnom=1
Uexp==0.01/1.45
Fcov=1

[COMP 9]
Type=TypBNormal
Definition='Uncertainty contribution to a_V of second length measurement (i.e. lenght)'
Unit=''
Description=5
Description[0]='Typically, two length measurements are required to calculate the surface area'
Description[1]='of a vessel. In this case, the item was approximated by a cylindrical geometry.'
Description[2]='Typical dimensions are between 1.0 and 2.0 dm, leading to an estimated'
Description[3]='uncertainty of 1 mm. The two length measurements required for this vessel were'
Description[4]='1.45 and 1.64 dm.'
Vnom=1
Uexp==0.01/1.64
Fcov=1

[COMP 10]
Type=TypBNormal
Definition='Uncertainty contribution to a_V due to imperfect geometry'
Unit=''
Description=4
Description[0]='The item is not a perfect geometric shape (cylinder in this case). Therefore'
Description[1]='the real surface area may deviate from the caluclated one. This deviation was'
Description[2]='estimated to be 5% at 95% confidence level. To obtain the standard uncertainty'
Description[3]='the possible deviation is divided by 1.96.'
Vnom=1
Uexp==0.05/1.96
Fcov=1

[COMP 11]
Type=Result
Definition='Mass of cadmium leached per unit area'
Unit='mg/dm^2'
Description=0
Fcov=2
NomUnit=
UncUnit=
CovID=1
UncID=0
Vnom=0.0362398312236287
Ustd=0.00341777839010857
Neff=169
HB=1
HC=0
HR=1
IO=0

[COMP 12]
Type=TypBNormal
Definition='Content of cadmium in the extraction solution'
Unit='mg/L'
Description=8
Description[0]='The content of cadmium in the extraction solution is calculated using a'
Description[1]='calibration curve. For the calibration curve five calibration standards were'
Description[2]='prepared and measured 3 times each. Using a linear least square fit, the slope'
Description[3]='and intercept of the calibration curve have been calculated. Using this data,'
Description[4]='the concentration c_0 was calculated from a duplicate measurement of the actual'
Description[5]='leach solution. The calculation of the uncertianty of the least square fit is'
Description[6]='described in Appendix E3 of the EURACHEM / CITAC Guide. Only the final result'
Description[7]='of this calculation is used here.'
Vnom=0.26
Uexp=0.018
Fcov=1

[COMP 13]
Type=TypBNormal
Definition='Dilution factor (if used)'
Unit=''
Description=2
Description[0]='For this sample, no dilution of the leach solution was necessary, therefore no'
Description[1]='uncertainty needs to be introduced here.'
Vnom=1
Uexp=0
Fcov=1

[COMP 14]
Type=TypBNormal
Definition='Influence of the acid concentration'
Unit=''
Description=11
Description[0]='Data from two study on the effect of acid concentration on lead release was'
Description[1]='used to estimate this factor. One study showed that lead release was increased'
Description[2]='by approximately 0.1 when the acid concentration was increased from 4 to 5%'
Description[3]='v/v. Another study reported a 50% increase of the lead release for a change of'
Description[4]='acid concentration from 2 to 6% v/v. Assuming a liner effect, on can estimate a'
Description[5]='change of f_acid of 0.1 per 1% v/v change of acid concentration. In another'
Description[6]='experiment the concentration of the acetic acid and its standard uncertainty'
Description[7]='have been established using titration with standardised NaOH solution,'
Description[8]='resulting in an acetic acid concentration of 3.996 % v/v with a standard'
Description[9]='uncertainty of 0.008% v/v. The uncertainty of f_acid can then be calculated as'
Description[10]='0.008 \cdot\ 0.1.'
Vnom=1
Uexp==0.008*0.1
Fcov=1

[COMP 15]
Type=TypBRectang
Definition='Influence of the duration'
Unit=''
Description=7
Description[0]='For a relatively slow process such as leaching, the amount leached will be'
Description[1]='approximately proportional to the leaching time for small changes in that time.'
Description[2]='In a study, a mean change of concentration over the last six hours of leaching'
Description[3]='of approximately 1.8 mg \cdot\ L^-1 (=0.3% / h) was found. The leaching time is'
Description[4]='specified in the method as 24 ±0.5 h, the content of Cd in the extraction'
Description[5]='solution therefore needs to be corrected by a factor of 1 ±(0.5 \cdot\ 0.003).'
Description[6]='A rectangular distribution is assumed for this factor.'
Vnom=1
Hlim==0.5*0.003

[COMP 16]
Type=TypBRectang
Definition='Influence of the temperature'
Unit=''
Description=9
Description[0]='A number if studies on the effect of temperature on metal release from ceramic'
Description[1]='ware have been undertaken. The temperature effect is substantial, and a'
Description[2]='near-exponential increase in metal release with temperature is observed until'
Description[3]='limiting values are reached. Nevertheless, only one study gives information for'
Description[4]='the temperature range 20-25°C. The metal release approximately linear wit'
Description[5]='temperature in this temperature range, with a gradient of approximately 5%'
Description[6]='°C^-1^. For the ±2°C range allowed by the empirical method, this leads to a'
Description[7]='factor f_temperature of 1 ± 0.1. A rectangular distribution is assumed for this'
Description[8]='factor.'
Vnom=1
Hlim=0.1

[Correlations]
Description=0