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Example4_1 Analysis Example4_1 Analysis Slide 53 Example4_1 Analysis Slide 55 Example4_1 Analysis Slide 57

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	4.2 Example: Preparation of a Cd calibration standard







	Quantity, Xi	Estimate, xi		Standard unc., u(xi)		Probability	Sensitivity coeff., ci		Uncertainty contribution, ui		Notes on the determination
i	Description	Value	unit	Value	unit	distribution	Value	unit	Value	unit	of the standard uncertainty
1	balance readings with the metal	100.28	mg	0.03	mg	normal	9.999	1/l	0.29997	mg/l	standard deviation of recorded readings
2	balance readings without the metal	0	mg	0.01	mg	normal	9.999	1/l	0.09999000000000001	mg/l	standard deviation of recorded readings after taring
3	non-linearity of the balance	0	mg	0.017320508075688773	mg	rectangular	9.999	1/l	0.17318776024881205	mg/l	According to calibration, the non-linearity is less than ±0.03 mg
4	non-ideal repeatability of the balance	0	mg	0.011547005383792516	mg	rectangular	9.999	1/l	0.11545850683254137	mg/l	According to repeated measurements in calibration of the balance, the repeatability is less than ±0.02 mg
5	non-ideal resolution of the balance	0	mg	0.005773502691896258	mg	rectangular	9.999	1/l	0.057729253416270686	mg/l
6	purity of the metal	0.9999		5.7735026918962585E-5		rectangular	1002.8	mg/l	0.05789668499433568	mg/l	Manufacturer's certificate states that the purity of the metal is 0.9999 ± 0.0001
7	non-ideal dissolving	0		1.1547005383792517E-4		rectangular	1002.8	mg/l	0.11579336998867136	mg/l	According to repeated preparations the efficiency is larger than 99.98 %
8	inner volume of the flask	100	ml	0.05	ml	normal	-10.0269972	g/l^2	-0.50134986	mg/l	The flask was calibrated by weighing with distilled water. The result was (100 ± 0.1) ml with k=2
9	thermal expansion of the measured volume	0	ml	0.04849742261192857	ml	rectangular	-10.0269972	g/l^2	-0.48628352073702447	mg/l	Because the thermal expansion of glass is much smaller than water, only the water (2.1 x 10^-4 1/°C) is taken into account. Temperature variation is ± 4 °C at maximum.
10	filling error	0	ml	0.02	ml	normal	-10.0269972	g/l^2	-0.200539944	mg/l	standard deviation from ten fillings and weighings
								combined standard uncertainty:	0.8315269564293184	mg/l
	Estimate:	1002.69972	mg/l					Expanded uncertainty:	1.6630539128586368	mg/l


	Measurement result:	1002.69972	mg/l ±	1.7	mg/l

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	Example 4.1: Preparation of a Cd calibration standard







	Quantity, Xi	Estimate, xi		Standard unc., u(xi)		Probability	Notes on the determination
i	Description	Value	unit	Value	unit	distribution	of the standard uncertainty
1	balance readings with the metal	100.28	mg	0.03	mg	normal	standard deviation of recorded readings
2	balance readings without the metal	0	mg	0.01	mg	normal	standard deviation of recorded readings after taring
3	non-linearity of the balance	0	mg	0.017320508075688773	mg	rectangular	According to calibration, the non-linearity is less than ±0.03 mg
4	non-ideal repeatability of the balance	0	mg	0.011547005383792516	mg	rectangular	According to repeated measurements in calibration of the balance, the repeatability is less than ±0.02 mg
5	non-ideal resolution of the balance	0	mg	0.005773502691896258	mg	rectangular
6	purity of the metal	0.9999		5.7735026918962585E-5		rectangular	Manufacturer's certificate states that the purity of the metal is 0.9999 ± 0.0001
7	non-ideal dissolving	0		1.1547005383792517E-4		rectangular	According to repeated preparations the efficiency is larger than 99.98 %
8	inner volume of the flask	100	ml	0.05	ml	normal	The flask was calibrated by weighing with distilled water. The result was (100 ± 0.1) ml with k=2
9	thermal expansion of the measured volume	0	ml	0.04849742261192857	ml	rectangular	Because the thermal expansion of glass is much smaller than water, only the water (2.1 x 10^-4 1/°C) is taken into account. Temperature variation is ± 4 °C at maximum.
10	filling error	0	ml	0.02	ml	normal	standard deviation from ten fillings and weighings

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	Quantity, Xi	Estimate, xi		Standard unc., u(xi)		Probability	Sensitivity coeff., ci		Notes on the determination
i	Description	Value	unit	Value	unit	distribution	Value	unit	of the standard uncertainty
1	balance readings with the metal	100.28	mg	0.03	mg	normal	9.999	1/l	standard deviation of recorded readings
2	balance readings without the metal	0	mg	0.01	mg	normal	9.999	1/l	standard deviation of recorded readings after taring
3	non-linearity of the balance	0	mg	0.017320508075688773	mg	rectangular	9.999	1/l	According to calibration, the non-linearity is less than ±0.03 mg
4	non-ideal repeatability of the balance	0	mg	0.011547005383792516	mg	rectangular	9.999	1/l	According to repeated measurements in calibration of the balance, the repeatability is less than ±0.02 mg
5	non-ideal resolution of the balance	0	mg	0.005773502691896258	mg	rectangular	9.999	1/l
6	purity of the metal	0.9999		5.7735026918962585E-5		rectangular	1002.8	mg/l	Manufacturer's certificate states that the purity of the metal is 0.9999 ± 0.0001
7	non-ideal dissolving	0		1.1547005383792517E-4		rectangular	1002.8	mg/l	According to repeated preparations the efficiency is larger than 99.98 %
8	inner volume of the flask	100	ml	0.05	ml	normal	-10.0269972	g/l^2	The flask was calibrated by weighing with distilled water. The result was (100 ± 0.1) ml with k=2
9	thermal expansion of the measured volume	0	ml	0.04849742261192857	ml	rectangular	-10.0269972	g/l^2	Because the thermal expansion of glass is much smaller than water, only the water (2.1 x 10^-4 1/°C) is taken into account. Temperature variation is ± 4 °C at maximum.
10	filling error	0	ml	0.02	ml	normal	-10.0269972	g/l^2	standard deviation from ten fillings and weighings

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	Quantity, Xi	Estimate, xi		Standard unc., u(xi)		Probability	Sensitivity coeff., ci		Uncertainty contribution, ui		Notes on the determination
i	Description	Value	unit	Value	unit	distribution	Value	unit	Value	unit	of the standard uncertainty
1	balance readings with the metal	100.28	mg	0.03	mg	normal	9.999	1/l	0.29997	mg/l	standard deviation of recorded readings
2	balance readings without the metal	0	mg	0.01	mg	normal	9.999	1/l	0.09999000000000001	mg/l	standard deviation of recorded readings after taring
3	non-linearity of the balance	0	mg	0.017320508075688773	mg	rectangular	9.999	1/l	0.17318776024881205	mg/l	According to calibration, the non-linearity is less than ±0.03 mg
4	non-ideal repeatability of the balance	0	mg	0.011547005383792516	mg	rectangular	9.999	1/l	0.11545850683254137	mg/l	According to repeated measurements in calibration of the balance, the repeatability is less than ±0.02 mg
5	non-ideal resolution of the balance	0	mg	0.005773502691896258	mg	rectangular	9.999	1/l	0.057729253416270686	mg/l
6	purity of the metal	0.9999		5.7735026918962585E-5		rectangular	1002.8	mg/l	0.05789668499433568	mg/l	Manufacturer's certificate states that the purity of the metal is 0.9999 ± 0.0001
7	non-ideal dissolving	0		1.1547005383792517E-4		rectangular	1002.8	mg/l	0.11579336998867136	mg/l	According to repeated preparations the efficiency is larger than 99.98 %
8	inner volume of the flask	100	ml	0.05	ml	normal	-10.0269972	g/l^2	-0.50134986	mg/l	The flask was calibrated by weighing with distilled water. The result was (100 ± 0.1) ml with k=2
9	thermal expansion of the measured volume	0	ml	0.04849742261192857	ml	rectangular	-10.0269972	g/l^2	-0.48628352073702447	mg/l	Because the thermal expansion of glass is much smaller than water, only the water (2.1 x 10^-4 1/°C) is taken into account. Temperature variation is ± 4 °C at maximum.
10	filling error	0	ml	0.02	ml	normal	-10.0269972	g/l^2	-0.200539944	mg/l	standard deviation from ten fillings and weighings
								combined standard uncertainty:	0.8315269564293184	mg/l
	Estimate:	1002.69972	mg/l					Expanded uncertainty:	1.6630539128586368	mg/l


	Measurement result:	1002.69972	mg/l ±	1.7	mg/l