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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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Koesuunnittelu | |||||||||||

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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Koesuunnittelu | |||||||||||

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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Koesuunnittelu | |||||||||||

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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Koesuunnittelu | |||||||||||

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 | |

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 | |

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 | |||||||