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Quantifying & Propagation of Uncertainty

Quantifying & Propagation of Uncertainty. Module 2 Lecture TWO (2-4) 2/23/05. The average of sample i. where. Determine Uncertainty from Multiple sample. In the case multiple samples M are used, the estimate of the mean is referred to as.

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Quantifying & Propagation of Uncertainty

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  1. Quantifying & Propagation of Uncertainty Module 2 Lecture TWO (2-4) 2/23/05

  2. The average of sample i where Determine Uncertainty from Multiple sample • In the case multiple samples M are used, the estimate of the mean is referred to as Statisticians refer to as the average of the averages

  3. Determine Uncertainty from Multiple sample • The random uncertainty in is determined as Where Sxcis the combined standard deviation vxc is the combined degrees of freedom

  4. Combined Standard Deviation where Siis the standard deviations of sample i

  5. Combined Degrees of Freedom where viis the degrees of freedom of sample i

  6. Example on Multiple sample Units in volt

  7. Calculate

  8. Calculate Combined Sxc

  9. Calculate combined Vxc

  10. Calculate From Table 8.4 using 9 degrees of freedom at confidence level of 95%

  11. Table 8.4

  12. Uncertainty of the Mean µ = 10.05 + 0.75 volt Question? How will you calculate the uncertainty on individual unit (measurement)?

  13. Single Measurement

  14. M samples Multiple Measurement ONE sample

  15. Overall (total) Uncertainty • In a typical measurement system, there are a large number of error sources that are known as elemental error sources.

  16. A word about Bias and Random Errors Elemental Uncertainty

  17. Overall (total) Uncertainty • Normally, there are several elemental error sources, in the measurement of each variable x. • The uncertainty in x will be a combination of the uncertainties in each source. This is referred to as the Overall Uncertainty

  18. Combined standard deviation of Elemental Sources Determine Overall Uncertainty Combined degrees of freedom of Elemental Sources • Use similar equations to those used to determine uncertainty for M samples. #Elemental sources Overall Uncertainty of the Measurand

  19. Example : This week’s lab • Each resistor Ri has uncertainty Si • Calculate (predict) the Overall Uncertainty that will be caused by the uncertainties in the resistors • Determine the Overall Uncertainty from the measurements of Req

  20. What have you learned so far? • Determine Random Uncertainty in the Measurement of the Measurand • Using Single measurement • Using ONE sample • Using M samples • Determine Overall Random uncertainty caused by Elemental Errors

  21. End of lecture TWO

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