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Measurement Uncertainty

Measurement Uncertainty. Overview. Factors which decide System Performance Types of Error in Measurement Mean, Variance and Standard Deviation. Error = Xm - Xtrue Xm-> Measured Value Xtrue->Actual Value. What is the “true” value? Is it possible to take measurement data without any error?

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Measurement Uncertainty

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  1. Measurement Uncertainty

  2. Overview • Factors which decide System Performance • Types of Error in Measurement • Mean, Variance and Standard Deviation

  3. Error = Xm - Xtrue Xm-> Measured Value Xtrue->Actual Value • What is the “true” value? • Is it possible to take measurement data without any error? • What is the source of error? • How can we minimize the impact of these errors ?

  4. System Performance Depends on the following factors : ->System accuracy is the magnitude of the maximum expected error. Usually specified as percentage of full scale. ->System precision is an estimate of repeatability .The more precise a system, the less random error affects the result. ->System resolution is the smallest possible discernible increment .Higher the resolution, smaller the smallest increment !

  5. Types of Error • Systematic errors (or “bias” errors): Occur in a repeatable fashion (i.e., every time a measurement is made under similar conditions). • Offset error: is a constant error which occurs every time a measurement is taken. Offset Error: Xm = Xtrue ± Constant Xm=Measured value Xtrue=Actual value

  6. Types of Error contd. • Scale error: Xm = Xtrue x Constant implies Xtrue = Xm / Constant • Nonlinear errors: Can result from poor design or from inappropriate system use Ex: y= x2, y = cos xt, or y = log x

  7. Types of Error contd. • Drift Errors: • Ambient temperature, humidity and aging can change the characteristics of an electronic component. • Random errors: Absolutely random in nature !

  8. Definitions Sample median - The middle value when the measurements are arranged from smallest to largest. Sample mean: (Sum / No. of Samples)

  9. Definitions contd. • Sample Mean: Xmean=sum(Xi)/n • Sample deviation: Difference between the measured value and the sample mean Deviation = X – Xmean • Sample variance = sum(Xi-Xmean)²/(n-1)

  10. Definitions contd. • Sample Standard Deviation: s=sqrt(sum(Xi-Xmean)²/(n-1)) Sample standard deviation gives us an estimate of the variability of the sample in the same units as the data . • Components manufactured with a small standard deviation, cost more than components that are manufactured to a looser standard.

  11. clear all R1=5.1 V=24 R2=13.8:0.1:15.2 V1=(R1/(R1+R2))* V I1=V / (R1+R2) figure(1) subplot(2,1,1) plot(R2,V1) subplot(2,1,2) plot(R2,I1)

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